PhD Thesis

Resolution in coherent and incoherent optical imaging with two–photon excitation microscopy By E LI S LENDERS

Faculty of Sciences H ASSELT U NIVERSITY

A dissertation submitted to the University of Hasselt in accordance with the requirements of the degree of D OCTOR OF P HILOSOPHY in Physics.

O CTOBER 31 ST, 2018

Micrograph of an 1879 Carl Zeiss microscope 39 x 68 µ m2

More information on p. 140

M EMBERS OF THE JURY

Chairman Prof. dr. Marc Gyssens, Hasselt University, Diepenbeek, Belgium

Promoter Prof. dr. M. Ameloot, Hasselt University, Diepenbeek, Belgium

Co-promoter Prof. dr. L. Michiels, Hasselt University, Diepenbeek, Belgium

Other members Prof. dr. M. vandeVen, Hasselt University, Diepenbeek, Belgium Prof. dr. J. Hooyberghs, Hasselt University, Diepenbeek, Belgium and Flemish Institute for Technological Research, VITO, Mol, Belgium Prof. dr. P. Vanden Berghe, University of Leuven, Leuven, Belgium Prof. dr. K. Braeckmans, Ghent University, Ghent, Belgium M.E.R. dr. L. Bonacina, University of Geneva, Geneva, Switzerland

P REFACE

riven by both curiosity and applications in healthcare, biomedical scientists seek to understand the complex machinery that is the human body. As a biophysicist, I contribute to this quest by developing new lab techniques. Tissues, cells, cell organelles,... the small sizes of many biological structures explain the need for increasingly better–performing imaging systems. Because diffraction limits the resolution in conventional optical microscopes to several hundred nanometers, other methods are needed to study biological samples at the desired resolution.

D

In this work, several possible ways to challenge the diffraction limit are presented. The thesis starts with two general chapters, the first being an introduction in microscopy, the second providing the necessary mathematics describing the image formation process. In the other chapters, of which three are based on original publications, several methods to circumvent the diffraction limit are described. Finally, a brief summary and an outlook are presented in the conclusion.

TABLE OF C ONTENTS

Page List of Acronyms

vii

List of Symbols

ix

List of Figures

xiii

List of Tables

xix

1

Introduction

1

1.1

Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.1.1

Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.1.2

Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.1.3

Deep tissue imaging . . . . . . . . . . . . . . . . . . . . . . . 13

1.2

Obtaining subdiffraction information without circumventing the diffraction limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 2

Research aims and outline . . . . . . . . . . . . . . . . . . . . . . . . 15

Theory and methods 2.1

2.2

19

Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1

Theory of diffraction . . . . . . . . . . . . . . . . . . . . . . . 20

2.1.2

Image formation as a diffraction process . . . . . . . . . . . 24

2.1.3

The resolution limit . . . . . . . . . . . . . . . . . . . . . . . 25

2.1.4

The point spread function and the optical transfer function 27

2.1.5

Laser scanning microscopy . . . . . . . . . . . . . . . . . . . 32

2.1.6

Lateral resolution enhancement . . . . . . . . . . . . . . . . 35

Intensity fluctuation imaging . . . . . . . . . . . . . . . . . . . . . . 43 i

TABLE OF CONTENTS

2.2.1

Fluorescence correlation spectroscopy and coherence correlation spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 44

2.2.2 3

Image correlation spectroscopy . . . . . . . . . . . . . . . . 48

Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating point scatterers — A comprehensive theoretical study 3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.3

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.4 4

3.3.1

cSTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3.2

cRICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.3.3

cTICS and cCS . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.4

Diffusion with flow . . . . . . . . . . . . . . . . . . . . . . . . 65

3.3.5

Low particle concentration limit . . . . . . . . . . . . . . . . 68

3.3.6

High particle concentration limit . . . . . . . . . . . . . . . 70

3.3.7

2D diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.3.8

Sensitivity to noise for parameter retrieval . . . . . . . . . 70

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Image correlation spectroscopy with second harmonic generating nanoparticles in suspension and in cells

5

57

75

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2

Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.1

Harmonic nanoparticles . . . . . . . . . . . . . . . . . . . . . 78

4.2.2

Measurements in suspension . . . . . . . . . . . . . . . . . . 79

4.2.3

Measurements in cells . . . . . . . . . . . . . . . . . . . . . . 82

4.2.4

Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.3

Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Structured illumination in laser scanning microscopy for multiphoton imaging

105

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.2

Two–photon fluorescence excitation imaging . . . . . . . . . . . . . 106 ii

TABLE OF CONTENTS

5.3

Structured illumination in laser scanning microscopy . . . . . . . 108 5.3.1

Why structured illumination microscopy with point–detection does not work . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.3.2

6

5.4

Combining SIM with two–photon excitation microscopy . . . . . . 113

5.5

Stage drift induced reconstruction artifacts . . . . . . . . . . . . . 115

5.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Two–photon fluorescence excitation image scanning microscopy119 6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.2

Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.3

6.4 7

Structured illumination microscopy with camera detection 110

6.2.1

Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.2.2

Reconstruction with pixel reassignment . . . . . . . . . . . 123

6.2.3

FRC analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.3.1

Alignment and magnification of the system . . . . . . . . . 127

6.3.2

Beads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.3.3

Fixed cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.3.4

Mouse brain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Image scanning microscopy in non–descanned detection for improved nonlinear excitation imaging with a commercial laser scanning microscope

8

135

7.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.2

Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

7.3

Using the setup for SIM and ISM . . . . . . . . . . . . . . . . . . . . 140

7.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Dynamics of the phospholipid shell of microbubbles: a fluorescence photoselection and spectral phasor approach

147

8.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

8.2

Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . 151 8.2.1

Laurdan fluorescence . . . . . . . . . . . . . . . . . . . . . . 151

8.2.2

Microbubble preparation . . . . . . . . . . . . . . . . . . . . 153 iii

TABLE OF CONTENTS

9

8.2.3

Microscopy imaging . . . . . . . . . . . . . . . . . . . . . . . 155

8.2.4

GP analysis protocol . . . . . . . . . . . . . . . . . . . . . . . 156

8.3

Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 159

8.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Conclusions and outlook

171

9.1

Correlation spectroscopy with harmonic nanoparticles . . . . . . . 172

9.2

Resolution enhancement in multiphoton imaging . . . . . . . . . . 174

9.3

Combining correlation spectroscopy and ISM . . . . . . . . . . . . 175

9.4

Microbubble shell characterization . . . . . . . . . . . . . . . . . . . 176

A Derivation of the coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating point scatterers

179

A.1 Derivation of the cIFM . . . . . . . . . . . . . . . . . . . . . . . . . . 180 A.2 The two dimensional cIFM . . . . . . . . . . . . . . . . . . . . . . . . 193 A.3 The general fIFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 A.4 Intensity fluctuation autocorrelation spectroscopy . . . . . . . . . 195 A.4.1

cSTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

A.4.2

cRICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

A.4.3

cTICS and cCS . . . . . . . . . . . . . . . . . . . . . . . . . . 196

A.4.4

Diffusion with flow . . . . . . . . . . . . . . . . . . . . . . . . 198

A.5 The limiting behavior of the general cIFM . . . . . . . . . . . . . . 198 A.5.1

The cIFM in the low particle concentration limit . . . . . . 198

A.5.2

The limit for large N . . . . . . . . . . . . . . . . . . . . . . . 200

A.6 Parameter retrieval in data fitting . . . . . . . . . . . . . . . . . . . 201 A.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A.8 List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Summary

207

Nederlandstalige samenvatting

209

Bibliography

213

Curriculum Vitae

231 iv

TABLE OF CONTENTS

Dankwoord

235

v

L IST OF A CRONYMS

1PE

One–Photon Fluorescence Excitation

2PE

Two–Photon Fluorescence Excitation

ACF

Autocorrelation Function

AOM

Acousto–Optic Modulator

APD

Avalanche Photodiode

aPSF

Amplitude Point Spread Function

B

Bottom

cCS

Coherent Correlation Spectroscopy

cIFM

Coherent Intensity Fluctuation Model

CLSM

Confocal Laser Scanning Microscope

cOTF

Coherent Optical Transfer Function

cRICS

Coherent Raster Image Correlation Spectroscopy

cSTICS

Coherent Spatiotemporal Image Correlation Spectroscopy

cTICS

Coherent Temporal Image Correlation Spectroscopy

DAQ

Data–Acquisition

DMSO

Dimethyl Sulfoxide

DPPC

1,2–dipalmitoyl–sn–glycero–3–phosphocholine

EMCCD

Electron–Multiplying Charge–Coupled Device

EYFP

Enhanced Yellow Fluorescent Protein

FCS

Fluorescence Correlation Spectroscopy

fIFM

Fluorescence Intensity Fluctuation Model

FRC

Fourier Ring Correlation

GP

Generalized Polarization

HWP

Half–Wave Plate

ICS

Image Correlation Spectroscopy

iOTF

Incoherent Optical Transfer Function

vii

LIST OF ACRONYMS

iPSF

Intensity Point Spread Function

IR

infrared

ISM

Image Scanning Microscopy

KD*P

Potassium Dideuterium Phosphate

L

Left

MPEM

Multiphoton Excitation Microscopy

NA

Numerical Aperture

NIR

near–infrared

NP

nanoparticle

OTF

Optical Transfer Function

PALM

Photoactivated Localization Microscopy

PBS

Phosphate Buffered Saline

PCR

Photon Count Rate

PFB

Perfluorobutane

PMT

Photomultiplier Tube

PSF

Point Spread Function

QWP

Quarter–Wave Plate

R

Right

RICS

Raster Image Correlation Spectroscopy

S-FCS

Scanning FCS

SHG

Second Harmonic Generation

SIM

Structured Illumination Microscopy

SPAD

Single–Photon Avalanche Diode

SPT

Single Particle Tracking

STED

Stimulated Emission Depletion

STICS

Spatiotemporal Image Correlation Spectroscopy

STORM

Stochastic Optical Reconstruction Microscopy

T

Top

THG

Third Harmonic Generation

TICS

Temporal Image Correlation Spectroscopy

TTL

Transistor–Transistor Logic

US

ultrasound

UV

ultraviolet

viii

L IST OF S YMBOLS

~

Fourier transform

⊗

Convolution product

〈·〉

Average

α

Angle of incidence [rad]

δ

Dirac delta function

δr

Pixel size [m]

δ x, δ y

Spatial shifts in the x, y direction [m]

δI

Difference between the current intensity and the mean intensity [a.u.]

²

Vacuum permittivity [8.85 x 10−12 F/m]

θ

Angle of the SIM pattern [rad]

κq

Gouy phase shift per unit length [rad/m]

λ

Wavelength [m]

ξ

Number of pixels shifted in the x direction [dimensionless]

ρ

Spatial shift [m]

ρ x, ρ y

Spatial shift in the x, y direction [m]

τ

Lag time [s]

τ p , τl

Reciprocal scan speed [s/m] in the x, y direction

τ

Reciprocal scan speed [s/m] in the x, y and z direction

ϕ

Phase shift [rad]

χ

Electric susceptibility [dimensionless]

ψ

Number of pixels shifted in the y direction [dimensionless]

ψQ

Scalar electric field wave [a.u.]

ω

Photon angular frequency [rad/s] or angular spatial frequency [rad/m], depending on the context

ix

LIST OF SYMBOLS

ω0

Lateral 1/e2 width (radius) of the one–photon excitation intensity point spread function [m] or SIM pattern angular spatial frequency [rad/m], depending on the context

ωc

Angular spatial cut–off frequency [rad/m]

A

Ratio A Q /d 1 [a.u.] or SIM pattern amplitude [a.u.], depending on the context

Aq

Electric field amplitude point spread function [V /m]

A q0

Maximum electric field amplitude [V /m]

AQ

Strength of a light point source [a.u.]

B

Ratio b/d [a.u.] or Bottom, depending on the context

b

Strength of the scattering process [a.u.]

c

Local or overall particle concentration [/m3 ], depending on the context

C

Condenser lens

Cϕ

Phase correlation function

dx

Infinitesimal change in any variable x [units of x]

d

Distance between a point in the sample and the point of detection [m] or the periodicity of a grating pattern [m]

d1

Distance between the point light source and a point in the sample [m]

D

Diffusion coefficient [µ m2 /s]

E

Electric field [V /m]

f

Photon frequency [/s] or spatial frequency [/m], depending on the context

fs

Scattering function of the specimen [a.u.]

fc

Spatial cut–off frequency [/m]

f cex f cem

Excitation cut–off frequency [/m]

F

Focal length [m], fluorescence intensity [a.u.] or Fourier plane, de-

Emission cut–off frequency [/m] pending on the context

G

GP correction factor [dimensionless]

G

Autocorrelation function [dimensionless] or Gaussian function [a.u.], depending on the context

GN

Autocorrelation normalization factor

x

h

Planck constant [6.626 x 10−34 m2 k g/s]

h1

Excitation intensity point spread function [a.u.]

h2

Emission intensity point spread function [a.u.]

h02

Detection point spread function [a.u.]

i

Imaginary unit

I

Intensity [a.u.]

I det

Detector element image

IB

Intensity in the blue channel [a.u.]

Iq

Intensity of the q–th order signal [a.u.]

I re f

Central detector element image

IR

Intensity in the green (red–shifted) channel [a.u.]

J1

First–order Bessel function of the first kind

k0

Wave vector magnitude [rad/m]

L

Lens or Left, depending on the context

l, m, n

Vector components of the unit vector pointing from the origin to the point of detection [m]

m

Modulation depth [dimensionless]

n

Refractive index [dimensionless]

N

Average number of particles in the focal volume [dimensionless]

O

Origin or objective, depending on the context

P

Point of detection or illumination strength [a.u.], depending on the context

Pe f f

Effective illumination strength [a.u.]

q

Order of the scattering process [dimensionless]

Q

Point light source

r0

Position [m]

r

Distance from the center of the pupil [m]

R

Lens radius [m] or Right, depending on the context

s

Sample response to the illumination amplitude [a.u.]

S

Sample

t

Time [s] or sample response to the illumination intensity [a.u.], depending on the context

T

Tube lens or Top, depending on the context

u, v

Optical coordinates k 0 l, k 0 m [dimensionless]

xi

LIST OF SYMBOLS

v

Flow speed [m/s]

vx , v y

Flow speed in the x, y direction [m/s]

Ve f f

Effective focal volume [m3 ]

W

Aperture function [a.u.]

x

0

Position in the image plane [m]

xD

Position of the detector [m]

xL

Laser position [m]

z0

Axial 1/e2 height of the one–photon excitation intensity point spread function (compare ω0 ) [m]

xii

L IST OF F IGURES

F IGURE

Page

1.1

Illustration of spatial frequencies in a kiwifruit image. . . . . . . . . .

3

1.2

The OTF for a widefield fluorescence microscope. . . . . . . . . . . . .

4

1.3

Comparison of the resolution obtained in optical microscopy and electron microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4

5

Jablonski diagram displaying the energy levels of a fluorescent molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

1.5

Illustration of Moiré fringes. . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.6

Transmission microscopy vs. fluorescence microscopy. . . . . . . . . . 10

1.7

Jablonski diagram of 2PE and illustration of the energy levels in SHG. 12

2.1

Illustration of light produced by a point source Q that is diffracted by a specimen S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2

Calculation of the diffraction image formed in a plane infinitely far from the sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3

Imaging of the Fraunhofer diffraction pattern using lenses. . . . . . . 23

2.4

Imaging of a sample using two conjugated lenses. . . . . . . . . . . . . 24

2.5

Illustration of the resolution limit for parallel incident illumination on a grating pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.6

A plane wave focused by an objective creates the same pattern as the image of an infinitely small sample formed by an objective and a tube lens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.7

Overview of the PSF and the OTF functions in coherent and incoherent imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.8

Coherent versus incoherent imaging of point objects. . . . . . . . . . . 30

2.9

Beam path laser scanning microscopy with non–descanned detection. 33 xiii

L IST

OF

F IGURES

2.10 Beam path confocal microscopy. . . . . . . . . . . . . . . . . . . . . . . . 34 2.11 Comparison of the optical transfer function for incoherent imaging in widefield mode and in confocal mode. . . . . . . . . . . . . . . . . . . 36 2.12 Effect of structured illumination on the sample information obtained in Fourier space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.13 Beam path in image scanning microscopy. . . . . . . . . . . . . . . . . 40 2.14 Stochastic interpretation of ISM in one dimension. . . . . . . . . . . . 42 2.15 The ISM iPSF is in between the excitation and the detection iPSF. . 43 2.16 Particles diffusing through the volume created by a focused laser beam and the corresponding intensity trace. . . . . . . . . . . . . . . . 44 2.17 Calculation of the ACF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.18 Definition of the lateral size of the PSF. . . . . . . . . . . . . . . . . . . 47 2.19 Effect of the particle concentration and the diffusion coefficient on the FCS curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.20 Principle of scanning FCS. . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.21 Principle of RICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.22 Example of a RICS ACF. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.23 The effect of flow on the RICS ACF. . . . . . . . . . . . . . . . . . . . . . 55 3.1

Plots of the ACF with respect to the lateral spatial shift ρ x and ρ y in a cSTICS simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.2

Plots of the ACF with respect to the temporal shift. . . . . . . . . . . . 67

3.3

Comparison between the SHG and fluorescence autocorrelation functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.4

2D histograms of the fit results obtained by fitting 1000 simulated ACFs for 21 noise levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.1

Distribution of the diameter of the LiNbO3 NPs. . . . . . . . . . . . . . 79

4.2

Illustration of the cos4 dependence of the SHG intensity as a function of the orientation of the illumination polarization plane for three LiNbO3 NPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.3

Illustration of the SHG intensity as a function of the orientation of the illumination polarization plane for a fixed LiNbO3 NP and scanning electron microscopy image of the same sample. . . . . . . . . 80

4.4

Data analysis protocol cRICS. . . . . . . . . . . . . . . . . . . . . . . . . 87 xiv

L IST

4.5

OF

F IGURES

cRICS frame with LiNbO3 NPs and RICS frame with blue fluorescent carboxylate–modified microspheres. . . . . . . . . . . . . . . . . . . . . 90

4.6

Summed SHG intensity for each frame as a function of the exposure time for a cRICS measurement. . . . . . . . . . . . . . . . . . . . . . . . 90

4.7

cRICS autocorrelation curve from LiNbO3 NPs suspended in water at room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.8

Plots of the normalized central autocorrelation line for LiNbO3 in water at room temperature at different scan speeds. . . . . . . . . . . 91

4.9

ACF of LiNbO3 NPs in ultrapure Milli–Q water at room temperature, measured with a Zeiss LSM 510 META. . . . . . . . . . . . . . . . . . . 92

4.10 Comparison of the cRICS ACF for 50 nm BaTiO3 NPs and the RICS ACF for 100 nm blue fluorescent carboxylate–modified microspheres. 92 4.11 cRICS ACF for LiNbO3 NPs in the water–glycerol mixture at room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.12 SHG image and ACF from dried LiNbO3 NPs. . . . . . . . . . . . . . . 93 4.13 SHG image and ACF from dried LiNbO3 NPs. . . . . . . . . . . . . . . 94 4.14 G(ξ, ψ = 0) cross–section, with the three central points omitted, and fit. 95 4.15 LiNbO3 cRICS fit residuals from the ACFs using the cIFM and the fluorescence model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.16 Transmission image of an A549 cell not exposed to NPs, an A549 cell exposed for 24 hours to LiNbO3 NPs and a z–stack with xz and yz cross sections of a CellTracker labeled A549 cell exposed to LiNbO3 NPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.17 cSTICS measurement of LiNbO3 NPs in an A549 cell. . . . . . . . . . 99 4.18 cSTICS ACF for a region in an A549 cell at 37 ◦ C. . . . . . . . . . . . . 101 4.19 Colocalization between the LiNbO3 NPs and the lysosomes and the endosomes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.1

Comparison of one and two–photon optical transfer functions. . . . . 108

5.2

Applying structured illumination in a laser scanning microscope by means of spatiotemporal intensity modulation. . . . . . . . . . . . . . 108

5.3

Beam path laser scanning microscope with spatiotemporal structured illumination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.4

Relative illumination modulation depth as a function of the relative spatial frequency of the SIM pattern. . . . . . . . . . . . . . . . . . . . 112 xv

L IST

OF

F IGURES

5.5

Laser power as a function of the scan position for scanning SIM and the corresponding total intensity received at each position at the sample plane during a frame scan. . . . . . . . . . . . . . . . . . . . . . 113

5.6

Experimental evidence for modulation smoothing in point–scanning SIM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.7

Simulation of the effect of stage drift on the SIM reconstruction process.117

6.1

Scheme of the ISM beam path. . . . . . . . . . . . . . . . . . . . . . . . 122

6.2

Pixel reassignment protocol illustrated with fluorescent beads. . . . . 125

6.3

Average number of photons collected per detector element per laser position for fluorescent beads and the corresponding images recorded by three of the detector elements. . . . . . . . . . . . . . . . . . . . . . . 128

6.4

Total shift applied during the ISM reconstruction as a function of the real distance between the detector element and the detector center for the beads sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.5

Comparison of confocal microscopy with ISM using fluorescent beads. 130

6.6

Comparison of confocal microscopy with ISM using fixed cells. . . . . 132

6.7

Comparison of confocal microscopy with ISM in a mouse brain with neurons expressing EYFP. . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.1

Pockels cell setup for controlling the laser power during the scan process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.2

The Pockels cell output power as a function of the applied voltage. . . 139

7.3

Optocoupler system with an inverter Schmitt trigger. . . . . . . . . . . 140

7.4

Rhodamine–B calibration pattern imaged with homogeneous and structured illumination. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.5

Possible setup for ISM in non–descanned detection with an EMCCD. 143

7.6

More efficient setup for ISM in non–descanned detection with an EMCCD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

7.7

First frame in a grid ISM series of the rhodamine–B calibration sample.144

8.1

Model of the Laurdan molecule and illustration of the photoselection effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.2

Corrected Laurdan fluorescence spectrum in DMSO at 25 ◦ C. . . . . . 152 xvi

L IST

8.3

OF

F IGURES

Laurdan in DMSO calibration for various temperatures and for various amounts of water added. . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.4

Generalized polarization analysis protocol illustrated with a DPPC– PFB microbubble at 42 ◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . 157

8.5

Illustration of the phasor approach. . . . . . . . . . . . . . . . . . . . . 160

8.6

Photoselection and generalized polarization observed in Laurdan stained DPPC–PFB microbubbles imaged with 2PE laser scanning microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

8.7

Excitation polarization dependence of the fluorescence of Laurdan in the equatorial plane of a DPPC–PFB microbubble at 25 ◦ C. . . . . . . 163

8.8

Phase separation in a DPPC–PFB microbubble at 42 ◦ C. . . . . . . . 163

8.9

Phasor plot of the shell dynamics at 25 ◦ C of a single Laurdan stained DPPC–PFB gas–filled microbubble collected over a time interval of almost five hours and phasor plot of 11 DPPC–PFB microbubbles at 25 ◦ C and 10 microbubbles at 42 ◦ C. . . . . . . . . . . . . . . . . . . . . 164

8.10 Microbubble diameter as a function of time for the shrinking microbubble in Fig. 8.9 and corresponding fluorescence intensity in the blue and green channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.11 Proposed configurations for the Laurdan and DPPC molecules across the shell surface, both for a large microbubble with a T–B photoselection pattern and a smaller microbubble with an L–R fluorescence intensity pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 A.1 Plots of the ACF with respect to the lateral spatial shift ρ x and ρ y in a cSTICS simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 A.2 Computer simulation of the temporal ACF with noise and the fitted curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 A.3 2D histograms of the fits for the parameters described in Figure A.2. 202 A.4 Histograms of the fit results with the same parameter values as in Figure A.3, but with κ q as an additional fit parameter. . . . . . . . . . 203

xvii

L IST OF TABLES

TABLE

Page

4.1

LSM 880 instrumental settings for the cRICS measurements. . . . . 81

4.2

Diffusion coefficient heterogeneity for different regions in an A549 cell. 99

A.1 Terms in Eq. A.26 with their respective counterpart in Eq. A.19. . . . 188 A.2 Typical values for some parameters. . . . . . . . . . . . . . . . . . . . . 189 A.3 Summary of the derived ACFs. . . . . . . . . . . . . . . . . . . . . . . . 204 A.4 List of symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

xix

HAPTER

C

1

I NTRODUCTION

CHAPTER 1. INTRODUCTION

T

he nature of light has always intrigued humanity. Ancient civilizations started exploring the field of optics and developed the first lenses. The contributions made by the Arab scholar Ibn Al–Haytham in the 11th

century marked the start of modern optics [1]. Since then, many advances have seen the light of day, from Isaac Newton’s corpuscular theory and Christiaan Huygens’ wave theory to Maxwell’s equations in which the fields of electricity, magnetism, and optics were brought together [2]. To explain black–body radiation and the photoelectric effect, Max Planck and Albert Einstein offered in the 20th century a quantum theory of light, which started the field of quantum mechanics [2].

Together with the theoretical developments, optical instruments were invented. Hans and Zacharias Janssen were probably first in 1590 to invent the compound microscope [3]. Around the same time, Galileo Galilei made his own telescope and discovered Jupiter’s moons and Saturn’s rings [2]. As lenses became increasingly better in the 17th and 18th century with the work of Robert Hooke and Antoni van Leeuwenhoek, a magnification of 270x was reached, and microorganisms were discovered [3]. However, the idea that the imaging performance solely depends on the quality of the lenses was abruptly brought to an end in the 19th century by Ernst Abbe, who showed that diffraction of light sets a fundamental limit to the resolution that can be obtained with a conventional lens system [4]. Since then, researchers have come up with several ideas to circumvent this limit and further improve the imaging properties.

1.1

Microscopy

Studying the complex machinery of the human body is impeded by the small sizes of the biological structures making up any living organism. Microscopes are a crucial and possibly the most ubiquitous tool in biological imaging [5], helping to visualize cells, cell organelles, and supramolecular structures such as muscle fibers. However, the imaging quality of a microscope and the instrument’s value to answer a specific research question depend on many parameters. The two main criteria used to discuss the optical performance of a microscopy design are resolution and contrast. 2

1.1. MICROSCOPY

1.1.1

Resolution

The parameter resolution refers to the size of the smallest structures in a sample that can still be resolved with the microscope or, equivalently, the width of the Point Spread Function (PSF), i.e. the image of a point source [6]. As Abbe derived in 1873, the resolution of an optical microscope is limited by diffraction and depends on the wavelength of the light involved in the image formation process and on the Numerical Aperture (NA) of the objective lens [4]. The shorter the wavelength and the higher the NA, the better the resolution. Resolution can also be defined in frequency space by Fourier transforming the PSF. The resulting function is called the Optical Transfer Function (OTF) and specifies how well each spatial frequency in the specimen is imaged. Rough structures and fine details in the sample correspond to low and high spatial frequencies, respectively, as illustrated in Fig. 1.1. Resolution is then defined as the inverse of the largest spatial frequency with a non–zero OTF value. A typical representative example of a microscope OTF is shown in Fig. 1.2. Original image

=

low frequencies

+

high frequencies

Figure 1.1: Illustration of spatial frequencies in a kiwifruit image. An image consists of low and high spatial frequency information. Low frequencies correspond to rough structures, i.e. they contain a blurred version of the original image. High frequencies encode for small details, e.g. the black seeds, and sharpen up edges, e.g. the skin of the kiwifruits. In this example, only the lowest 0.19 % of the frequencies encoded in the original image were used to build the low–frequency image. The other 99.81 % of the information was used for the high–frequency image, together with a green offset. Structures smaller than about 250 nm cannot be resolved with conventional optical microscopes. Exemplary images produced by an optical microscope and 3


1

Amplitude [a.u.]

0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

3

Normalized spatial frequency

Figure 1.2: The OTF for a widefield fluorescence microscope. The lens system of a microscope behaves as a low–pass filter. High spatial frequencies in the specimen structure are less well imaged than low spatial frequencies. The resolution limit is defined by the cut–off value, in this example 2. The unit of normalized spatial frequency will be discussed in Chapter 2. Frequencies above this value are completely absent in the image and the corresponding details in the specimen structure can by no means be retrieved in post–processing.

an electron microscope are compared in Fig. 1.3. Although the latter instrument makes use of a beam of electrons instead of photons, the Abbe criterion still applies. The De Broglie wavelength associated with the electron beam can easily be a 1000 times smaller than the wavelength for visible light, resulting in a much better resolution. Despite its superior resolution, electron microscopy is far less frequently employed in biomedical research than its optical counterpart. The main reason for the limited success is the complex sample preparation, which involves fixation, dehydration and thin sectioning [7]. Furthermore, electron microscopes are operated under vacuum conditions and the electron beam may damage the specimen, making the method incompatible with live–cell imaging [7, 8]. Therefore, during the last decades, a main focus of research has been the development of optical instruments with a resolution beyond the diffraction limit. As explained in more detail in Chapter 2, the Abbe limit was derived for scalar fields, linear processes, time–independent samples, and homogeneous illumination. Any super–resolution method must circumvent one of these properties. 4

1.1. MICROSCOPY

(a)

(b)

Figure 1.3: (a) Comparison of the resolution obtained in (a) optical microscopy and (b) electron microscopy. The same sample of immobile 50 nm BaTiO3 nanoparticles (NPs) was imaged with optical Second Harmonic Generation (SHG) microscopy (see Section 1.1.2) and scanning electron microscopy. Scale bar 10 µ m. The indicated area of 1.56 x 1.56 µ m2 is enlarged in the insets. Individual NPs can easily be distinguished with electron microscopy, while the optical microscopy image is blurry.

Toraldo di Francia was first in 1952 to theoretically show that subdiffraction resolution – or super–resolution – can be achieved, provided a high enough photon density is used [9]. The method he proposed consisted of replacing the pupil lens with a series of ring–shaped apertures of different radii and alternating phases of 0 and π. Constructive and destructive interference induced by the phase mask creates a dim, but super–resolved image of the specimen. Although the idea was complex to put into practice, Toraldo di Francia had shown that the Abbe criterion can be circumvented, thereby starting the competition in bringing the resolution limit to smaller and smaller values. In 1961, Minsky patented the confocal microscope [10], a design in which a lens was used to focus the light source onto the specimen and the scattered light was collected by a second lens and focused onto a point detector. Light originating from out–of–focus planes was blocked by a pinhole placed in the conjugate focal plane, producing the optical sectioning effect [6, 11]. The sample stage was laterally moved to build an image. Three–dimensional information could be obtained by taking an image at different axial positions of the sample. In 1977, Sheppard and Choudhury [12] developed a theoretical framework for scanning microscopy and Cox et al. [13] showed in 1982 that a factor of two in 5


resolution enhancement can be obtained by substantially reducing the pinhole diameter, but again at the cost of a dimmer image. Later, a scanning laser beam instead of a moving sample stage was used for imaging. The Confocal Laser Scanning Microscope (CLSM) was born. Many super–resolution techniques require fluorophore labeling of the sample [14, 15]. In fluorescence microscopy, the wavelength of the illumination light is chosen to efficiently excite fluorescent molecules in the specimen. After some time, typically in the nanosecond range, an excited molecule will relax to the ground state, thereby emitting a photon. Due to energy losses in the vibrational levels of the molecules, the fluorescence photons have a lower energy than the excitation photons. The fluorescence is redshifted, i.e. the emitted light has a longer wavelength than the excitation light. This difference is called the Stokes shift. The principle of fluorescence is illustrated in the Jablonski diagram of Fig. 1.4. Vibrational relaxation S1 Excitation

hfI

hfF

Fluorescence

S0

Figure 1.4: Jablonski diagram displaying the energy levels of a fluorescent molecule. h is the Planck constant. f I and f F are the frequency of the illumination light and the fluorescence, respectively. Black arrows indicate non–radiative transitions. The super–resolution technique Stimulated Emission Depletion (STED) microscopy, developed by Hell and Wichmann in 1994 [16], uses the principle of stimulated emission to selectively deplete part of the fluorescence. First, a pulse from the focused scanning excitation laser beam excites the fluorescent molecules within the small focal volume. Then, the coaligned STED laser at the emission wavelength de–excites the fluorescence within the outer regions of the excitation focal volume. The doughnut–shaped de–excitation volume is obtained by letting the circularly polarized laser beam pass through a helical phase ramp. The remaining spontaneous fluorescence emission must originate 6

1.1. MICROSCOPY

from the center of the focal volume. A better–defined origin of the fluorescence signal is directly related to a better imaging resolution. STED microscopy is capable of resolving 35 nm. Localization microscopy is a collection of widefield microscopy techniques such as Photoactivated Localization Microscopy (PALM) [17] and Stochastic Optical Reconstruction Microscopy (STORM) [18] which are capable of resolving individual fluorescent molecules. Both methods, introduced in 2006, obtain super–resolution by breaking the time–independent–sample Abbe condition. At each point in time, a sparse subset of the fluorescent proteins (PALM) or the switchable organic fluorophores (STORM) in the sample is stochastically activated by a laser pulse and then excited with a second laser. Due to the limited number of simultaneously active molecules, the resulting fluorescence image contains a collection of non–overlapping PSFs. The fluorophore’s positions can be fitted from the images in post–processing with subdiffraction accuracy. The active molecules are then deactivated (STORM) or bleached (PALM), and the process is repeated with a different subset of molecules. Knowing the position of all fluorophores allows an image of the specimen with a resolution of about 20 nm to be created. Although STED, PALM, and STORM have excellent resolution properties, these nanoscopy methods also have severe limitations. E.g. the STED laser beam requires peak intensities of up to 1 GW/cm2 [19]. Such high powers not only lead to photobleaching of the fluorophores, but also to photodamaging of live cells [20, 21]. Although multiphoton microscopy (see Section 1.1.2) requires an ever higher peak photon flux, typically several hundreds of GW/cm2 , the much shorter wavelength used in STED is significantly more phototoxic [20]. STED microscopy is therefore not fully compatible with live–cell imaging, even though exceptions have been reported [22–24]. The limitations in localization microscopy include, among others, complex sample preparations, long acquisition times and, again, cell toxicity of the illumination light, in particularly in PALM in which near– ultraviolet radiation is used for photoactivation of the fluorophores [25]. A crucial aspect of localization microscopy for live–cell imaging is choosing the optimal probes and buffer systems for a given sample [26]. The photoswitching rate defines the integration time for each frame and therefore the global recording 7


time, which is typically several seconds to minutes for thousands of frames [27]. Choosing a certain buffer system can on the one hand help to prevent photobleaching, e.g. by using an oxygen–scavenging buffer system [26], but may, on the other hand, also affect the cell integrity [27]. The situation becomes obviously even more complex when multicolor imaging is desired. None of these limitations are present in linear Structured Illumination Microscopy (SIM). Unlike STED, PALM and STORM, linear SIM can theoretically not provide unlimited resolution, and should therefore not be considered as a super–resolution technique, but rather as a resolution enhancement method. The idea of SIM was first proposed in 1966 by Lukosz [28] but was only decades later put into practice by Gustafsson [29]. SIM is a widefield microscopy method in which a fluorescent sample is not homogeneously illuminated. Ideally, a striped sinusoidal intensity pattern with a spatial frequency close to the objective cut–off frequency is applied. Interference between the illumination pattern and the spatial frequencies in the sample structure creates Moiré fringes and shifts previously unattainably high spatial frequency information into the pass– band of the objective, as illustrated in Fig. 1.5. To extract this information, at least three images are needed with different phase shifts of the illumination pattern. Next, the pattern is rotated over 60

◦

and several images are again

recorded with different phase shifts. The same process is repeated for a rotation over 120 ◦ , resulting in a total of 9 recorded images. The high–frequency information is shifted to the correct position in Fourier space in post–processing. As discussed in Chapter 2, a twofold improvement in lateral resolution can be expected with linear SIM under optimal conditions, combined with a similar optical sectioning effect as in confocal microscopy. In the nonlinear extension of SIM, called saturated SIM, the sinusoidal illumination intensity is drastically increased to generate higher harmonics in the fluorescence response [30]. While this method is theoretically able to provide unlimited resolution, saturated SIM requires an artifact sensitive reconstruction process and is limited by photobleaching [30]. The main advantage of SIM is the flexibility of the technique. Since SIM can be combined with most standard fluorophores and labeling protocols [27], employing this method does not necessitate specific sample preparations. In addition, 8

1.1. MICROSCOPY Sample structure

Illumination pattern

Moiré fringes

Figure 1.5: Illustration of Moiré fringes. Mixing of high spatial frequencies in the sample structure with high spatial frequencies in the illumination pattern creates Moiré fringes in the image which contain lower spatial frequencies. The high sample structure frequencies can be derived from the measured Moiré image and the operator controlled illumination pattern.

illumination intensities are comparable to conventional widefield fluorescence microscopy [31]. Image Scanning Microscopy (ISM) with pixel reassignment, proposed by Sheppard in 1988 [32], is a technique intrinsically identical to SIM, but with a laser scanning implementation similar to a CLSM. In ISM, the point–detector of a CLSM is replaced by a small camera consisting of about 10 to 40 detector elements and placed in the conjugate focal plane, where the pinhole is located in a CLSM. Each detector element records an image while a focused laser beam scans the specimen. As discussed in detail in Chapter 2, the information contained in each image is slightly different. All information is combined by an algorithm in post–processing, resulting in a single image with the same resolution improvement as in SIM.

1.1.2

Contrast

Equally important to resolution is the contrast in the image. Contrast may refer to two different properties. The term can, on the one hand, refer to the ability of 9


an optical system to image the high spatial frequencies with a modulation depth similar to the depth obtained for the low spatial frequencies. Instead of a decreasing OTF as shown in Fig. 1.2, an ideal system would have a constant OTF, extending from 0 to the cut–off frequency. In this way, all sample information regarding spatial frequencies below the cut–off value would be present in the image in exactly the same way as in the sample structure. Most imaging modalities, however, have a non–constant OTF. Although this unwanted filtering effect can, in theory, be completely reversed by applying a deconvolution algorithm in post–processing, unfiltering is in reality limited by the signal–to–noise ratio. Contrast may, on the other hand, refer to the selectivity of the system, i.e. the possibility to discriminate specific sample structures from the background or from other structures. Making use of fluorescence has been a major leap forward, as demonstrated by Fig. 1.6. A live–cell is simultaneously imaged with transmission, fluorescence, and SHG (see below) microscopy. The small differences in absorption between the different cell structures barely generate contrast in the transmission image, while the fluorescence and SHG are clearly observable. Since there is no autofluorescence of the sample in this example, a fluorescent dye was added to visualize specific organelles within the specimen. (a)

(b)

Figure 1.6: (a) Transmission microscopy vs. (b) laser scanning fluorescence microscopy of a human lung cancer (A549) cell of which the lysosomes were stained with the fluorescent probe LysoTracker Green DND-26 (red). LiNbO3 NPs were added to the cell and imaged simultaneously with SHG microscopy (green). Scale bars 30 µ m. A crucial aspect responsible for the high contrast in fluorescence microscopy is 10

1.1. MICROSCOPY

the Stokes shift [33], which gives the fluorescence a different color than the illumination light. Blocking the excitation light and transmitting the fluorescence by placing a color filter in front of the detector or the ocular provides a huge contrast. A second important advantage of fluorescence microscopy is the ability to specifically stain different structures in a cell with different labels, each label requiring a particular combination of excitation wavelength and fluorescence filter. In this way, multichannel imaging is possible, with each channel showing the fluorescence from a specific structure. Despite the high contrast and the many possibilities for acquiring super– resolution images (see Section 1.1.1), fluorescence microscopy is limited by several drawbacks. Many fluorophores emit in the blue wavelength range and are excited with phototoxic and highly scattering ultraviolet (UV) radiation. Furthermore, the number of excitation–relaxation cycles is limited due to photobleaching, i.e. the molecule permanently loses the ability to fluoresce [34]. Destruction of the dye often affects other structures in cells and tissue and is therefore also a major source of phototoxicity [35]. In addition, fluorescent molecules can temporarily switch to a dark state, leading to blinking in the fluorescence intensity, and are prone to dye saturation, i.e. there is a maximum number of photons that can be emitted in a certain time [34]. Fluorescence excitation with longer wavelengths is possible by means of nonlinear light–matter interactions, such as Two–Photon Fluorescence Excitation (2PE) [36]. In 2PE, two photons with half the required excitation energy are semi–simultaneously, i.e. within 0.5 f s [37], absorbed by the fluorescent molecule, producing normal fluorescence emission. Not only are the longer wavelengths of the infrared (IR) radiation less absorbed by the specimen [38] and therefore much less phototoxic [20], there is also less scattering, which allows imaging at large penetration depths, up to 1 mm in ideal circumstances [39]. Moreover, due to the requirement of an extremely high photon flux, a condition typically met by spatially and temporally focusing of a laser beam, 2PE microscopy is intrinsically confocal. The fluorescence can be detected close to the sample, without needing a complex emission beam path with a pinhole. Another nonlinear microscopy technique, circumventing all issues with fluorescent probes, is SHG imaging. SHG is a second–order optical process in which 11


two photons of frequency ω interact with non–centrosymmetric structures in the specimen to produce a single scattered photon with frequency 2ω [40]. The energy levels involved in this process are compared with 2PE in Fig. 1.7. In Third Harmonic Generation (THG), the energy of three photons is combined to produce a single photon with frequency 3ω [41]. THG does not require non– centrosymmetric structures. SHG

2PE S1

hfI

hfI

hfSHG

hfF hfI

hfI

S0

Figure 1.7: Jablonski diagram of 2PE and illustration of the energy levels in SHG. h is the Planck constant, f I , f F and f SHG are the frequency of the illumination, the fluorescence, and the SHG light, respectively. Dashed lines represent virtual energy levels. Black arrows indicate non–radiative transitions. SHG imaging was one of earliest forms of nonlinear microscopy with biological samples [42–44]. The condition of non–centrosymmetry is met in several biological materials, such as collagen type I and II [43, 45], myosin [46], and microtubules in some cases [47], which can thus be imaged label–free. Structures which do not generate a second harmonic signal may be labeled with SHG nanocrystal probes. Several inorganic materials, often used in the form of nanoparticles, called harmonic NPs, have a non–centrosymmetric crystal structure and produce a bright SHG signal, e.g. KTiOPO4 [48], KNbO3 [49], LiNbO3 [50], Fe(IO3 )3 [51], ZnO [52] and BaTiO3 [53]. Recently, Dubreil et al. presented a method for labeling human skeletal muscle–derived stem cells with SHG and THG producing bismuth ferrite NPs, allowing long–term cell tracking [54]. Not only can harmonic NPs be employed as a labeling method, investigating NP interactions with cells is in itself important for e.g. nanomaterial safety studies [55] and can be done label–free with SHG NPs. Unlike fluorescence, SHG does not experience photobleaching [35], allowing for long–term observations. Furthermore, the operator has a broad flexibility in the choice of illumination wavelength and the SHG signal is coherent and at exactly half this wavelength [53]. Narrow bandpass filters can thus be installed, providing a high imaging 12

1.1. MICROSCOPY

contrast. Of course, the absence of a true emission spectrum makes multiplexing with SHG significantly more challenging than with fluorescence. On the other hand, because of the ultrafast response time, the SHG scattering process cannot, unlike fluorescence, be saturated [35]. In addition, the long near–infrared (NIR) illumination wavelength has the same biocompatibility advantages as 2PE.

1.1.3

Deep tissue imaging

Due to strong scattering of the UV radiation or the visible light used in One– Photon Fluorescence Excitation (1PE) microscopy, this technique is limited to penetration depths of a few tens of microns in biological samples [56, 57]. Apart from all other advantages present in nonlinear imaging, the longer illumination wavelength used in two–photon microscopy also allows a much deeper penetration, i.e. more than 100 µ m. However, even with IR radiation, the number of photons reaching the focal volume without being scattered decreases exponentially with increasing focal depth [58]. The quadratic dependence on the illumination intensity of the signal generated in two–photon processes further limits the depth penetration [57]. Deeper imaging is feasible by using acoustic waves instead of light. In ultrasound (US) imaging, sound waves are reflected or backscattered by the sample, detected, and processed to form an image [59]. The contrast in US imaging is rather low, though, since soft tissues, blood, and water all have a similar acoustic impedance [59]. In contrast–enhanced US imaging, microbubbles, having a much lower acoustic impedance, are used as a contrast agent [60]. Microbubbles are spherical gas bubbles with a diameter between 0.1 and 100 µ m, surrounded by a stabilizing surfactant shell [61]. In US imaging with microbubbles, the contrast in the image thus arises from the difference in acoustical response between regions with and without microbubbles. However, the benefit of using microbubbles is not limited to providing acoustical contrast. More information can be collected by fluorescence staining of the microbubbles. E.g. the emission spectrum of a fluorescent molecule may be sensitive to its direct environment, thereby providing information about the local pH, relative tissue oxygenation or other disease indicators [62]. Imaging of the microbubble fluorescence could be performed with a hybrid acousto–optic technique [62, 63]. The compressibility 13


difference between the gas in the microbubble and the surrounding environment makes the microbubble oscillate in size when exposed to US [63]. For an even distribution of a fluorescent, self–quenching dye in the shell, the fluorescence intensity will be modulated at the US frequency, due to periodic self–quenching of the fluorescence when the microbubble is at its smallest. Fluorescence from microbubbles outside of the US focal volume, together with noise and autofluorescence from the sample, will not be modulated at the US frequency and can be filtered out at the detectors by using a lock–in amplifier [63]. In this way, the remaining signal originates from the microbubbles in the ∼ 1 mm3 acoustic focal volume and its spectrum can be analyzed to locally check the tissue.

1.2

Obtaining subdiffraction information without circumventing the diffraction limit

Conventional optical microscopy is limited in resolution by diffraction. One way to deal with this issue is by searching for imaging methodologies that overcome this limit, as discussed in Section 1.1.1. Alternatively, one can try to extract information, e.g. diffusion and flow properties, about nanometer–sized structures by inventively utilizing a diffraction limited system and using the power of statistics. Fluorescence intensity fluctuation imaging is a collection of ensemble–based microscopy tools which are able to measure, among other parameters, the mobility of subdiffraction sized fluorescent particles [64, 65]. Fluorescence Correlation Spectroscopy (FCS), Raster Image Correlation Spectroscopy (RICS), Spatiotemporal Image Correlation Spectroscopy (STICS) and Temporal Image Correlation Spectroscopy (TICS) are all variations of this principle. The technique is based on the probability theory involved in the random walk process that each individual particle is assumed to undergo. The fluorescence intensity measured in a sample of randomly diffusing fluorescent particles depends on the number of particles in the focal excitation volume at the moment of the measurement. Brownian motion causes the intensity to fluctuate over time and, in case of a moving excitation volume, over space. Calculating the autocorrelation function of the measured data set produces a curve that can be fitted to a model to mea14

1.3. RESEARCH AIMS AND OUTLINE

sure the diffusion coefficient and flow velocity. Because of the random motion of the particles, this model can be analytically drafted [66]. Note that the diffusion coefficient of subdiffraction sized particles can be measured with this technique, even when, on average, multiple particles reside simultaneously in the focal volume. Diffusion measurements on such high concentration samples are not possible with e.g. Single Particle Tracking (SPT), a technique that requires imaging of individual particles, each one well separated from the others [66], and measuring the mobility by analyzing individual tracks. This example illustrates that fluorescence intensity fluctuation imaging really can, unlike SPT, resolve subdiffraction information, provided the a priori knowledge that all particles are undergoing Brownian motion. A second technique that uses the power of measuring ensemble averages of subdiffraction structures is fluorescence photoselection imaging. When a fluorescent molecule is illuminated with linearly polarized light, the probability of absorbing a photon depends on the angle θ between the electrical transition dipole moment of the fluorophore and the electric field vector of the illumination light [67]. The absorption probability is proportional to cos2 θ for 1PE and cos4 θ for 2PE. By rotating the polarization plane of the incident light and tracking the resulting fluorescence intensity, the orientation of a single molecule can be determined. If the focal volume contains a collection of fluorescent molecules, this technique can measure the average orientation of the ensemble. The techniques fluorescence intensity fluctuation imaging and photoselection imaging are thus somewhat related. Both methods rely on fluctuations in the fluorescence signal, i.e. spontaneous fluctuations over time or operator controlled fluctuations over excitation polarization angle, to obtain ensemble averaged information on the behavior, i.e. the mobility or the orientation, of the subdiffraction sized structures.

1.3

Research aims and outline

The qualitative ideas of image formation, resolution, and super–resolution described in this chapter are given a mathematical foundation in Chapter 2, together with the fundamentals of fluorescence intensity fluctuation imaging. 15


Having a thorough knowledge of the general theory helps to appreciate the work described in the other chapters. Long–term fluorescence intensity fluctuation measurements are impeded by photobleaching. This effect is especially problematic when studying the diffusion properties of cellular structures over time. SHG NPs are a great alternative since they produce an extremely stable signal. However, the current analytical model used to analyze fluorescence intensity fluctuation measurements requires the signal generated by the particles to be incoherent. SHG is a scattering process and therefore preserves the phase information. A new model is therefore needed, taking into account the coherence of the SHG process. Chapter 3 is devoted to the analytical derivation of this model. The theoretical model must be verified with experimental data. We therefore apply the model to experiments with SHG active LiNbO3 and BaTiO3 NPs. As a first test, the NPs are studied under the most basic circumstances, i.e. under plain diffusion in aqueous suspension, without flow, and immediately after the sample preparation. In a second phase, the NP diffusion coefficient is measured in live cells. The results are presented in Chapter 4. We investigate the possibility to apply SIM to 2PE microscopy, with the ultimate goal to arrive at label–free super–resolution microscopy with SHG. Resolution enhancement is especially welcome with these imaging modalities because of the long illumination wavelengths. Both 2PE and SHG require an extremely high photon flux, and can therefore not be combined with widefield imaging. Instead, scanning of the specimen is needed. The combination of 2PE with SIM by modulating the illumination power during the scan process is explored in Chapter 5. An alternative approach for multiphoton resolution enhancement is ISM since this technique by default makes use of a scanning laser beam. Upgrading a 1PE ISM set–up to make it compatible with 2PE is relatively straightforward. Both the technical implementation and the results in 2D and 3D samples are discussed in Chapter 6. A second alternative ISM method for multiphoton resolution enhancement is ex16

1.3. RESEARCH AIMS AND OUTLINE

plored in Chapter 7. Instead of employing a custom–built setup, we present an idea to start from a commercial CLSM and add a camera to the non–descanned port. Technical challenges and possible ways to circumvent experimental issues are considered. US imaging is a useful tool for imaging at large penetration depths. Employing microbubbles for contrast–enhanced US imaging or for the hybrid technique acousto–optic imaging demands a method to characterize the shell properties of individual microbubbles. Being able to monitor the shell rigidity of microbubbles is a crucial step towards the development of more stable bubbles, i.e. microbubbles that can reside in circulation for a longer time before dissolving. A technique based on the photoselection effect and the emission spectrum of fluorescently labeled microbubbles to measure the shell rigidity and the molecular organization is demonstrated in Chapter 8. A general conclusion and outlook are presented in Chapter 9.

17

HAPTER

C

2

T HEORY AND METHODS

CHAPTER 2. THEORY AND METHODS

T

his work focuses on optical microscopy, on how this technique may be improved and in what ways image analysis can provide quantitative information about the sample. This chapter contains two sections. In the

first part, the mathematics behind the image formation process in a microscope is explained, followed by a selection of techniques for resolution enhancement.

The second part provides an overview of intensity fluctuation analysis methods for quantitatively characterizing diffusion and flow of particles in a sample. Throughout this chapter, we continuously pay attention to the differences between coherent and incoherent imaging modalities, since conclusions about one type of microscopy cannot simply be applied to the other type.

2.1

Optical microscopy

Understanding the optics of any microscope setup is essential to comprehend both the strengths and the limitations of the corresponding imaging process. Therefore, we begin by mathematically describing the image produced by light that is diffracted by a specimen, resulting in the Fraunhofer diffraction equation. We do not intend to give a detailed derivation of the fundamentals of microscopy, but understanding the basic principles of the image formation and resolution limits is necessary to be able to appreciate any architecture for resolution enhancement. More detailed information can be found in the literature [2, 11].

2.1.1

Theory of diffraction

Consider light emitted from a point source Q at position z = − z1 , see Fig. 2.1. Instead of describing the radiation from the light source as an oscillating electric and magnetic field, we simplify the setup by assuming a single scalar electric field wave ψQ with angular frequency ω, corresponding wave vector magnitude k 0 and wavelength λ and a strength A Q . In the sample plane, this scalar wave can be described as:

ψQ =

AQ d1

exp (i(k 0 d 1 − ω t)) .

20

(2.1)

2.1. OPTICAL MICROSCOPY

The time–dependent factor exp(− i ω t) is of no importance in the current derivation and will be omitted from this point on. S ψQ dS

d1 Q -z1

0

d

P dψP z

Figure 2.1: Illustration of light produced by a point source Q that is diffracted by a specimen S. The wave amplitude at P can be calculated using the diffraction integral from Eq. 2.3. The incident light is diffracted by the specimen S(x, y). The sample can therefore be considered as a light source with amplitude b f S ψQ , with f S (x, y) the scattering function of the specimen and with b a constant factor expressing the strength of the scattering process. The function f S can be complex to reflect a possible position–dependent phase delay between the incident and the scattered light, but the derivation in this section will be restricted to coherent scattering. The contribution d ψP of a small part of the sample dS to the total amplitude of the wave ψP at P, located at a distance d from the specimen plane, is then:

dψP =

bA Q f S dd 1

exp (ik 0 (d + d 1 )) dS.

(2.2)

Evidently, ψP is obtained by integrating over the entire sample plane:

ψP =

bA Q f S

Ï S

dd 1

exp (ik 0 (d + d 1 )) dS.

(2.3)

Eq. 2.3 can be easily adjusted for plane wave illumination by moving the point source to −∞ and making the source infinitely bright while maintaining a constant ratio A =

AQ d1 :

21


ψP = Ab exp (ik 0 z1 )

Ï S

f S (x, y) exp (ik 0 d) dS. d

(2.4)

P' S B

P

d O

A

z

Figure 2.2: The diffraction image formed in a plane infinitely far from the sample (d → ∞) can be calculated by summing the contributions (in P, P 0 , ...) of the waves produced by the sample (in O, B, ...) and emitted in the same direction. BP 0 is parallel to OP, O A is the projection of OB on OP. Similarly, consider the image formed in a plane at z → ∞ for an infinitely bright sample, b → ∞, such that B =

b d

remains constant. As illustrated in Fig. 2.2, the

signal reaching a point P can be calculated by summing the contributions of all waves produced by the specimen, that are emitted in the same direction. Let (l, m, n) be a unit vector in the same direction as OP. The projection of OB = (x, y, 0) on OP is then lx + m y. Consequently, BP 0 = OP − lx − m y = d − lx − m y. Plugging everything into Eq. 2.4 yields:

ψl,m = AB exp (ik 0 (z1 + d))

Ï S

f S (x, y) exp (− ik 0 (lx + m y)) dS.

(2.5)

The index P has been replaced by the direction cosines l, m to clarify that ψ holds the information emitted in a certain direction, rather than at a certain location. This result can be simplified by ignoring all prefactors and employing the substitutions u = k 0 l and v = k 0 m:

ψ(u, v) =

Ï x,y

f S (x, y) exp (− i(ux + v y)) dxdy.

22

(2.6)


Eq. 2.6 is known as the Fraunhofer diffraction equation. Since both the light source and the imaging plane have to be located infinitely far from the sample, the equation is also known as the far–field diffraction equation. However, an almost identical result can be achieved in a finite space by introducing a condenser lens and an imaging lens, see Fig. 2.3. L C

F

S

Q z

Figure 2.3: Imaging of the Fraunhofer diffraction pattern using lenses. The condenser lens C collects the coherent light from the point source Q, resulting in a plane wave illuminating the sample S. The diffraction pattern is imaged by a lens L, creating an image F. Q is placed in the front focal plane of C, S and F are located in, respectively, the front and back focal plane of L. For the setup of Fig. 2.3, The Fraunhofer diffraction pattern ψ is the two– dimensional Fourier transform of the specimen transmission function. Note that what is experimentally observed is in general |ψ|2 and, consequently, no phase information is collected. Placing a camera at z → ∞ in Fig. 2.2 or, equivalently, at the back focal plane of the lens in Fig. 2.3 and performing the inverse Fourier transform in post–processing will therefore not produce an image of the specimen. Although the proper method for image formation will be discussed in detail in Section 2.1.2, it is at this point noteworthy to qualitatively derive why the lens system of Fig. 2.3 cannot provide unlimited resolution. Suppose the sample contains a periodic structure, e.g. a diffraction grating. After passing through the sample, the light will be scattered over several orders. The zeroth order falls normally upon the lens, similarly to the dashed lines in Fig. 2.3. The first orders, however, will be diffracted at a non–zero angle, see the dotted lines in Fig. 2.3. 23


The smaller the periodicity of the specimen pattern is, the bigger this angle becomes. When the diffracted light misses the lens because the angle is too big, the resulting image F will only contain the zeroth order. All information about the grating structure is lost. Consequently, there exists a certain minimum periodicity, corresponding to a maximum angle, for which the first order can still be collected by the lens.

2.1.2

Image formation as a diffraction process

To obtain an image of the specimen, a second lens can be installed in the setup of Fig. 2.3. When the lenses are conjugated, i.e. the front focal plane of the second lens coincides with the Fourier plane, the reasoning from Section 2.1.1 can be applied twice. The image, created in the back focal plane of the second lens, will be the Fourier transform of the Fourier transform of the specimen, which is the mirror counterpart of the specimen, as illustrated below. L2 I

L1 S

F1'

F

F1 F2'

F2 z

Figure 2.4: Imaging of a sample using two conjugated lenses. The sample S is placed in the front focal plane of the objective lens L 1 , with focal length F1 . The Fourier plane F coincides with the front focal plane of the tube lens L 2 with focal length F2 . An F2 /F1 times magnified image of S is produced in the image plane, I. To obtain a magnified image of the specimen, the second lens must have a larger focal length than the first lens. Consider the setup from Fig. 2.4, containing two conjugated lenses. The first and second lens have focal lengths of F1 and F2 , respectively. The specimen is placed in the anterior focal plane of the first 24


lens. For simplicity, a one–dimensional sample is presumed; the generalization to two dimensions is trivial. Ignoring prefactors and assuming small angles of incidence on L 1 and L 2 and infinitely large lenses, the obtained amplitude in the back focal plane of the second lens ξ(x00 ) is:

00

ξ(x ) =

Z ·Z

µ ¶ ¸ µ ¶ ik 0 x0 x ik 0 x00 x0 f (x) exp − dx exp − dx0 . F1 F2

(2.7)

Here, x, x0 , x00 refer to the coordinates in the sample plane, the Fourier plane, and the image plane, respectively. Let u =

00

ξ(x ) =

Z ·Z

k 0 x0 F1

and v =

F 1 00 F2 x .

Then Eq. 2.7 reduces to:

µ ¶ F1 00 f (x) exp(− iux)dx exp(− ivu)du ∼ f (−v) ∼ f − x . F2 ¸

(2.8)

The image is inverted and magnified by a factor F2 /F1 with respect to the specimen. The same result can be realized by using a single lens if the object is placed before the front focal plane. However, using a two–lens system is common practice in optical microscopes since this configuration is convenient to obtain larger magnifications with less effect of aberrations.

2.1.3

The resolution limit

All sample information contained in the light that is not incident on the first lens is lost in the final image. The minimum resolvable periodicity d of a grating structure depends on the maximum angle of incidence α that is still admitted by the lens: d = λ/sin α. The vacuum wavelength λ can be decreased by a factor of n by introducing a liquid medium with refractive index n between the sample and the lens. The resulting resolution limit is

d=

λ

n sin α

=

λ

NA

.

(2.9)

Fig. 2.5 illustrates the effect of a finite NA on the imaging capabilities of a lens system. If the zeroth order and at least one of the two first orders from the 25

CHAPTER 2. THEORY AND METHODS L2

L1

(a) S

I

F α

F1'

S

F1'

z

L2

L1

(b)

F2

F1 F2'

F

F1 F2'

I

F2 z

Figure 2.5: Illustration of the resolution limit for parallel incident illumination on a grating pattern with (a) the limiting periodicity that can be imaged and (b) a periodicity that is too small to be resolved by this lens system. The labels are explained in the caption of Fig. 2.4. Note that the observed pattern in (a) is a smoothed mirror image of the grating.

diffracted light can be collected by the first lens, the periodicity of the grating pattern will be correctly reproduced. Loss of information from the missing higher orders results in a smoothed image of the grating pattern. If the sample periodicity becomes smaller, the first orders will be scattered at angles larger than α, thereby not hitting the lens. Eq. 2.9 holds when the incident light travels parallel to the optical axis. A twofold better resolution can, however, be achieved when the illumination beam reaches the sample at the angle α, i.e. by oblique illumination [68]. The zeroth order will simply pass through, while one of the first orders will not be incident on the lens. The other first order may be scattered at the angle 2α. Hence, the 26


periodicity of the grating can be halved:

d=

λ

2N A

.

(2.10)

Eq. 2.10 is the Abbe diffraction limit, which for a conventional coherent optical imaging system is entirely defined by the NA and the illumination wavelength. As can be seen, this diffraction limit is completely magnification independent.

2.1.4

The point spread function and the optical transfer function

The Abbe diffraction limit defines the minimum resolvable periodicity of a grating, but the formula does not provide quantitative information on how well a resolvable grating is imaged. The PSF of an optical system and its Fourier transform, the OTF, help to describe the optical performance of a microscope. The PSF of an imaging system is defined as the image obtained from a point object. Equivalently, the PSF is the image pattern formed in the front focal plane of a lens that is illuminated by a plane wave, as illustrated in Fig. 2.6. Applying Eq. 2.6 to the aperture function W(r) corresponding to a circular lens of radius R and focal length F, the resulting Amplitude Point Spread Function (aPSF) for on–axis illumination is [12]

aPSF(r) =

2J1 (2πRr/λF) . 2πRr/λF

(2.11)

Here, r is the distance from the optical axis and J1 is the first–order Bessel function of the first kind. For small angles of incidence and assuming no immersion medium is applied, the ratio R/F is equal to the NA of the lens. If the sample is not a point object, coherent scattering by the sample produces an amplitude image given by the convolution product (⊗) of the PSF and the sample structure s. The function s describes the local response of the sample, including a potential phase delay to the applied electric field. In Fourier space, denoted with 27

CHAPTER 2. THEORY AND METHODS Q

C

O

PSF

z

S

O

T

PSF

Figure 2.6: A plane wave, e.g. generated by a point light source Q and a condenser lens C, focused by an objective O creates the same pattern (PSF) in the front focal plane as the image of an infinitely small sample S formed by an objective and a tube lens T.

a ‘∼’ symbol, the amplitude image is the product of se and the Coherent Optical Transfer Function (cOTF). High frequencies in se correspond to small details in the sample structure and vice versa. The cOTF is a circular window function with radius f c = R/λF = N A/λ, as depicted in the overview image, Fig. 2.7. All spatial frequencies below the cut–off frequency f c are transmitted equally (upper right panel of Fig. 2.7). All other spatial frequencies are not present in the amplitude image. The resolution limit in Fourier space is thus characterized by the value of f c . Note that the same limit was obtained more intuitively in Section 2.1.3 (Eq. 2.9).

28


F* Aperture: W(r)

F

2J (2Rr/F) aPSF = W = 1 2Rr/F ~

cOTF

R

fc =

R F

Coherent imaging

3.83 F 2R

I = |s aPSF|2 F iPSF = |aPSF|2 =

2J1(2Rr/F) 2Rr/F

2

= F -1 (W W)

fc =

2R F

Incoherent imaging

3.83 F 2R

2 iOTF = (cos-1(f/fc) - f/fc 1-(f/fc)2 ) = W W

I = t iPSF Frequency space

Real space

Figure 2.7: Overview of the PSF and the OTF functions in coherent and incoherent imaging. A circular lens with radius R and focal length F is assumed. The symbol F denotes the Fourier transform. The asterisk refers to the coordinate transformation needed to bring the diffraction pattern from infinity to the focal plane. For air objectives, R/F is equal to the NA. For immersion objectives, λ must be replaced by the reduced wavelength λ/n.

29


The amplitude image shows a perfect reconstruction of all sample structures with periodicity larger than 1/ f c . What is observed by the human eye or recorded by a camera, however, is an intensity image I, which does not contain phase information:

I = | s ⊗ aPSF |2 .

(2.12)

The microscopy image will thus be influenced by constructive and destructive interference of the scattered light. Fig. 2.8 shows two point objects at various distances from each other. If the coherent incident light is scattered in phase by the two particles, the resulting image contains two partially overlapping point spread functions. There is a limiting distance at which the two point objects can still be resolved. For a phase difference of π radians between the two point sources, the image will always consist of two blobs, however close the point objects may be [2]. The distance between the two blobs does not reflect the true particle–particle separation if this separation is smaller than the Abbe limit. This example illustrates that, because of the amplitude–to–intensity–conversion, defining resolution for coherent imaging modalities is not straightforward. Sample

Coherent In phase

Coherent Incoherent In anti-phase

Figure 2.8: Coherent versus incoherent imaging of point objects, simulated with Eq. 2.12. Characterizing the imaging quality in terms of the PSF and the OTF is easier for truly incoherent imaging. An important example is fluorescence microscopy, in which fluorophores in the sample emit light at random times after absorption 30


of the excitation light. In this case, the image is the convolution product of the sample structure t and the Intensity Point Spread Function (iPSF). The parameter t describes the response of the sample to the excitation intensity, i.e t ∼ | s|2 . The iPSF is proportional to |aPSF |2 . The central peak of the pattern is called the Airy disc and extends to the first zero. The Fourier transform of the iPSF is the Incoherent Optical Transfer Function (iOTF). One can show [12] that the shape of the iOTF is the convolution product of the lens aperture function W(r) with itself, i.e.

  s µ ¶ µ ¶2 2  −1 f f f . cos iOTF = − 1− π fc fc fc

(2.13)

The cut–off frequency for incoherent imaging is f c = 2R/λF = 2N A/λ. The incoherent counterpart, unlike the cOTF, is not a window function. Instead, the iOTF declines in a continuous way from the maximum value at the center to zero at f = f c . Higher spatial frequencies are thus transmitted more weakly than lower spatial frequencies: the objective behaves as a low–pass filter. In the absence of noise, this effect can be fully compensated in post–processing by dividing the Fourier transform of the image by the filter function (iOTF) for all frequencies smaller than f c . Transforming back to real space then produces the final image. Note that this deconvolution process rescales all frequencies present in the image to their correct contributions, but the cut–off frequency remains f c . The process of unfiltering the image does not improve the resolution, but the resulting contrast does arguably result in a better image. An overview of the PSFs and the OTFs is presented in Fig. 2.7. For practical purposes, the aPSF and the iPSF in the xy–plane are often approximated by Gaussian functions. For coherent imaging, the aPSF in the z–direction must take into account the phase shift introduced by the focusing of coherent light by a lens [41], see e.g. Eq. 2.30 in Section 2.2. For incoherent microscopy, a plain Gaussian may be used.

31


2.1.5

Laser scanning microscopy

The PSF and the OTF are the main building blocks used to describe the optical performances of different microscope modalities. Consider first the laser scanning microscopy architecture from Fig. 2.9 combined with a fluorescent sample. The laser light is focused by the objective, which creates a diffraction limited excitation iPSF h 1 at position vector xL in the specimen. The fluorescence is collected by the objective and focused onto a photodetector, without passing via the scan mirrors, i.e. non–descanned detection. Assuming fluorescence excitation occurs solely within the focal plane, the emission signal I collected by the photodetector can be described as

Ï

I(xL ) =

t(x) · h 1 (x − xL )d2 x = t ⊗ h 1 .

(2.14)

Consequently, the non–descanned configuration has a spatial cut–off frequency of 2N A/λ, with λ the excitation wavelength. Note that the surface area of the detector must be large enough to collect the emission signal for all positions of the laser beam. As a result, detection is in general restricted to Photomultiplier Tubes (PMTs). This imaging technique performs slightly better than widefield fluorescence microscopy. The resolution of the latter method is also limited to 2N A/λ, but here, λ is the longer fluorescence emission wavelength. For infinitely small, spatially well separated fluorescent particles, t becomes a sum of Dirac delta functions at different positions and the observed image is a collection of excitation iPSFs. Non–descanned imaging of fluorescent microspheres is therefore particularly suited to check the excitation beam path of a microscope. The assumption that the fluorescence is exclusively generated in the two– dimensional focal plane is certainly not valid for thick specimens. To reduce the thickness of the optical slice, non–descanned detection is in general only used in combination with multiphoton excitation. Multiphoton Excitation Microscopy (MPEM) requires an extremely high photon flux, a condition that is only met within the small focal volume. Alternatively, the out–of–focus fluorescence light 32


Obj.

M

DBS

Figure 2.9: Beam path laser scanning microscopy with non–descanned detection. Laser light (blue) is reflected by a (dichroic) mirror (red) to the scan mirrors (gray). The laser beam passes a dichroic beam splitter (DBS) and is focused by the objective (Obj.), exciting fluorescent molecules in the sample. The resulting emission signal, which has a different color because of the Stokes shift, is again collected by the objective, reflected by the dichroic beam splitter and passes through the emission filter (M). The light is focused by a lens and collected by a large area photodetector.

can be blocked by placing a pinhole at the conjugate focal plane, i.e. confocal microscopy, as illustrated in Fig. 2.10. The pinhole can remain at a fixed position since the lateral movement of the emission signal is undone by descanning the fluorescence beam. An additional advantage of this configuration is the possibility to employ detectors with a small surface area, such as Avalanche Photodiodes, which for many applications provide superior quality compared to PMTs.

The out–of–focus signal is blocked by setting the pinhole diameter to about 1 Airy unit, i.e. detection is restricted to the Airy disc. However, Cox et al. realized that a better lateral resolution is obtained when setting the pinhole diameter to an infinitesimal value [13]. To understand this quality improvement, consider the same excitation beam path as before. For each position of the laser beam, the fluorescence produced by the sample is the product of t(x) and h 1 (x − xL ). A fluorescent point source in the sample plane would produce an image equal to 33


Obj.

DBS

M

Figure 2.10: Beam path confocal microscopy. Laser light (blue) is reflected by a dichroic beam splitter (DBS) to the scan mirrors (gray). The laser beam is focused by the objective (Obj.) and excites fluorescent molecules in the sample. The resulting emission signal, which has a different color because of the Stokes shift, is again collected by the objective, descanned by the scan mirrors and transmitted by the dichroic beam splitter and the emission filter (M). The light is focused by a lens and collected by a photodetector. A pinhole is placed at the conjugate focal plane of the lens to block fluorescence from above and below the objective focal plane.

the emission iPSF h 2 . All excited fluorophores combined thus produce an image given by

I = [t(x)h 1 (x − xL )] ⊗ h 2 (x + xL ).

(2.15)

The emission PSF must contain the shift vector +xL to account for descanning the signal. The Airy disc of h 2 is in general larger than the pattern of h 1 due to the longer wavelength of the emission light. Writing out the integral form yields 34


I(x0 , xL ) =

Ï Ï

=

t(x)h 1 (x − xL )h 2 (x0 − x − xL )d2 x

(2.16)

t(x + xL )h 1 (x)h 2 (x0 − x)d2 x.

(2.17)

The vector x0 is the spatial coordinate in the image space. By substantially reducing the pinhole diameter, only the signal from x0 = 0 is collected. Eq. 2.17 can, for even functions h 1 and h 2 , be reduced to

Ï

I(xL ) =

t(x + xL )h 1 (x)h 2 (x)d2 x

= h 1 h 2 ⊗ t.

(2.18) (2.19)

The overall PSF in a confocal microscope is therefore the product of the excitation PSF and the emission PSF. The effect on the imaging quality can be appreciated in Fourier space. The confocal transfer function in absence of a Stokes shift is obtained by taking the convolution product of the OTF for incoherent imaging, from Eq. 2.13, with itself. The result, plotted in Fig. 2.11, shows that the cut–off frequency increases from 2N A/λ for widefield imaging to 4N A/λ for confocal microscopy with a substantially reduced pinhole diameter. Theoretically speaking, the confocal microscope has a twofold better resolution. However, the confocal OTF has dropped to less than 1 % already at a normalized frequency (units of N A/λ) of 3. The resolution is thus not only limited by the maximum transmitted spatial frequency but also by the signal–to–noise ratio of the detection system. Reducing the pinhole diameter will in practice only p yield a resolution enhancement of about 2 . The same number is found when approximating h 1 and h 2 by identical Gaussian functions with a 1/e2 value of p ω. The product h 1 h 2 is then a new Gaussian with a 1/e2 value of ω/ 2 . A large Stokes shift will, of course, broaden h 2 , limiting the improvement even further.

2.1.6

Lateral resolution enhancement

In most experimental cases, the pinhole must be set to at least 1 Airy unit in order to collect a sufficient amount of fluorescence. The potential of the 35

CHAPTER 2. THEORY AND METHODS (a)

(b)

100

Widefield Confocal

0.8

Normalized amplitude


1

0.6 0.4 0.2

Widefield Confocal

10-2

10-4

10-6 0

0 0

1

2

3

4

1

2

3

4

Normalized spatial frequency [NA/ ]

Normalized spatial frequency [NA/ ]

Figure 2.11: Comparison of the OTF for incoherent imaging in widefield mode and in confocal mode with (a) a linear and (b) a logarithmic y scale. The horizontal axis is expressed in units of N A/λ, the amplitudes are normalized to 1 for the zero frequency. The widefield and the confocal OTF meet the horizontal axis at 2N A/λ and 4N A/λ, respectively. confocal setup in terms of resolution is thus not fully exploited. However, confocal microscopy is highly appreciated for its ability to obstruct out–of–focus light, thereby limiting the imaging volume to a thin optical slice. Measuring a stack of images at different depths in the specimen allows making a three–dimensional reconstruction of the sample. Surpassing the lateral resolution limit by a factor of two without wasting precious photons in return and still maintaining the optical sectioning effect is feasible by means of SIM [69]. In this incoherent widefield microscopy technique, a sinusoidal pattern with a spatial frequency close to the cut–off frequency is projected onto the sample, after which the emission signal is detected by a camera. To show that SIM doubles the cut–off frequency, consider first a one–dimensional ¡ ¡ ¢¢ situation. Let P(x) = A 1 + m sin ω0 x + ϕ be the position–dependent illumination intensity. The parameters m, ω0 and ϕ describe the modulation depth, the angular spatial frequency, and the phase, respectively. For low enough excitation intensities, the fluorescence signal F is proportional to P [70]:

¡ ¡ ¢¢ F = A 1 + m sin ω0 x + ϕ t(x).

36

(2.20)


The image is given by F convoluted with the emission iPSF:

£ ¡ ¡ ¢¢ ¤ I = A 1 + m sin ω0 x + ϕ t(x) ⊗ h 2 (x).

(2.21)

Calculating the Fourier transform yields:

h ³ ´ i m m f2 (ω) e ω) = A δ(ω) + e iϕ δ(ω − ω0 ) + e− iϕ δ(ω + ω0 ) ⊗ et(ω) · h I( 2 2 h ³ ´i m m f2 (ω). = A et(ω) + e iϕ et(ω − ω0 ) + e− iϕ et(ω + ω0 ) · h 2 2

(2.22) (2.23)

If the modulation depth is zero, i.e. under widefield illumination, the image will not contain any information corresponding to spatial frequencies higher than f2 . For nonzero values of m, however, two additional the cut–off frequency of h terms appear: et(ω − ω0 ) and et(ω + ω0 ). Previously inaccessible information has e ω) is a sum of now shifted into the passband of the imaging system. Since I( three unknown terms (et(ω), et(ω + ω0 ) and et(ω − ω0 )), at least three images with f2 is known in advance different values of ϕ are needed to solve the problem. If h and the applied angular frequency of the pattern ω0 is close to the cut–off value 2π f c , the resolution of the reconstructed image is effectively doubled. More generally, the resolution is 2π( f cex + f cem ), with f cex and f cem the excitation and emission cut–off frequencies, respectively. These values will not be equal in the presence of a Stokes shift. f2 (ω) Expanding the theory to two dimensions is straightforward. The term et(ω) h

now represents all spatial frequencies in the sample within the circle defined by the emission OTF. The other two terms equivalently describe shifted versions of this circle, as visualized in Fig. 2.12. After reconstruction, the image contains all information from the three domains combined. The cut–off frequency in the horizontal direction has now doubled. Similarly, by repeating the measurement with an illumination pattern first rotated over 60 ◦ and subsequently rotated over 120 ◦ , the union of all 7 circles approaches a circle with radius 2ω c . Therefore, the lateral resolution limit is surpassed by a factor of two in all directions. 37

CHAPTER 2. THEORY AND METHODS ωy

O

~ ~ ~ ~ t(ω) h(ω+ω0) t(ω) h(ω)

ωc

ωx

~ ~ t(ω) h(ω-ω0)

Figure 2.12: Effect of structured illumination with ω0 = ω c on the 2D sample information obtained in Fourier space. Each circle represents part of the Fourier f2 . A modulation pattern transform of the sample structure et(ω) confined to h along the x–axis provides the information indicated by the black circles. The frequency domain can be expanded in the other directions by rotating the pattern over 60 ◦ and over 120 ◦ , illustrated by the gray circles. For notation purposes, angular spatial frequencies are used, e.g. ω c = 2π f c . For simplicity, we limit the SIM theory to both two–dimensional and linear samples. One can show, however, that the optical sectioning strength of a widefield SIM setup in a three–dimensional specimen is comparable to what is obtained with a confocal microscope [69]. This property is not discussed in further detail in this thesis since our main focus is MPEM in which no out–of–focus light is produced anyway. Note that exploiting the nonlinear relationship between the excitation intensity and the fluorescence response for high illumination powers, so–called saturated SIM, may theoretically provide an unlimited lateral resolution by adding an infinite amount of circles to Fig. 2.12 [30]. Though multiphoton excitation is a nonlinear process as well, the sample response with respect to the illumination intensity is purely quadratic for conventional laser powers. The absence of higher orders sets a fundamental limit to the resolution which can be obtained with multiphoton SIM. Obviously, an important aspect in SIM is creating the illumination pattern with a spatial frequency close to f c . This requirement is difficult to accomplish with a point scanning system, as will be explained in more detail in Chapter 5. Most SIM implementations therefore make use of widefield illumination and camera detection, although exceptions have been reported [71, 72]. Further38


more, thorough knowledge of the iPSF is necessary to properly perform the reconstruction.

An elegant solution to these limitations is ISM with pixel reassignment. ISM can be thought of as the point scanning version of SIM, in which the sinusoidal illumination pattern is replaced by the diffraction–limited PSF. An image is recorded for each position of the laser beam. The total number of images can therefore easily exceed 250000, which is significantly more than the three times three images needed in conventional SIM. ISM can, however, be combined with descanned detection, which limits the emission signal in the detection plane to a small region surrounding the optical axis, resulting in the camera only needing about 20 to 30 pixels.

The working principle of ISM is illustrated in Fig. 2.13. The point detector of a conventional confocal microscope is replaced by an array detector consisting of several detector elements, i.e. a low–resolution camera. All elements combined span an area equal to about 1 Airy disc, but the size of each detector element is much smaller. Similarly to confocal microscopy with an almost closed pinhole, the signal collected by an individual detector element at position xD is, from Eq. 2.17, given by

Z

I(xD , xL ) =

t(x + xL )h 1 (x)h 2 (xD − x)dx.

(2.24)

The one–dimensional system considered here for simplicity can be generalized to two dimensions.

Approximating h 1 and h 2 by Gaussian functions with the same width ω0 yields: 39


Figure 2.13: Beam path in ISM. All components are identical to Fig. 2.10, except for the pinhole, which is replaced in this example by a 5x5 array detector. An Airy disc sized pinhole is drawn for scale.

Z

I(xD , xL ) =

Ã

t(x + xL ) exp −

ω20

!

Ã

exp −

2(x − xD )2 ω20

!

dx

·µ ¶2 ¸! p 1 1 2 = t(x + xL ) exp − 2 2 x − p xD + xD dx 2 ω0 2   Ã ! µ ¶2  Z  x2D 2 1   dx. = t(x + xL ) exp − 2 exp − µ ¶2 x − x D    2 ω0 ω0 p 2 Z

Ã

2x2 2

(2.25) (2.26)

(2.27)

The image recorded by the detector element can thus be described as

Ã

Ã

I(xD ) = t ⊗ G exp −

x2D ω20

!

! ω0 x D ,p , . 2 2

(2.28)

Here, G(a, b, c) is a Gaussian function with amplitude a, 1/e2 radius b and lateral shift c. All three values provide essential information about ISM. The 40


first parameter shows that the farther a detector element is located from the optical axis, i.e. the larger | xD |, the lower the amplitude of the signal. In other words, detector elements in the center have a better signal–to–noise ratio than elements near the sides. This means that, in practice, increasing the number of detector elements for a better imaging quality is only effective to a certain extent. The second parameter shows that the image from each detector element is the convolution product of the sample structure with a Gaussian of width p p ω0 / 2 . The images taken with each element therefore have 2 better resolution compared to widefield imaging. The same effect is observed by substantially reducing the pinhole diameter in a conventional confocal microscope, see Section 2.1.5. ISM, however, is significantly more photo–efficient, since all detector elements combined cover a much larger area. The third parameter expresses the lateral shift in the field–of–view between a detector element at position xD and the central detector element. Characterizing this difference is crucial to obtain a proper reconstruction. Each pixel element at a distance xD will have its corresponding field–of–view shifted by − xD /2. The minus sign arises from the fact that the image is the mirror counterpart of the sample structure. The field– of–view shift is corrected in post–processing, the so–called pixel reassignment process. All pixels are shifted over a distance xD /2. This method is repeated for all detector elements after which all images are simply summed. This results in p a final image which has 2 enhanced resolution compared to an image produced using confocal microscopy while maintaining the signal–to–noise ratio. The pixel reassignment process in ISM is in a certain way a special case of a stochastic reconstruction algorithm. To intuitively grasp this idea, one should not think in terms of an emission iPSF, but instead of a detection iPSF [73]. This reasoning is illustrated in Fig. 2.14. The illumination source is focused by the objective. The resulting excitation iPSF can be thought of as the probability density for a fluorophore at a given position to be excited. If a fluorescence photon is produced, its lateral position at the detection plane is determined by the emission iPSF, which defines the spatial distribution of the probability density. The same principle applies the other way around: e.g. the probability density that a photon is collected by the detector element at position B is given by the emission PSF centered at position A. Consequently, the detection PSF h02 is found by flipping the emission PSF h 2 over the optical axis. Evidently, a 41


photon can only be detected if the fluorophore was first excited. Hence the total ISM PSF is the excitation iPSF h 1 multiplied by the detection iPSF h02 . For two identical Gaussian functions, the result is a Gaussian centered at a position halfway in between the centers of h 1 and h02 , see Fig. 2.15. In summary, all photons hitting a detector element are reassigned to their most probable origin. The difference with the super–resolution method STORM is that in STORM only an optically resolvable subset of fluorophores is activated per image, while in ISM all fluorophores within the focal volume may be excited simultaneously. The single molecule resolution of STORM can therefore not be reached with ISM. Q

Sample

Detector

A

z B

Figure 2.14: Stochastic interpretation of ISM in one dimension. A point source Q is focused by the objective into an excitation iPSF (blue). A point source at the sample plane produces an emission iPSF at the detector plane (yellow). Alternatively, the probability density that a fluorescence photon is collected by a specific detector element is given by its detection iPSF, shown in red for the fourth detector element. Ignoring the magnification of the system, points A and B are equally distant from the optical axis. Both vertical arrows represent the same objective.

If h02 is wider than h 1 because of the Stokes shift, the overall iPSF will not be centered in between h 1 and h02 . Instead, the peak of the product h 1 h02 will move towards h02 . Although this shift as such is not problematic, it must be taken into consideration when designing the instrument. More specifically, for ISM microscopes in which the pixel reassignment process is performed all–optically in real time [74], this shift needs to be known before starting the measurement. The reconstruction for the ISM approach from Fig. 2.13 is performed digitally in post–processing and does not require this information beforehand. 42

2.2. INTENSITY FLUCTUATION IMAGING Excitation Detection iPSF iPSF

ISM iPSF

x

Figure 2.15: The ISM iPSF is in between the excitation and the detection iPSF and is less high and less wide than either iPSFs. The relative position of the ISM iPSF is called the reassignment factor and takes values between 0 (peak locations of ISM iPSF and excitation iPSF overlap) and 1 (peak locations of ISM iPSF and detection iPSF overlap). The reassignment factor is in this example 1/2 due to the absence of a Stokes shift.

2.2

Intensity fluctuation imaging

In addition to observing nanometer– and micrometer–sized structures, optical microscopy can be employed for quantitative analyses of samples. In FCS, for example, the temporal intensity fluctuations in a fluorescent sample are analyzed to obtain information on the process causing these fluctuations [75, 76]. Similarly, in the Coherent Correlation Spectroscopy (cCS) method presented in Chapters 3 and 4, the intensity trace from SHG NPs is studied. In this case, the process responsible for the fluctuations is the Brownian motion of the NPs into and out of the focal volume, possibly with a flow velocity superimposed.

This section provides a description of the fundamentals of FCS and cCS in the first part, with extensions to these techniques being illustrated in the second part. 43


2.2.1

Fluorescence correlation spectroscopy and coherence correlation spectroscopy

The principle of FCS/cCS for quantifying particle dynamics is illustrated by Fig. 2.16. Particles in the diffraction–limited volume of a focused laser beam produce fluorescence (FCS) or a higher harmonic signal (cCS). The random movement of the particles in the sample results in fluctuations δ I in the measured intensity trace. The Autocorrelation Function (ACF) calculated from the data set can be fitted to a theoretical model to obtain information on the translational diffusion coefficient, the flow properties, and the particle concentration. 3

Intensity [a.u.]

2.5

I(t)

2 1.5

1 0.5 0 0

2

4

6

8

10

Time [a.u.]

Figure 2.16: (Left) Particles diffusing through the volume created by a focused laser beam. (Right) The movement of the particles creates deviations δ I(t) from the mean intensity 〈 I 〉 over time. The horizontal line with the label 〈 I 〉 corresponds to the mean observed intensity over the complete trace. Importantly, the diffraction–limited focal volume is typically in the femtoliter range. The average number of particles residing simultaneously in the focal volume is evidently lower for a smaller volume. As a consequence, the relative intensity fluctuations caused by the movements of the particles become larger, which is beneficial in the presence of instrumental noise. The on/off behavior of the particles upon entering and exiting the focal volume as depicted in Fig. 2.16 and described at the beginning of this section is, of course, a simplification of the real situation. For a linear sample response and incoherent emission – a typical FCS experiment – the emission intensity from each particle is proportional to the iPSF value at the corresponding position. 44

2.2. INTENSITY FLUCTUATION IMAGING

Ignoring prefactors, the total observed intensity I(t) is then simply the sum of the individual signals:

Ñ

I(t) =

iPSF(x)c(x, t)d3 x.

(2.29)

The concentration variable c can be viewed as a space– and time–varying sum of Dirac delta functions. The iPSF must be approximated by a Gaussian function in order to find an analytical expression for the corresponding autocorrelation curve. The dimensions of the iPSF can be measured with immobile fluorescent microspheres, or calibrated in a reference measurement using a fluorescent dye with known diffusion properties. For nonlinear, coherent samples such as SHG NPs, the measured intensity must be derived from the amplitude (Eq. 2.12):

¯Ñ ¯2 ¯ ¯ ¡ ¢ q ¯ . I(t) = ¯¯ y, z)) exp − i κ z c(x, y, z, t)dxdydz (aPSF(x, q ¯

(2.30)

The parameter q describes the order of the scattering process (q = 2 for SHG, q = 3 for THG,...). The phase of a focused laser beam differs from a plane wave of the same frequency. This phenomenon is called the Gouy phase shift, after L. G. Gouy who first described the effect in 1890 [77]. The shift near the focal plane (z = 0) can be approximated by adding a linear phase factor in the propagation ¡ ¢ direction: exp − i κ q z . The fluctuations in the intensity are analyzed by calculating the ACF G(τ), defined as

G(τ) =

〈δ I(t)δ I(t + τ)〉 〈 I(t)〉2

=

〈 I(t)I(t + τ)〉 − 〈 I(t)〉2 〈 I(t)〉2

.

(2.31)

The brackets 〈·〉 indicate averaging over t. The variable δ I(t) holds the difference between I(t) and the mean intensity 〈 I(t)〉: 45


δ I(t) = I(t) − 〈 I(t)〉 .

(2.32)

The first part of the calculation of G(τ) is sketched in Fig. 2.17. δ I(t) is shifted over a lag time τ and the product δ I(t)δ I(t + τ) is computed in the interval where both functions are defined, colored green in Fig. 2.17. The average of this product is calculated and the result is normalized by dividing by the square of the mean intensity. This process is repeated for all relevant values of τ.

t

I(t)

τ

I(t-τ)

t

I(t)I(t-τ)

t

Figure 2.17: Calculation of the ACF. Note that shifting δ I(t) to the right yields δ I(t − τ), with a minus sign in the argument. However, because of the symmetry of the calculation, G(τ) = G(−τ). The direction of the shift does not play a role.

The analytical ACF for pure diffusion in 3 dimensions and incoherent processes is [78] 46


G(τ) =

q 3/ 2

. ¡ ¢q 〈 c〉 π3/2 4qD τ + ω20 4qD τ + z02

(2.33)

Here, D is the diffusion coefficient (units m2 /s) and 〈 c〉 is the average concentration (units /m3 ) of the particles. The width and the height of the Gaussian iPSF are given by ω0 and z0 , respectively. These parameters refer to the 1/e2 value of the one–photon iPSF. The parameter q automatically takes care of the quadratic or third power relationship with the excitation intensity for two– or three–photon fluorescence excitation. If the size of the iPSF is measured with multiphoton excitation, this effect must, however, be taken into account, see Fig. 2.18. 1

1-photon amplitude 1-photon intensity

Normalized PSF

0.8

2-photon intensity

0.6 0.4

1/e

0.2

1/e2 1/e4

0

0

-2

0

-

0

0

0

2

x

Figure 2.18: Definition of the lateral size ω0 of the PSF in Eq. 2.33. For one– photon excitation, ω0 is the 1/e2 value of the intensity. Consequently, for two– photon excitation, ω0 is the 1/e4 value. G(τ) is a continuously decreasing function, converging to zero for large lag times. The start value of the ACF, i.e G(0), is equal to

G(0) =

q 3/ 2 〈 c〉 π3/2 ω20 z0

47

=

1 1 = , 〈 c〉 Ve f f N

(2.34)


with Ve f f the so–called effective focal volume and N the average number of particles inside Ve f f . Small values of ω0 and z0 are desired since the resulting relative intensity fluctuations will be larger. Eq. 2.34 shows that the concentration of the particles is inversely proportional to G(0). The diffusion coefficient cannot be obtained from the starting value. Instead, this property is related to the time scale around which G reaches about half its initial value G(0). A lower diffusion coefficient shifts G to higher τ values and vice versa. The effect of the concentration and the diffusion coefficient are illustrated in Fig. 2.19. 0.2

D = 0.8 m2/s

0.1

0.05

0 10-4

D = 0.08 m2/s D = 8 m2/s

0.15

G( )

0.15

G( )

0.2

N=5 N = 10 N = 20

0.1

0.05

10-2

100

0

102

[s]

10-3

10-1

101

103

[s]

Figure 2.19: Effect of the particle concentration (left) and the diffusion coefficient (right) on the FCS curve. The parameters are ω0 = 680 nm, z0 = 5ω0 , q = 1. D = 0.8 µ m2 /s in the left panel and N = 5 in the right panel.

2.2.2

Image correlation spectroscopy

The word imaging in the title of Section 2.2 refers to the collection of spatial information, either by recording images with a camera or by scanning the illumination volume. Scanning FCS (S-FCS) was first introduced in 1976 to determine the molecular weight of fluorescently labeled DNA molecules, based on the average number of fluorophores in the observation volume [79]. In S-FCS, the sample or the illumination source is moving, often in a circular pattern. Provided that the movement is much faster than the diffusion, many statistically independent volumes are probed. In this type of measurement, the correlation function reveals a more accurate fluorophore concentration compared to FCS, particularly 48


in slow processes that would otherwise require long integration times [80]. Additionally, the scan movement reduces the exposure of the fluorophores to the excitation light, which limits photodegradation effects.

Although S-FCS collects spatio–temporal data, the measured intensity trace was initially only used to determine the concentration of macromolecules, while the effects of diffusion were considered negligible. For faster diffusion processes though, the temporal correlation intrinsically present in a continuous circular scan process can be exploited as well [81, 82]. The intensity data I(x, t) can be split into segments I x (t), with the index x representing the position along the scan path. This type of carpet analysis yields conventional FCS curves, from which the probe concentration and the diffusion coefficient can be calculated for all positions on the path, see Fig. 2.20.

Figure 2.20: Principle of S-FCS. Each point along the path results in an autocorrelation curve from which the diffusion coefficient and the particle concentration can be fitted.

In Image Correlation Spectroscopy (ICS), images of a stationary sample are correlated in space to quantify the distribution and the density of the fluorescent structures [83, 84]. A scanning microscope can be used if the sample dynamics are significantly slower than the scan process. Alternatively, all pixels may be recorded simultaneously by using a camera with a short exposure time.

The spatial ACF is defined similarly to Eq. 2.31, with the averaging now over x and y: 49


G(ρ x , ρ y ) = =

〈δ I(x, y)δ I(x + ρ x , y + ρ y )〉

(2.35)

〈 I(x, y)〉2 〈 I(x, y)I(x + ρ x , y + ρ y )〉 − 〈 I(x, y)〉2 〈 I(x, y)〉2

.

(2.36)

The analytical ACF is, under the same assumptions as before [85],

Ã ! q(ρ 2x + ρ 2y ) 1 G(ρ x , ρ y ) = exp − . N ω20

(2.37)

The concentration of the fluorescent structures can be obtained by fitting the data to the theoretical model, where N and ω0 are the fit parameters. Since ICS analyzes a stationary image, no information on the diffusion properties can be acquired. If the diffusion is slow enough, one can, however, record a sequence of images and analyze the temporal evolution in each pixel separately. This pixel–wise FCS method is called TICS. Obviously, the main advantage of TICS is the parallel sampling in hundreds of thousands of locations [86], significantly reducing the acquisition time needed compared to FCS. Unless performed in a spinning disk confocal microscope [86] or a total internal reflection microscope [87], the limited temporal resolution restricts TICS measurements to dynamics in the seconds to minutes range. Conventional FCS, on the other hand, probes the microsecond to millisecond range. The gap can be bridged by RICS, which provides information from the microsecond to the second timescale [88]. In RICS, the relatively slow movement of the excitation beam in a CLSM setup couples the spatial and the temporal correlation. The principle of RICS is illustrated in Fig. 2.21. Images are constructed by a conventional CLSM, which repeatedly scans the sample pixel by pixel and line by line. The measured intensity is now a function of space – different particles are observed at different locations – and time – the particles are moving during the scan process. The two variables are linked through the scan speed. Let the scan time per unit distance (units of [s/m]) in the horizontal and vertical 50


direction be τ p and τl , respectively. A lateral shift (ρ x , ρ y ) then corresponds to a lag time equal to

τ(ρ x , ρ y ) = ρ x τ p + ρ y τl .

(2.38)

If the lateral pixel size is defined as δ r and ξ and ψ are, respectively, the pixel and line number, the lag time can alternatively be expressed as

τ(ξ, ψ) = δ r ξτ p + δ r ψτl .

(2.39)

Figure 2.21: Principle of RICS. A scanning laser beam records the spatiotemporal intensity variations produced by particles diffusing into and out of the focal volume. The autocorrelation must take into account both the particle diffusion and the scan movement. Before describing this function, we first present the general Fluorescence Intensity Fluctuation Model (fIFM), which correlates any two points in 3D space and time [85]:

G(ρ , τ) =

Ã

q3/2

exp − q ¡ ¢q 〈 c〉 π3/2 4qD |τ| + ω20 4qD |τ| + z02 Ã ! (ρ z − v z τ)2 · exp − q . 4qD |τ| + z02 51

£ ¤! (ρ x − v x τ)2 + (ρ y − v y τ)2

4qD |τ| + ω20 (2.40)


The vector v = (v x , v y , v z ) describes any directed flow present in the sample. FCS and all aforementioned fluorescence variations can be analyzed using this model. As an example, G(ρ , τ) reduces to Eq. 2.33 for ρ = 0 and v = 0. Similarly, G((ρ x , ρ y , 0), 0) yields Eq. 2.37. Writing the spatial shifts as a function of the pixel size and plugging Eq. 2.39 into the fIFM produces the general RICS ACF. For ρ z = 0 and in the absence of flow, the ACF simplifies to

q 3/ 2

G(ξ, ψ) =

¡ ¢q 〈 c〉 π3/2 4qD |δ r ξτ p + δ r ψτl | + ω20 4qD |δ r ξτ p + δ r ψτl | + z02 Ã ! (δ r ξ)2 + (δ r ψ)2 · exp − q . (2.41) 4qD |δ r ξτ p + δ r ψτl | + ω20

Even in the presence of flow, the ACF shows inversion symmetry around the origin and the maximum value of G(ξ, ψ) is always found at (0, 0). The measurement parameters must be chosen carefully in a RICS experiment. The pixel size must be small enough in order to have sufficient oversampling of the PSF. A large pixel size will lead to few data points of the ACF above the noise level. Using the proper scan speed is crucial as well. When the pixel dwell time and the line scan time are too high, the ACF has dropped to virtually 0 already at ψ = 1 (and at ψ = −1) and no information can be extracted from the slow ψ–axis. On the other hand, the diffusion coefficient cannot be obtained from a very fast scan either. Setting τ p = τl = 0 in Eq. 2.41 to mimic fast scanning results in

G(ξ, ψ) =

q 3/ 2 〈 c〉 π3/2 ω20 z0

Ã

exp − q

(δ r ξ)2 + (δ r ψ)2 ω20

!

.

(2.42)

Provided that the size of the PSF is known, the only sample parameter that can be recovered from fitting the ACF is the particle concentration. This outcome is to be expected since fast scanning is formally equivalent to ICS. The same conclusion can be drawn when comparing Eq. 2.42 and Eq. 2.37, which are 52


identical. Fast scanning is, however, an elegant way to accurately determine the lateral size of the PSF. The value of ω0 can directly be derived from the width of the ACF. In a CLSM, the pixel dwell time and the line scan time can be chosen independently. For the Zeiss LSM 880, for example, the user can define the line scan time via the scan speed and the pixel dwell time via the number of pixels per line. In a typical RICS experiment, a sequence of images at a single field–of–view is recorded to obtain a statistically better–defined result, after which the ACF of each frame is calculated. No correlation will be found between consecutive images due to the relatively long frame times in a CLSM. The average ACF is fitted to the model of Eq. 2.40 which in addition to the diffusion coefficient also yields the flow properties and the particle concentration. A theoretical example of an ACF is given in the left panel of Fig. 2.22. The central line of the ACF in the fast axis direction G(ξ, ψ = 0) contains in general little information on the diffusion coefficient since the pixel dwell time is shorter than the diffusion time. Instead of calibrating ω0 with a fast scan, one can therefore fit ω0 from this line and use the resulting value to fit the diffusion coefficient from the other lines, keeping ω0 fixed at the previously found value. With this two–step analysis protocol, a single measurement is sufficient to measure the diffusion coefficient. No additional calibrations are needed, except for the PSF height z0 . However, as shown in Chapter 4, the ACF is not profoundly influenced by this parameter. The right panel of Fig. 2.22 shows G(ξ, ψ = 0) and the corresponding fit. RICS not only allows the measurement of the concentration and the diffusion coefficient of the particles but also directed motion, i.e. lateral flow superimposed on the random walk. Flow in the x–direction shifts the ACF peak location of each line l, defined as (ξ, ψ = l), parallel to the fast axis. The position of the maximum is roughly equal to the flow speed multiplied by l τl . Flow in the y– and z–direction also influences the shape of the ACF, but retrieving v y and v z is cumbersome since different flow values can produce comparable ACFs. Furthermore, a specific combination of the line scan time, the diffusion time 53

CHAPTER 2. THEORY AND METHODS (a)

(b)

0.3

= 0)

0.2

0.2

G( ,

G( ,

)

0.3

0.1

0.1

0 10 0 -10

-10

0

10

0 -10

0

10

Figure 2.22: (a) Example of a RICS ACF. The simulation parameters are ω0 = 680 nm, z0 = 5ω0 , q = 1, N = 3, δ r = 166 nm, τ x = 16.4 µ s, τl = 9.8 ms. The diffusion coefficient is 8.58 µ m2 /s, corresponding to particles with a diameter of 25 nm suspended in water at 20 ◦ C. (b) Cross section of the ACF (bullets) and fit (continuous line). The fit parameters are 〈 c〉 and ω0 . All other parameters are set to the simulation values. The exact values of 〈 c〉 and ω0 are recovered by the fit. When the diffusion coefficient is unknown but low enough, D = 0 may be used since the fast ξ–axis is only slightly influenced by the particle movement. The resulting fit values for this example deviate less than 0.2 % from the real values.

and the flow speed is required to be able to observe the latter parameter in the ACF. To estimate v y , for example, the diffusion time must be significantly larger than the line scan time in order to keep the correlation sufficiently high over multiple lines. Moreover, the scan speed in the y–direction should approach v y , as this results in the ACF being stretched in the ψ–direction, which leads to a more accurate estimate of v y . Examples of the effect of flow on the RICS ACF are presented in Fig. 2.23. Analyzing directed motion in the y– and z–direction with RICS is tricky, but flow in the x–direction can easily be recognized. RICS may thus be applied to study optical trapping of the particles by the scanning excitation beam since a laser power dependent flow is expected. A more thorough examination of 2D, or even 3D, directed motion is available through STICS [85]. In this extension of ICS, several images are taken at different time points at the same field–of–view. Each image is recorded quickly enough to not observe movement in a single frame. Correlating these images, however, provides information on the concentration, 54

2.2. INTENSITY FLUCTUATION IMAGING (a)

(b)

)

0.3

0.2

G( ,

G( ,

)

0.3

0.1 0

0.2 0.1 0

10

10

10

0 -10

10

0

0

-10

-10

(c)

0 -10

(d)

10

10 10

10

0

0 0 -10

0 -10

-10

-10

Figure 2.23: The effect of flow on the RICS ACF. (a) v x is equal to 0.3 % of the scan speed in the x–direction (v x = 30.4 µ m/s). All other simulation parameters are identical to the values used in Fig. 2.22. (b) v y is equal to 80 % of the scan speed in the y–direction (v y = 67.6 µ m/s). The pixel dwell time and the line scan time are 5 times shorter than in panel (a). (c, d) Top view of panels (a, b), respectively.

the diffusion coefficient and the lateral flow. A fast z–stack would theoretically also allow the flow in the z–direction to be measured. Consequently, STICS is a great tool to create flow vector maps by locally analyzing the directed motion. Many more implementations and variations of FCS have been developed throughout the years, such as image cross–correlation spectroscopy and particle ICS. Elaborate discussions of these methods are not the goal of this thesis and can be found elsewhere [66, 89]. All analytical expressions for the ACF described in this section (Eqs. 2.33, 2.34, 2.37, 2.40, 2.41, 2.42) were derived presuming that the radiation emitted by all 55


particles is incoherent, i.e. no constant phase difference between the amplitude fields is observed. However, this assumption is no longer valid for coherent imaging modalities such as SHG imaging, or even coherent ultrasound imaging. In this measurement technique, the observed intensity depends on the interference between the amplitude fields, as shown by Eq. 2.30. The corresponding ACF for the specific case of cCS was first calculated by Geissbuehler et al. [90]. Corrections to this model and extensions to all ICS variants were published by us in 2015 [91]. Due to the complexity of this work, a complete chapter of this thesis is devoted to this derivation, see Chapter 3 and Appendix A.

56

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3

C OHERENT INTENSITY FLUCTUATION MODEL FOR AUTOCORRELATION IMAGING SPECTROSCOPY WITH HIGHER HARMONIC GENERATING POINT SCATTERERS

–

A COMPREHENSIVE THEORETICAL STUDY

This chapter is based on Slenders E., vandeVen M., Hooyberghs J., Ameloot M. “Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating point scatterers – a comprehensive theoretical study”, Physical Chemistry Chemical Physics, 17, 2015.

CHAPTER 3. COHERENT INTENSITY FLUCTUATION MODEL

W

e present a general analytical model for the intensity fluctuation autocorrelation function for second and third harmonic generating point scatterers. Expressions are derived for a stationary laser beam

and for scanning beam configurations for specific correlation methodologies. We discuss free translational diffusion in both three and two dimensions. At low particle concentrations, the expressions for fluorescence are retrieved, while at high particle concentrations a rescaling of the function parameters is required for a stationary illumination beam, provided that the phase shift per unit length of the beam equals zero.

3.1

Introduction

FCS has been widely used for several decades to quantify ensemble dynamics [92, 93]. Applications on both the fundamental and applied level comprise the study of ligand binding to macromolecules [65], protein aggregation in the cell membrane [94], and molecular diffusion in solutions and living cells [95, 96]. Using laser scanning microscopy, the correlation spectroscopy technique was extended to account for both temporal and spatial correlations, which made it possible to determine slow membrane and cytoplasm dynamics [80, 82, 97–100], to quantify the cell surface receptor distribution [83], and to map motility and flow velocity vectors [85]. In FCS, information on the concentration and diffusion properties can be obtained by measuring the fluctuating emission intensity profile produced by the randomly moving fluorophores in the focal volume of the stationary laser beam [89]. Similarly, fluorescence fluctuation imaging in space and/or time comprises well–known methods such as TICS, STICS and RICS. In STICS [83, 85] microscopy images taken at a single region of interest are recorded repeatedly over a certain time span. These data are then correlated both in space and time, not only resulting in a translational diffusion coefficient value but also in the characterization of directed flow or motility present in the sample, enabling the construction of flow vector maps. Alternatively, in TICS, only the time correlation is considered for the various regions of the image [89]. The time information hidden in the motion of the scanning laser beam is explicitly used in RICS confocal measurements [98]. The dynamics of the moving particles determine 58

3.1. INTRODUCTION

the speeds selected for the scanning laser beam [88, 100, 101]. Even though fluorescence–based methods carry advantages such as molecular specificity, a good contrast and single molecule sensitivity [102], they are limited by several drawbacks: probes are sensitive to photobleaching and saturation [90, 102], which restricts the illumination intensity and complicates the time– consuming study of slow processes, and to intersystem crossing between excited singlet and triplet states, resulting in on/off–blinking [103]. Additionally, a background signal due to the autofluorescence of the environment may overwhelm the fluorescence signal. This effect is especially apparent in biological materials, such as tissue, serum, and blood [103] which contain a plethora of fluorescent molecules. To the benefit of both applications and fundamental research, this plethora of shortcomings can be overcome by using higher harmonic generating materials [34, 40, 53, 104–106]. Pantazis et al. [34] recently showed that tetragonal barium titanate (BaTiO3 ) nanomaterial produces an extremely stable and strong SHG signal in vivo. Liu et al. [103] made use of this same crystalline material in correlation spectroscopy experiments. Depending on the application, many other SHG active materials can be selected, such as KTiOPO4 [107, 108], ZnO [108], or KNbO3 [90, 108]. Numerous are the advantages in choosing the SHG approach over fluorescence– based techniques. The instantaneous SHG light has a high intensity, caused by the coherent nature of this nonlinear scattering process [105]. SHG is typically not produced by the environment surrounding the nanoparticle, thereby creating an optimal contrast in the recorded image. The absence of photobleaching makes long–term imaging feasible, without degradation effects. Moreover, a flexible choice in the laser wavelength is combined with a narrow and well–defined wavelength band of the SHG signal. As only a small amount of the incident light is absorbed by the SHG active particles [109], they do not heat up as would be the case with metal nanoparticles [110]. This is of particular interest when imaging delicate biological materials. Above all, SHG imaging makes label–free microscopy feasible, thus circumventing all limitations accompanying the use of probes [34, 105, 111]. However, the critical component is the availability of non–clustering, uniform, non–toxic nanoparticles. 59


The SHG coherent scattering process can be described by expressing the induced sample polarization P(t) as a power series in the applied electric field strength vector E(t) under the assumption that the medium responds instantaneously [41, 112]:

h i P(t) = ²0 χ(1) E(t) + χ(2) E 2 (t) + χ(3) E 3 (t) + ... ,

(3.1)

where ²0 is the vacuum permittivity, χ(1) is the scalar linear susceptibility, χ(2) and χ(3) are respectively second and third rank susceptibility tensors, E 2 (t) can be represented as a column matrix containing all 9 permutations of E i E j and E 3 (t) all 27 permutations of E i E j E k with E i , E j , and E k the x, y, and z component of E(t). The second and third term give rise to respectively a contribution of frequency 2ω (SHG) and 3ω (THG) under a sufficiently strong electric field of frequency ω [41]. For infinite centrosymmetric specimens, i.e. materials that exhibit perfect inversion symmetry, all χ(2n) terms with n ∈ N in Eq. 3.1 vanish. Hence a monocrystal or other type of periodic structure must be non–centrosymmetric to produce a bulk SHG signal. For THG there is no such restriction. In contrast to fluorescence, the emitted light produced by SHG and THG is coherent, with a possible phase mismatch between the photons, e.g. caused by the Gouy shift in a focused laser beam [113]. Several papers describe the signal emanating from SHG samples as observed through a multiphoton microscope [53, 113–115], but the interpretation of the ACF of SHG/THG intensity fluctuations has so far been limited to a non–scanning laser beam [90, 116]. Very recently, rotational motion of nanodoublers has been observed in a cellular environment [117]. Progress has been made in expanding theoretical aspects of SHG emission such as multipole contributions [118] and signals from ensembles of irregularly shaped nanoparticles [119]. These building blocks will help to describe the complex dynamic behavior of possibly polydisperse, aggregating and corona protein covered nanoparticles in a crowded intracellular environment as observed by a strongly focused laser beam. 60

3.1. INTRODUCTION

Here, we will partially rely on the work by Geissbuehler et al. [90] to develop a general Coherent Intensity Fluctuation Model (cIFM). The cIFM will allow us to analytically describe the coherent counterparts of the fluorescence–based methods FCS, TICS, STICS, and RICS. A lowercase c in the acronyms stresses the coherent behavior of this process: cCS, Coherent Temporal Image Correlation Spectroscopy (cTICS), Coherent Spatiotemporal Image Correlation Spectroscopy (cSTICS) and Coherent Raster Image Correlation Spectroscopy (cRICS), pronounced as e.g. cohSTICS.

In our model, the spatial distribution of the illumination amplitude is approximated by a 3D Gaussian function, and the Gouy phase shift across the focal volume in the direction of the beam is approximated by a linear function. Although analysis of the rotational diffusion of SHG particles has been described before [117, 120], our representation does not account for the orientational dependence of the SHG signal. The theory is thus restricted to measurements in which the rotational dynamics are averaged out and uncoupled from the spatial movement, e.g. in a low viscosity medium. The point–particle assumption also restricts the theory to (nano)particles that are small enough to not feel a gradient in the illumination intensity.

In the following, we develop first the expressions for the general cIFM. This will be the theoretical framework from which the analytical expressions of the ACFs of all coherent autocorrelation techniques described above will be derived. The comprehensive modular way in which the expressions are written allows the straightforward derivation of the formulas for special cases, such as the low and high particle concentration limit and 2D diffusion. An in–depth comparison with the fluorescence expressions is made. To gain an understanding of the influence of noise on the parameter retrieval in the fitting procedure of experimental data, simulated autocorrelation curves for a steady stationary illumination beam setup case are presented. This helps to ascertain the numerical stability of solutions against the appearance of parasitic local minima in the parameter optimization process that could lead to ambiguous conclusions on the obtained parameter values. 61


3.2

Theory

Consider a system of randomly diffusing non–interacting point particles illuminated by a Gaussian laser beam. Each particle scatters light at twice and three times the laser light frequency, with the electric field amplitude depending on the particle position. Let I q (r, t) be the total detected far field intensity induced by all particles when position r is imaged at time t. The index q reflects the order of the higher harmonic that is produced (q = 2 in SHG and q = 3 in THG). In a cSTICS, cRICS, cTICS or cCS measurement, the correlation between the intensity fluctuations in the microscopy images at different positions and/or time points can be described by the normalized ACF G(ρ , t) [121]:

G(ρ , τ) =

〈δ I q (r 0 , t)δ I q (r 0 + ρ , t + τ)〉 〈 I q (r 0 , t)〉2

,

(3.2)

where δ I q (r 0 , t) is the fluctuating difference between the detected intensity at position r 0 at time t and the mean intensity calculated over all positions and all time points. The brackets 〈·〉 represent averaging, which, depending on the experimental configuration and data analysis method, can be temporal (cTICS and cCS) or spatiotemporal (cSTICS and cRICS). The quantities ρ and τ respectively describe the spatial and temporal lag between two data points that are considered in the calculation of the ACF. Eq. 3.2 can be written in an equivalent, but computationally less demanding form:

G(ρ , τ) =

〈 I q (r 0 , t)I q (r 0 + ρ , t + τ)〉 − 〈 I q (r 0 , t)〉2 〈 I q (r 0 , t)〉2

.

(3.3)

The calculation of the intensity I q (r, t) is based on the assumption of a Gaussian focal volume with 1/e2 beam waist ω0 in the radial direction and z0 in the axial direction. The axial Gouy phase shift is approximated to be linear, i.e. a constant 62

3.3. RESULTS

shift per unit length, κ q [90]. The amplitude and phase of the electric field of the focused laser beam are then given by Eq. 3.4 [112]:

Ã

A q (r) = A q0 exp −

x 2 + y2 ω20 /q

!

Ã

exp −

z2 z02 /q

! ¡ ¢ exp − i κ q z ,

(3.4)

with A q0 the maximum electric field amplitude produced by the light source. In this coordinate system, the x– and y–axis are within the focal plane and the z–axis is along the laser beam propagation direction, with the focus of the laser beam at x = 0, y = 0, z = 0. The intensity observed for a laser beam at position r 0 is then calculated as [122]

¯2 ¯ ¯ ¯Z ¯ ¯ ( q) ¯2 ¯¯ I q (r 0 , t) = ¯χ ¯ ¯ A q (r − r 0 )c(r, t)dV ¯¯ .

(3.5)

Here, χ( q) is the dielectric susceptibility tensor and dV is the shorthand notation for the cubic volume element dxd ydz. The assumed infinitely small particles are represented by a position and time–dependent particle density function c(r, t), which is a sum of Dirac delta functions [95]. Since A q (r) is an even function in x and y and because of the symmetry in the z–direction after taking the squared modulus to calculate the intensity, the integral can be interpreted as the convolution of A q (r) with c(r, t).

3.3

Results

The comprehensive details of the ACF for point scattering particles exhibiting free translational diffusion are given in Appendix A. The general solution to the cIFM is a sum of 29 terms of which 12 cancel out and 8 terms are zero for symmetry reasons. The resulting 9 terms are split into 3 groups, denoted with the letters A, B and C to emphasize their similar origin:

G(ρ , τ) = (A3 + A4 + A5 + A7 + B6 + B7 + B9 + C5 + C7)/G N , 63

(3.6)


where G N is the normalization factor, 〈 I q (r 0 , t)〉2 as in Eq. 3.2. All terms of the numerator are functions of the system parameters ω0 , z0 and κ q , and the sample parameters N, the average number of particles in the

focal volume, as well as D, the translational diffusion coefficient. The spatial evolution of G is plotted in Fig. 3.1 for typical parameter values. The peak height is directly related to the concentration of the scatterers; the higher the particle density, the lower G(0, t). The peak width of G decreases with an increasing diffusion coefficient value and the height drops for increasing time lags in a similar way as for 1PE [89], although the absolute values can differ significantly [123]. This fact proves that one cannot simply use the fluorescence expressions to fit experimental data from SHG particles to obtain information about the concentration and the diffusion rate. In the following, we briefly list modifications to be made to the cIFM for the specific approaches listed above. We also explore the low and high particle concentration limits. Attention is paid to the specific case of 2D diffusion as well.

3.3.1

cSTICS

To adapt the general cIFM for cSTICS type measurements, one must discretize the spatial variables in the expressions to simulate the pixel structure of a digital image. This includes one substitution in the cIFM: ρ = (ρ x , ρ y , ρ z ) = (δ r ξ, δ r ψ, δ sφ) with δ r and δ s the pixel size in the lateral and axial direction and ξ, ψ and φ the pixel number in the x–, y–, and z–direction, respectively.

3.3.2

cRICS

In cRICS, a laser beam scans each pixel sequentially in a raster pattern to obtain a complete image. This results in a definite relation between the spatial and temporal part of the equation, depending on the experimental settings: G(ρ , τ) becomes now an implicit function of time only, G(τ(ρ )), with τ(ρ ) = ρ x τ x + ρ y τ y + ρ z τ z = ρ · τ. Everywhere in Eq. 3.6, the substitution τ = ρ · τ must be

made, with τ a three–dimensional constant vector containing respectively the pixel dwell time, the line scan time and the frame time (units of time/length). Consider as an example a typical 2D frame scan of 1024x1024 pixels with a field of view of 300x300 µ m2 and with a scan speed of 15 seconds for a complete 64

3.3. RESULTS

image. This is about 14.3 µ s/pixel, 14.6 ms/line and 15 s/frame, or equivalently, 48.8 s/m in the x–direction, 49.8e3 s/m in the y–direction and no z–direction scan time. The vector τ is then (48.8, 49.8e3, 0).

3.3.3

cTICS and cCS

For a steady laser beam, the spatial information can be omitted from the cIFM (ρ = 0) resulting in a much more compact ACF G q (τ). Evidently, the same expression can be used in cTICS. In Fig. 3.2 a comparison with the corresponding fluorescence expression for the same parameter values is plotted, indicating that the difference between the two techniques can be significant. Similarly to Fig. 3.1, one can observe the effect of the coherence of the SHG signal by comparing the SHG and the fluorescence curve. Geissbuehler et al. [90] directly derived a formula for this technique, but, as shown in this same Fig. 3.2, our results are different. This discrepancy is caused by the omission of the B and C labeled terms and an additional term in the denominator in the cited article.

3.3.4

Diffusion with flow

The cIFM of Eq. 3.6 can readily be adjusted for diffusion with flow. The approach taken in Appendix A can be intuitively understood as follows. Consider a 1– dimensional system of particles freely diffusing in the x–direction. The ACF G(ρ x ) then relates each point x with the point x + ρ x . On average, the distance between the beam position at x + ρ x and the particles that were imaged at position x is equal to ρ x . However, if there is a flow component v x present, this distance decreases by an amount of v x τ with τ the time lag between the imaging of the two points. An analogous argument can be made in 3 dimensions, leading to the following substitutions for each component of ρ in Eq. 3.6: ρ x → ρ x − v x τ, ρ y → ρ y − v y τ and ρ z → ρ z − v z τ.

65


SHG

Eq. 6

Fluorescence

0.4 0.2 40

0.2 40 0 0 20 −20 −20 ρy [µm] −40 −40 ρx [µm]

0

5

(d)

G

15

20

Fluorescence

0.02 0.01

20

40 0 0 20 −20 −20 ρ [µm] −40 −40 ρ [µm] y

0

−3

8

(e)

6

0

5

10 ρx [µm]

15

20

−3

x 10

x 10

(f)

SHGEq. 6

6

Fluorescence

G

4 2

40

10 ρx [µm]

SHGEq. 6

0.03

x

G

0

0.04

0.03 0.02 0.01 40

0.4

20

(c) G

(b)

0.6 G

G

0.8

(a)

0.6

4 2

20

20 40

0 −20 −20 0 ρy [µm] −40 −40 ρx [µm]

0

0

5

10 ρx [µm]

15

20

Figure 3.1: Plots of the ACF with respect to the lateral spatial shift ρ x and ρ y in a cSTICS simulation for time lags τ = 1 s (a)–(b), τ = 10 s (c)–(d) and τ = 30 s (e)–(f). The parameter values are ω0 = 2.7 µ m, z0 = 54 µ m, N = 10, D = 0.5 µ m2 /s and κ q = 0.3276 µ m−1 , similarly to the value used in [90]. The left panels show 3D plots of the temporal evolution of the SHG ACF. In the right panels the ACF cross section ρ y = 0 is plotted, as well as a comparison with the corresponding p fluorescence ACF. Since the SHG focal volume is a factor of 2 smaller in all directions comparedp to 1PE, thepbeam parameters for the fluorescence curves were adjusted to ω0 / 2 and z0 / 2 to obtain the same focal volume. The same figure with κ q = 0 is plotted in Appendix A for comparison.

66

3.3. RESULTS

0.5 A5, C5 A7, C7 B9

ACF terms

0.4 0.3 0.2 0.1

(a)

0 −2 10

0

2

10

4

10

10

−22

1.2

x 10

A3, B7 A4 B6

ACF terms

1 0.8 0.6 0.4 0.2 0 −2 10

(b) 0

2

10

4

10

10

3 SHGLIT SHGEq. 6

2 G(τ)

Fluor.

1 (c)

0 −2 10

0

10

2

τ [s]

10

4

10

Figure 3.2: Plots of the ACF with respect to the temporal shift, using the same parameter values as in Fig. 3.1. All nine terms of Eq. 3.6 that contribute to the ACF curve are plotted (a–b), as well as the total ACF, a comparison with the literature model used [90] (SHGLIT ) and the fluorescence expression (Fluor.) in (c). Note that for these parameter values, there is a huge difference in the order of magnitude between the terms of (a) and (b); the latter group can safely be ignored in this case for the total ACF calculation.

67


3.3.5

Low particle concentration limit

It is particularly interesting to investigate the behavior of Eq. 3.6 in the limit of a very low particle concentration, where the resulting expression will not depend on the phase shift per unit length κ q since the phase information is not relevant. For N ¿ 1 the only terms that remain are the ones containing the smallest exponent of N, i.e. A7, B9, and C7. Hence the autocorrelation is reduced to

G(ρ , τ) = (A7 + B9 + C7)/G 0N ,

(3.7)

with G 0N = N 2 /8. The full expression for 3D diffusion is µ ¡ 2 2¢ ¶ q ρ +ρ qρ 2 exp − 4 qDxτ+ωy 2 − 4 qD τz+ z2 0 0 . G(ρ , τ) = s ³ ´ 4qD τ 4 qD τ N ω2 + 1 +1 0 z02

(3.8)

Notice that the parameter κ q is – as expected – absent in the equation. Indeed, when N is small, the probability of multiple scatterers simultaneously being located inside the illumination volume is negligible. The coherent nature, and consequently the phase information of the scattered light, becomes irrelevant. Eq. 3.8 is the same equation as obtained in the fluorescence intensity fluctuation model. Evidently then, one can find the expressions for the several correlation spectroscopy methodologies by using the appropriate substitutions. For q = 1, i.e. one–photon illumination, ρ x = δ r ξ − v x τ, ρ y = δ r ψ − v y τ and ρ z = δ sφ − v z τ, Eq. 3.8 is the exact same equation as the STICS ACF [85], with δ r, δ s, ξ, ψ and φ as defined earlier. The spatial and temporal variables ρ and τ can be coupled as before with the substitution τ = ρ · τ to obtain the RICS expression. Evaluating Eq. 3.8 for a stationary beam (ρ = 0) yields the FCS expression for free diffusion and the substitutions ρ x = v x τ, ρ y = v y τ and ρ z = v z τ can be used as before to study diffusion with flow. Note that the minus signs can be omitted here since only the squared values appear in Eq. 3.8. All results in this paragraph apply to two–photon excitation fluorescence as well by substitution of q = 2. 68

3.3. RESULTS

These results prove that for very dilute suspensions, there is essentially no difference between the signal obtained from fluorescent emitters and higher harmonic generating scatterers. The simulated graphs of Fig. 3.3 show that for N < 0.1 the fluorescence autocorrelation curve deviates less than 10 % from the SHG curve. For larger values of N, one must use the SHG expressions, since the difference with the fluorescence formula will become too large to get reliable fit results, see Fig. 3.3 (c).

1000

15 SHGEq. 6

800

SHGEq. 6

10

G(τ)

600 400 200

Fluor.∗

Fluor.

5 (a)

0 −2 10

N = 0.001 0

2

10

10

(d) 4

10

15

0 −2 10

N = 0.1 0

2

10

10

4

10

1.5 SHGEq. 6

SHGEq. 6 Fluor.∗

Fluor.

1

G(τ)

10

5

0.5 (b)

0 −2 10

N = 0.1 0

2

10

10

(e) 4

10

2

0 −2 10

N=1 0

2

10

10

0.2 SHGEq. 6

G(τ)

SHGEq. 6

Fluor.

1.5

Fluor.∗

0.15

1

0.1

0.5

0.05 (c)

0 −2 10

4

10

N=1 0

10

2

τ [s]

10

(f) 4

10

0 −2 10

N = 10 0

10

2

τ [s]

10

4

10

Figure 3.3: Comparison between the SHG and fluorescence autocorrelation functions. The left graphs indicate the low particle limit for the SHG (κ q = 0.3276 µ m−1 ) and the fluorescence expressions using the same parameter values as in the legend of Fig. 3.1. The graphs on the right compare the high particle limit for the SHG (κ q = 0 µ m−1 ) and fluorescence (Fluor.∗ ) expressions, calculated p with half the diffusion coefficient (D/2) and a lower particle concentration (N/ 2 ), as denoted by the asterisk. One can readily observe the convergence of the SHG and fluorescence expressions in both limits. 69


3.3.6

High particle concentration limit

When evaluating Eq. 3.6 in the limit of a large value for N, the only leftover term in the numerator is A3:

G(ρ , τ) =

A3 , G 00N

(3.9)

with G 00N an adjusted normalization factor, dependent on particle concentration, z0 , κ q , and q. In a non–scanning system with a negligibly low Gouy phase factor value, this simplifies to p 2 G(τ) = N

N

³

2 qD τ ω20

+1

1 s ´ 2qD τ z02

.

(3.10)

+1

This is formally equivalent to the fluorescence expression under one–photon p excitation when substituting q = 1, N = 2 NF and D = 2D F , where the index F denotes the corresponding parameter for the fluorescent case. It can be noted that this simple rescaling cannot be used for the scanning implementations.

3.3.7

2D diffusion

The full expressions of all terms of the cIFM are written in such a way that one can straightforwardly retrieve from which integration each factor is coming. This allows one to obtain the formulas for a 2D system in a convenient way. Assume in this case that the excitation beam is perpendicular to the 2D movement of the particles. Now, one can simply remove all factors in brackets and all terms in exponents that contain z0 . The result is a sum of A terms only. Gassin et al. [116] derived directly the 2D ACF, but, unlike our expression, the proposed equation does not converge to the fluorescence model in the low particle limit.

3.3.8

Sensitivity to noise for parameter retrieval

In a typical autocorrelation spectroscopy experiment, the 1/e2 beam waist in the lateral direction ω0 and in the axial direction z0 are known parameters and kept 70

3.3. RESULTS

constant when the diffusion coefficient D and the particle concentration c are fitted. In order to check the fit stability of the parameter retrieval process for SHG/THG, several computer simulations for 3D diffusion (see Appendix A) were performed using the theoretical autocorrelation expression for cCS and typical experimental settings. Random noise was added to the theoretical curve and the resulting data were then fitted with the analytical equation. The starting values for the concentration and the translational diffusion fit parameters c and D were randomly chosen between 1/10 and 10 times the original value. This process was repeated 1000 times for each noise level. Fig. 3.4 shows the results. One can immediately conclude that – although the spread in the retrieved values increases with the noise level – the fit procedure will on average retrieve the original value of c and D. When κ q (Eq. 3.4) is left as a freely adjustable fit parameter, however, the additional degree of freedom creates a high probability of ending up in a local minimum far away from the set values, as illustrated in Appendix A. We therefore recommend to estimate κ q beforehand [123] from the known optical configuration and keep this parameter fixed during the fitting procedure.

71


(a)

0.16

2

Fitted D [µm /s]

0.18

0.14 0.12 0.1 0.08 0.06

(b)

3

Fitted c [/µm ]

0.6 0.55 0.5 0.45 0.4 0

0.02 0.04 Noise level a

Figure 3.4: 2D histograms of the fit results obtained by fitting 1000 simulated ACFs for 21 noise levels using the following parameter values: ω0 = 0.32 µ m, z0 = 0.982 µ m, c = 0.505 µ m−3 , D = 0.1 µ m2 /s and κ q = 0.249 µ m−1 . The pixel color represents the number of fits that ended up in that voxel (black = 0, white = 1000). The black dashed line indicates the simulation value. In a simultaneous fit of the diffusion coefficient (a) and the concentration (b), both parameters reproduce the exact value for a noiseless ACF. The spread in the recovered values increases with the noise level, but due to the symmetry, it is possible to average the results over multiple data sets.

72

3.4. CONCLUSIONS

3.4

Conclusions

The numerous shortcomings of FCS and fluorescence–based image correlation spectroscopy methods can be overcome by using SHG and THG materials. However, the fluorescence theory does not account for the coherent aspect of this scattering phenomenon. We show that the recently published restricted SHG and THG derivations should be expanded and corrected. In the next chapter, these theoretical observations will be validated on model systems in an experimental setup.

73

HAPTER

C

4

I MAGE CORRELATION SPECTROSCOPY WITH SECOND HARMONIC GENERATING NANOPARTICLES IN SUSPENSION AND IN CELLS

This chapter is based on Slenders E., Bové H., Urbain M., Mugnier Y., Sonay A. Y., Pantazis P., Bonacina L., Vanden Berghe P., vandeVen M., Ameloot M. “Image correlation spectroscopy with second harmonic generating nanoparticles in suspension and in cells”, The Journal of Physical Chemistry Letters, 9, 2018.

CHAPTER 4. ICS WITH SHG NANOPARTICLES...

T

he absence of photobleaching, blinking, and saturation combined with a high contrast provides unique advantages of higher–harmonic generating nanoparticles over fluorescent probes, allowing for prolonged

correlation spectroscopy studies. We apply the coherent intensity fluctuation model derived for spectroscopy analyses to study the mobility of second harmonic generating nanoparticles. A concise protocol is presented for quantifying the diffusion coefficient from a single spectroscopy measurement without the need for separate point–spread–function calibrations. The technique’s applicability is illustrated on nominally 56 nm LiNbO3 nanoparticles. We perform label–free raster image correlation spectroscopy imaging in aqueous suspension and spatiotemporal image correlation spectroscopy in A549 human lung carcinoma cells. In good agreement with the expected theoretical result based on the Stokes–Einstein equation, the measured diffusion coefficient in water at room temperature is (7.5 ± 0.3) µ m2 /s. Analyzing the same data set with the expressions for incoherent fluorescence yields (12 ± 4) µ m2 /s. The diffusion coefficient in the cells is more than 103 times lower, and heterogeneous, with an average of (3.7 ± 1.5) x 10−3 µ m2 /s.

4.1

Introduction

FCS has been successfully applied to numerous systems since its first introduction several decades ago [64, 65]. In particular, FCS has been used to study the molecular translational and rotational diffusion properties in solutions and living cells [95, 96, 124–126]. In FCS, quantitative information about the dynamics is derived from the temporal fluorescence intensity fluctuations produced by the random movement of fluorophores into and out of the diffraction limited volume of a focused illumination beam. Many variations on this principle exist. S-FCS allows measuring slower diffusion rates while reducing photobleaching [79–81]. FCS in combination with 2PE was developed to measure protein aggregation [97] and to probe the mobility of beads in the intracellular environment [94]. In ICS, fluctuations in two– or three–dimensional space are analyzed to quantify the aggregation and the average number of stationary or slowly moving fluorescently labeled structures [66, 83]. Both spatial and temporal intensity information can be combined in RICS [98, 127, 128] and in STICS [55, 85, 89, 129]. 76

4.1. INTRODUCTION

RICS is a variation on S-FCS in which the speed of the moving excitation volume in a laser scanning microscope is explicitly used to resolve shorter time scale dynamics than covered by STICS. STICS analyzes the spatial and temporal lags in a series of images collected with short acquisition times. This technique allows not only the measurement of the diffusion coefficient but also the mapping of flow velocities in a wide dynamic range. However, fluorescence based methods carry several disadvantages. Long–term studies of both slow and fast processes are impeded, as fluorophores are sensitive to photobleaching, blinking and saturation [34, 35, 90, 102]. In addition, autofluorescence of the environment, which is in particular problematic for imaging in cells and tissues [130], further complicates the use of fluorescent probes. These drawbacks are not, or at least a lot less, present in SHG imaging. SHG is a nonlinear scattering process, produced in the bulk of non–centrosymmetric crystal structures, such as BaTiO3 , LiNbO3 , ZnO and BiFeO3 [34, 108, 131]. The second harmonic signal is extremely stable and strong [34], providing a high contrast in samples that are not SHG active [132]. Harmonic NPs, i.e. higher harmonic generating NPs, are therefore ideal for long–term dynamics studies in complex biological specimens [34, 54, 133, 134]. In addition to harmonic NPs being employed as optically superior labels, investigating interactions between NPs and human cells is itself important, for example, in nanomaterial safety studies [55, 108]. The coherent nature of SHG requires a different model for analyzing the observed intensity fluctuations. Geissbuehler et al. presented the FCS variant with higher harmonic generating NPs circulating through a flow cell, which they termed nonlinear correlation spectroscopy, and derived the corresponding equations for interpreting the data [90]. This model was later extended to a general cIFM [91]. cIFM comprises a set of formulas describing the intensity correlation between any two points in space and time assuming free diffusion of the particles, with or without flow superimposed. Using for each technique the appropriate substitution, cIFM can be employed for the coherent counterparts of fluorescence–based correlation spectroscopies FCS, TICS, RICS, and STICS, 77


which were named cCS, cTICS, cRICS, and cSTICS, respectively. The prefix c, pronounced as coh, stresses the coherent aspect of the scattering process. Here, we verify the cIFM by performing cRICS measurements on SHG active LiNbO3 and BaTiO3 NPs suspended in water and in a water–glycerol mixture. We present a concise protocol for extracting the diffusion coefficient from a single measurement without the need for separate PSF calibrations. cSTICS is demonstrated in live adenocarcinomic human alveolar basal epithelial cells (A549 cell line) to illustrate the potential of dynamic SHG correlation spectroscopy measurements in livings cells with biocompatible [135] NPs. Quantitative characterization of the mobility of NPs within living cells and cell organelles allows gaining insight into the complexity of NP transport [117, 136].

4.2 4.2.1

Materials and methods Harmonic nanoparticles

Samples of BaTiO3 harmonic NPs of 50 nm were prepared according to the protocol described in Sugiyama et al. [137]. Phase–pure LiNbO3 NPs were manufactured according to the protocol described by Mohanty et al. [138] and then suspended in deionized water. Measurements on 200 nm pore filtered suspensions (Filtropur S 0.2, Sarstedt, Nümbrecht, Germany) with NP tracking analysis showed that more than 50 % of the particles have a diameter between 45 nm and 65 nm, with a maximum at 56 nm, see Fig. 4.1. The particles produce a bright and illumination polarization dependent SHG signal, as illustrated by Fig. 4.2 and 4.3. Polarization–SHG measurements were performed with a Zeiss LSM 510 META (Carl Zeiss, Jena, Germany) mounted on an Axiovert 200M. A femtosecond pulsed laser (Mai Tai DeepSee, Spectra–Physics Inc., Santa Clara, USA) tuned to a central wavelength of 810 nm with an average power of about 100 mW on the stage (measured with a thermal power sensor S175C, ThorLabs, Dachau/Munich, Germany) was used for two–photon excitation. The IR radiation was focused by a Plan–Apochromat 20x/0.75 objective after passing through a homebuilt system containing a rotatable Half–Wave Plate (HWP) and Quarter–Wave Plate (QWP). The orientation of the HWP was automatically controlled with stepper motors (Trinamic PD–110–42, Hamburg, Germany) to 78

4.2. MATERIALS AND METHODS

make a series of images with different orientations of the linearly polarized laser light, see Fig. 4.3. The SHG signal was collected in forward mode using a condenser lens. An FT442 nm beam splitter and a narrow bandpass filter BP400 − 410 nm were installed to block the illumination light and to select the SHG signal. For each particle, the pixel values in a small region comprising the

Relative particle concentration

particle were summed. 1.2 1 0.8 0.6 0.4 0.2 0 0

50

100

150

200

250

300

Diameter [nm]

Figure 4.1: Distribution of the diameter of the LiNbO3 NPs, measured with a NanoSight NS300 (Malvern Panalytical, Almelo, the Netherlands) NP tracking analysis device. Average over 5 x 60 seconds of measurement time, sCMOS camera at 25 frames per second, green laser (532 nm), slider gain 366, 5 x 1498 frames. The gray area indicates the standard error of the mean.

4.2.2

Measurements in suspension

For cRICS measurements, the LiNbO3 and BaTiO3 stock concentrations of 0.5 mg/mL and 1 mg/mL, respectively, were diluted a 100 times in Milli–Q ultrapure water (Merck Millipore, Overijse, Belgium). The suspension was sonicated for 15 minutes in an ultrasound water bath (Elmasonic S 40, 140 W, Elma Schmidbauer GmbH, Singen, Germany) and poured using a syringe through a 200 nm filter (Filtropur S 0.2, Sarstedt, Nümbrecht, Germany). An aliquot of 7 µL was transferred into a well created by mounting a spacer (Grace Bio–Labs SecureSeal imaging spacer, Sigma–Aldrich, St. Louis, USA, diameter 9 mm, height 0.12 mm) onto a microscope slide. The well was sealed by a cover slip. cRICS experiments with LiNbO3 were performed at room temperature using a Zeiss LSM 880 (Carl Zeiss, Jena, Germany) mounted on an Axio Observer frame. 79


Average intensity [a.u.]

30 28 26 24 22 0

100

200

300

Angle polarization plane [°]

Figure 4.2: Illustration of the cos4 dependence of the SHG intensity as a function of the orientation of the illumination polarization plane for three LiNbO3 NPs. The NPs were fixed onto a cover slip by air–drying a droplet of the suspension. Angles are defined as counterclockwise rotations with the zero angle being along the horizontal. The continuous lines show a cos4 fit. (a)

(b)

Figure 4.3: (a) Illustration of the SHG intensity as a function of the orientation of the illumination polarization plane for a fixed LiNbO3 NP. The polarization plane was rotated in steps of 20 ◦ . Scale bar 1 µ m. See the caption of Fig. 4.2 for more details on the experimental setup. (b) Scanning electron microscopy image of the same sample, showing three NPs. Scale bar 50 nm.

A Mai Tai DeepSee laser tuned to a central wavelength of 810 nm and with an average power of about 83 mW at the stage was used for two–photon excitation. The laser power was set to the minimum value providing a good signal–to–noise ratio. The IR radiation was focused by a 20x/0.8 objective (Plan–Apochromat 20x/0.8 M27) after passing through a homebuilt system containing an automated rotatable HWP and QWP combination. The orientation of the wave plates was tuned to obtain circularly polarized light at the stage. The SHG signal was 80


collected in backward mode using the same objective. A broad bandpass filter LBF 355/690+(R), a short pass dichroic filter FT442 nm and a narrow band pass filter BP400 − 410 nm, respectively, were used to completely block the illumination light and to select the SHG signal. One detector element from the non–descanned BiG.2 detection system was employed in photon counting mode.

Suspension measurements were repeated several times for different scan speeds. A single measurement consisted of a time series of at least 50 frames for the slowest scan speed. To compensate for the lower signal–to–noise ratio at shorter pixel dwell times, the number of recorded frames was increased for faster scan speeds, resulting in a comparable overall acquisition time, see Table 4.1 for further experiment detail. At the highest scan speed, about 2000 frames are required in a single experiment. Table 4.1: LSM 880 instrumental settings for the cRICS measurements. Pixel size 166 nm, 256 x 256 pixels per image. The beam waist is extracted from measurements 6–8, the diffusion coefficient from measurements 5–8. Measurement number 1 2 3 4 5 6 7 8

Scan speed [µ m/s] 936 1267 2534 5068 10135 20270 40540 54054

Dwell time [µ s] 177 131 65.5 32.8 16.4 8.19 4.10 3.07

Number of frames 50 100 150 200 400 800 1600 2000

Total acquisition time [minutes] 23 33 25 17 17 17 17 16

A RICS control experiment was performed with fluorescent carboxylated polystyrene beads (FluoSpheresT M , ex/em 350/440, Invitrogen, Thermo Fisher Scientific, Merelbeke, Belgium) with an average diameter of 100 nm. Before a measurement, the sample was diluted 10,000 times in ultrapure water (Milli–Q) and sonicated for 5 minutes in the aforementioned ultrasound water bath sonicator. The same experimental settings as for cRICS were used, apart from the fluorescence detection, for which a BP450 − 650 nm filter was employed, and the average laser power, which was 92 mW. 81


The cRICS control experiment with BaTiO3 was performed using the same setup as described for the LiNbO3 , except for the laser power, which was lowered to 46 mW. An additional control measurement was performed with fixed LiNbO3 harmonic NPs by pouring 7 µL of the LiNbO3 suspension onto a cover slip, waiting until the water has been fully evaporated, and subsequently mounting the cover slip on a microscope slide. A final control measurement consisted of a cRICS experiment in a water–glycerol mixture to increase the viscosity of the NP environment. 100 µL of the NP suspension was diluted in 900 µL Milli–Q, sonicated for 15 minutes, and poured through a 200 nm filter. 291 µL of the resulting sample was added to 2.86 mL glycerol (Sigma–Aldrich, St. Louis, USA) and placed on a hotplate (VMS–A, VWR, Leuven, Belgium) for 30 minutes at about 50 ◦ C while continuously mixing with a magnetic stirrer. Then, the sample was 1:2 diluted in Milli–Q and further mixed for several minutes before starting the cRICS measurement. To rule out possible system dependent artifacts, the cRICS measurement with LiNbO3 harmonic NPs was repeated with the Zeiss LSM 510 META system. Linearly polarized light from the Mai Tai DeepSee laser tuned to a central wavelength of 810 nm with an average power of about 190 mW on the stage was used for two–photon excitation. The IR radiation was focused by an LD C–Apochomat 40x/1.1 W objective. The SHG signal was collected in backward, non–descanned, analog mode after passing through the same filters as described for the LSM 880.

4.2.3

Measurements in cells

Adenocarcinomic human alveolar basal epithelial cells (A549 cell line, European Collection of Animal Cell Cultures, Wiltshire, UK), were maintained in modified eagle’s medium with glutamax (Gibco, Paisley, UK) supplemented with 10 % non–heat–inactivated fetal bovine serum (Biochrom AG, Berlin, Germany) and 1 % penicillin/streptomycin (Gibco) at 37 ◦ C, 5 % CO2 and 95 % humidity. At 80 − 90 % confluency, the cells were routinely subcultured using trypsin–EDTA to detach cells. Two days before the measurement, the cells were plated on Ibidi µ–slide 8 well plate chambers (Ibidi GmbH, Martinsried, Germany) at a density of 15,000 cells/chamber and incubated overnight to allow the cells 82


to adhere. After washing three times with Phosphate Buffered Saline (PBS), cells were treated with NPs. For this, the stock suspension of LiNbO3 NPs was diluted 5 times in complete culture medium, filtered through a 200 nm filter, and 300 µL/well was added to the plated cells. After 24 h exposure, cells were aspirated and washed three times with PBS before adding complete culture medium for imaging. To study the cytoskeleton mediated transport, we perturbed two of its most important constituents, actin and tubulin, by adding 0.25 µ M latrunculin A (Merck Millipore, Overijse, Belgium) and 20 µ M nocodazole (Sigma–Aldrich) in culture medium, respectively. After 30 min of incubation, cells were washed and cSTICS experiments were performed. To check cellular NP internalization, cells were treated with 12.5 µ M CellTrackerT M Green CMFDA (Life Technologies, Merelbeke, Belgium) for 45 min in serum– free cell culture medium and thereafter washed three times with PBS. For the NP internalization experiment, a z–stack was acquired with a total volume of 180 x 180 x 20 µ m3 comprising 20 images and a step size of 841 nm. The cellular lysosomes and endosomes were stained using 1 µ M LysoTracker Green DND–26 (30 min, Molecular Probes, Thermo Fisher Scientific, Merelbeke, Belgium) and CellLight Endosomes–GFP, BacMam 2.0 (16 h, 200,000 particles, Thermo Fisher Scientific, Germany), respectively. SHG and fluorescence were simultaneously imaged in descanned mode. The second harmonic signal was generated with the Mai Tai DeepSee at 810 nm and detected in the BP400 − 410 nm channel, while the fluorescence was excited with an Ar–ion laser at 488 nm and detected in the BP500 − 550 nm channel. Manders overlap coefficients, describing the fraction of NPs that are associated with the labeled cell organelles, were calculated using the Fiji plugin (ImageJ 1.52c, open source software, http://fiji.sc/Fiji) JACoP. A threshold was set to the approximated background value prior to the analysis. Note that coefficients are not dependent on the intensities of each channel and cross–talk between the different imaging channels was found to be negligible. cSTICS experiments were executed with linearly polarized light with an average biocompatible laser power [139] of about 16 mW at the sample position. Cells were kept at 37 ◦ C and 5 % CO2 during the experiments by means of a stage incubator. The acquisition time of each frame was about 5 s and 200 f rames were recorded in total. 83


4.2.4

Data analysis

Data analysis was performed according to our expressions derived in Slenders et al. [91] with custom written scripts in Matlab (Matlab R2017b, The Mathworks Inc., Eindhoven, The Netherlands). The ACF G(ξ, ψ) is a function of the spatial lags ξ and ψ in the x– and y–direction, respectively, which themselves are functions of time in cRICS. The parameters affecting the ACF shape are the PSF of the system and the concentration, the diffusion coefficient, and the flow velocity of the particles.

For cRICS, the ACF G of all frames was calculated using fast Fourier transforms. The series was subsequently ordered from the best to the worst autocorrelation curve by means of an adaptation of the spike cluster filtering algorithm presented by Ries et al. [140]. Details of the protocol can be found in Listing 4.1. The 25 % best autocorrelation curves were averaged, and the inverse of the square root of the variance was used as the fit weights in a nonlinear least squares approach. For representation purposes, the G(0, 0) noise peak was removed from the surface plots by setting this value to G(1, 0). The central line of the ACF in the fast scan direction (ψ = 0) was fitted separately from the other lines to extract ω0 , i.e. the lateral radius of the PSF. Following the notation used in the cIFM

[91], ω0 is defined as the 1/e4 value of the two–photon iPSF or, alternatively, the 1/e2 value of the corresponding one–photon iPSF, as illustrated in Fig. 2.18. Apart from ω0 , two other unknowns are the average particle concentration 〈 c〉 and the phase shift per unit length κ q which is present in a focused laser beam [141]. The variable 〈 c〉 was left as a second fit parameter. Slenders et al. showed, however, that when κ q is also left as a free parameter, the fit process becomes unstable [91]. We therefore estimated this variable a priori by performing the central line fit with ω0 and 〈 c〉 as the only freely adjusting parameters and we subsequently computed a new κ q based on the outcome. This process was iteratively repeated until the resulting value for the phase factor fluctuated less than 0.1 %. κ q is a parameter describing a linear approximation to the real Gouy phase shift and was calculated in each iteration as λ/(πω20 ), with λ the illumination wavelength. Although a value of 2λ/(πω20 ) is theoretically a better estimate of κ q near the focal plane for SHG imaging, the true phase shift would be severely overestimated near the top and bottom of the focal volume and the 84


iteration process does not converge. The lines ψ 6= 0 were subsequently fitted with the resulting ω0 value fixed and the diffusion coefficient D and 〈 c〉 as free parameters. A schematic summary of the data analysis protocol is presented in Fig. 4.4. Listing 4.1: Pseudocode autocorrelation sorting protocol. function G_sort = autocorr_sort(G) % INPUT: (m x m x n) autocorrelation matrix G with %

m the number of data points in the xi and psi direction and

%

n the number of frames in the time series

% % OUTPUT: (m x m x n) autocorrelation matrix G_sort, sorted from good to %

bad

% % PROTOCOL: % 1.

Create an empty list G_sort for storing the indices of the frame

%

numbers from good to bad. The quality of a frame is considered to

%

be higher when the corresponding ACF matches more closely the

%

average ACF of all other frames.

% % 2. if n >= 100: %

a) Calculate the average ACF . is an (m x m) matrix.

%

b) Calculate for each ACF the value dG, the overall mean squared

% % %

difference from . dG is a scalar. c) Find the 1 % highest dG values and the corresponding frame numbers

%

d) Add the frame numbers to G_sort

%

e) Remove these frames from G, n is now equal to the remaining

% %

number of frames f ) Repeat step 2 until n < 100

% % 3. if n < 100: %

a) Calculate for each frame i (from 1 to n) the average ACF of all

%

other frames. Store these together in an (m x m x n) matrix

%

85


%

b) Calculate for each ACF i (from 1 to n) dG, the overall mean

%

squared difference from (:, :, i ) . dG is a scalar.

%

c) Find the highest dG value and the corresponding frame number

%

d) Add the frame number to G_sort

%

e) Remove the frame from G, n is now equal to the remaining number

% %

of frames f ) Repeat step 3 until n == 1

% % 3. Add the remaining frame number to G_sort % % 4. Flip G_sort to change the list from good to bad % % The distinction between n >= 100 and n < 100 is made to speed up the % computation. For large n values, the overall average autocorrelation is % almost identical to the result obtained when frame i is left out. % Instead of throwing out only the worst autocorrelation, one can in addition % remove the 1 % worst autocorrelations in a single step.

The cSTICS analysis was performed similarly, except for two adjustments. Firstly, the immobile fraction was removed before the calculation of the ACF by subtracting the average image from each frame. The mean value of the average image was then added to all frames to keep the overall amount of photon counts constant. Secondly, the mobility was probed locally by considering specific regions of 64 x 64 pixels, rather than analyzing the full field–of–view [100]. Confidence intervals for all experiments were computed as the standard deviation of a set of measurements.

86


Measurement: N frame scans Typically N > 100

2

3

Raw data

Calculate ACFs

1.5 1.5 1 1.5 1 1.5 0.5 1 0.5 0 0.5 1 0 2 0.5 0 2 0 0 2

G( , ) G( , ) G( , ) G( , )

1

2 0 2 0 -2 -2 0 2 r [ m] 2 0 -2 -2 r [ 0m] 2 r [ m] 0 -2 -2 r [ 0m] r [ m] -2 -2 r [ m]

N images Randomly moving particle

Scanning laser beam

r

[ m]

r

N ACFs

Quality sorting ACFs See section 'Autocorrelation sorting protocol'

4

5

r

[ m]

r

G( , )

G( , ) G( , ) G( , ) G( , )

1.5 1.5 1 1.5 1 0.5 1 1 0.5 0 0.5 0 0.5 2 0 2 2 00 0 2 2 0 -2 -2 0 2 r [ m] 2 0 -2 -2 r [ 0m] 2 0 -2 r [ m] -2 r [ 0m] r [ m] -2 -2 r [ m]

Average 25 % best ACFs

1 0.5 0 2 0 -2

r

2

0

-2

[ m]

r

[ m]

[ m]

N ACFs

= 0) to find

6

Fit central fast axis line G( ,

Top view ACF step 5

Keep z0/

1.5

= 0)

1

0

1

G( ,

[ m]

-1

r

-2

0.5

0

r

-1

2

0

r

1

2

C lculat new q and repeat f t until 0 has conver ed

[ m]

[ m]

Corresponding lag times [s]

0) to find D

7

Fit other lines G( ,

-1

10

-2

Keep

-2

0

-3

10

1

-4

10

2

G( , )

10

-1

r

[ m]

q fixed

Fit parameters: ridge amplitude related 1/e4 2-photon iPSF radius 0 = 1/e2 1-photon iPSF radius

-2

-2

0

D, and

Fit function: cIFM

0

2

0,

1

0

r

[ m]

z0/

0,

and

q fixed

0.5 0 2

-2

0,

Fit function: cIFM

0

2

-2

r

[ m]

-2

0

r

2

Fit parameters: ACF amplitude related D Diffusion coefficient

[ m]

Figure 4.4: Data analysis protocol cRICS.

87

[ m]


4.3

Results and discussion

Typically observed cRICS (56 nm LiNbO3 NPs) and fluorescence RICS (100 nm beads) frames for comparison are depicted in Fig. 4.5. Note that the spatially summed SHG intensity over time, plotted in Fig. 4.6, is very stable, because of the absence of bleaching of the NPs. The combined movement of the LiNbO3 particles and the illumination beam results in a collection of stripes in the images, similar to what is observed for the fluorescent beads. There is, however, a difference between both images. While the signal from the beads is often detected in multiple consecutive lines, the NPs show a more discontinuous pattern, in which a particle can be found in one line before disappearing for some time, and then reappearing some lines later. Evidence for this behavior is provided by the ACF, G(ξ, ψ), shown in Fig. 4.7. The ACF is a function of the spatial lags ξ and ψ in the fast x– and slow y–direction, respectively, which themselves are functions of temporal lags in RICS/cRICS because of the scanning motion of the laser beam. The ψ = 0 line corresponds to lag times in the microsecond range, i.e. the same order of magnitude as the pixel dwell time. The other lines represent lag times in the millisecond range, i.e. the same order of magnitude as the line scan time. The shape of the ACF is affected by both system and sample related parameters. The first class comprises the lateral and axial radius of the PSF, ω0 and height z0 , respectively, and the Gouy phase shift per unit length κ q which is present in a focused laser beam [141]. The system parameters must be known prior to the analysis of extracting the sample information. The sample related parameters are the concentration 〈 c〉, diffusion coefficient D and directed flow velocity of the particles v. In the experimental ACF shown in Fig. 4.7, the central line G(ξ, ψ = 0) protrudes above the rest of the curve, with no effect of the selected scan speed, as indicated in Fig. 4.8. As a control to exclude sample and system related artifacts, we measured the same sample with a different setup (Fig. 4.9), and different samples (50 nm BaTiO3 NPs and 100 nm fluorescent microspheres) with the same setup (Fig. 4.10–4.11). An additional control experiment was performed with immobilized LiNbO3 NPs (Fig. 4.12). The fixed harmonic NPs and the fluorescent beads produce a conventional autocorrelation curve, without the central ridge. Although the effect is less pronounced in the water–glycerol mixture, all other experiments do show significant ψ = 0 peaks, independent of the illumination polarization. 88

4.3. RESULTS AND DISCUSSION

Consequently, this behavior must be attributed to the intrinsic movement of the particles. Because the effect is not predicted by the cIFM [91], it cannot be caused by free translational diffusion of the NPs. The microsecond range pixel dwell time is much shorter than the expected millisecond range diffusion time for the NPs, which further confirms the lack of free translational movement at the ψ = 0 time scale. A possible explanation for the drop in G from ψ = 0 to ψ = ±1

is rotational diffusion. The SHG signal is sensitive to the orientation of the harmonic NP with respect to the polarization of the incident light, see Fig. 4.2– 4.3. This angular dependency was well fitted with a cos4 function corresponding to a dipole response due to the projection of the optical c–axis of the harmonic NP trigonal cyrstal structure on the focal plane. This can be expected for SHG materials belonging to the 3m symmetry class, as has been reported for BiFeO3 [142, 143]. Even under circularly polarized illumination, the observed intensity depends on the angle between the induced SHG dipole moment and the sample plane [53]. One could expect to ‘lose’ part of the correlation from the ψ = 0 to the ψ = ±1 line because of changing orientations of the NPs during a line scan time. A spherical particle with a diameter of 56 nm suspended in water at room temperature has a characteristic rotational diffusion time, i.e. the inverse of the rotational diffusion coefficient, of 137 µ s. Except for the slowest scan speed, this value is longer than the pixel dwell time but significantly shorter than the characteristic translational diffusion time ω20 /4D, which is 14.8 ms. An additional motivation for the presence of rotational diffusion is presented in Fig. 4.13, which shows a cRICS stationary line measurement in which a single line, instead of a raster, was repeatedly scanned. The image shows that while some particles are translating slowly and can be observed in dozens of lines, the resulting traces are still discontinuous, showing an on/off pattern in the y–direction. This behavior may be explained as rotational diffusion of the harmonic NPs combined with the ‘photoselection effect’ shown in Fig. 4.3. It is unlikely that the missing links in the traces can be attributed to axial translational movement of the NPs out of the focal volume. A more plausible explanation is a change of the orientation of the NPs in which a lower second harmonic signal is produced. The corresponding ACF shows that the track gaps in the vertical time direction result in a strong decrease in G from the ψ = 0 to the ψ = ±1 line, which leads to the presence of the central ridge.

89


(a)

(b)

Figure 4.5: (a) cRICS frame with LiNbO3 NPs. Experimental settings: pixel size 166 nm, 256 x 256 pixels, pixel dwell time 16.4 µ s, 20x/0.8 objective, Mai Tai at 810 nm, 83 mW on the stage, sample at room temperature. SHG detection in the BP400 − 410 nm channel. (b) RICS frame with blue fluorescent carboxylate–modified microspheres (ex/em 350/440, Invitrogen, Belgium). Laser power 70 mW on the stage. Fluorescence detection in the BP450 − 650 nm channel. All other experimental settings are identical to the left image. Scale bars 10 µ m.

Total photon counts

6000 5000 4000 3000 2000 1000 0 0

200

400

600

800

1000

Time [s]

Figure 4.6: Summed SHG intensity for each frame as a function of the exposure time for cRICS measurement 6, see Table 4.1 for experimental details.

90


(a)

(b)

1

G( = 1, )

G( ,

)

1.2

0.5

1 0.8 0.6 0.4

0

0.2

2

2

0

r

[ m]

0

0 -2

-2

-2

r

-1

[ m]

0

r

1

2

[ m]

Figure 4.7: (a) cRICS autocorrelation curve from LiNbO3 NPs suspended in water at room temperature. (b) G(ξ = 1, ψ) cross–section. Pixel size 166 nm, pixel dwell time 8.19 µ s, image size 256 x 256 pixels, 20x/0.8 objective, and circularly polarized light. From the time series of 800 frames, the 200 best autocorrelation curves were averaged.

Normalized G( = 0)

1 54054 40540 20270 10135 5068 2534 1267 936

0.8 0.6 0.4 0.2 0 -2

-1

0

r

1

2

[ m]

Figure 4.8: Plots of the normalized central autocorrelation line G(ξ, ψ = 0) for LiNbO3 in water at room temperature at different scan speeds, in µ m/s. For each curve, the central data point and its nearest neighbors are set to zero. An overview of the corresponding instrumental parameters is presented in Table 4.1. No effect of the scan speed is observed, indicating that the particles are not significantly moving during the time the particles reside inside the focal volume, not even for the slowest scan speeds. The observed correlation is therefore a direct consequence of the PSF size.

91


)

0.06

G( ,

0.04 0.02 0 1

1

0

0

-1

r

-1

[ m]

r

[ m]

Figure 4.9: ACF of LiNbO3 NPs in ultrapure Milli–Q water at room temperature, measured with a Zeiss LSM 510 META. Measurement settings: pixel size 88 nm, 512 x 512 pixels per image, pixel dwell time 6.40 µ s, time series of 200 images, 40x/1.1 W objective. Mai Tai laser at 810 nm, 180 mW on the stage, linearly polarized along the horizontal scan direction. Detection in backward, non–descanned mode in the BP400 − 410 nm channel. For representation purposes, the G(0, 0) noise peak was removed from the plot by setting this value to G(1, 0). Harmonic nanoparticles

Fluorescent beads

)

1.5

20

G( ,

G( ,

)

30

10

1 0.5 0

0 1

r

[ m]

1

1

0 -1

r

1

0

0 -1

r

[ m]

[ m]

0 -1

-1

r

[ m]

Figure 4.10: Comparison of the cRICS ACF for 50 nm BaTiO3 NPs and the RICS ACF for 100 nm blue fluorescent carboxylate–modified microspheres (ex/em 350/440, Invitrogen, Belgium). The central ridge is only observed for the harmonic NPs. Settings: pixel dwell time 0.67 µ s, pixel size 83 nm, 256 x 256 pixels, time series of 1000 frames, laser wavelength 810 nm, power on the stage 46 mW (harmonic NPs) and 92 mW (fluorescent beads), circularly polarized excitation light, samples at room temperature. For representation purposes, the G(0, 0) noise peak was removed from the plot by setting this value to G(1, 0).

92


G( ,

)

2

1

0 2

2

0

r

[ m]

0 -2

-2

r

[ m]

Figure 4.11: cRICS ACF for LiNbO3 NPs in the water–glycerol mixture at room temperature. Illumination at 810 nm with about 105 mW of circularly polarized laser light on the stage. Pixel size 166 nm, pixel dwell time 32.8 µ s, 256 x 256 pixels per frame, 75 frames, 20x/0.8 objective. The central ridge is visible, but less pronounced compared to the harmonic NPs in less viscous medium from Fig. 4.10. For representation purposes, the G(0, 0) noise peak was removed from the plot by setting this value to G(1, 0).

(a)

(b)

G( ,

)

4 2 0 1

1

0 -1

r

[ m]

0 -1

r

[ m]

Figure 4.12: (a) SHG image from dried LiNbO3 NPs. Illumination at 810 nm with about 17 mW of linearly polarized laser light on the stage. Pixel size 92 nm, pixel dwell time 4.10 µ s, 512 x 512 pixels, 20x/0.8 objective. Scale bar 10 µ m. (b) Corresponding ACF. No central ridge is observed for fixed particles. For representation purposes, the G(0, 0) noise peak was removed from the plot by setting this value to G(1, 0).

93

CHAPTER 4. ICS WITH SHG NANOPARTICLES... (a)

(b)

G( ,

)

4

2

0 5 5

0

r

[ m]

0 -5

-5

r

[ m]

Figure 4.13: (a) Carpet plot of part of a line scan cRICS measurement with LiNbO3 NPs in Milli–Q water at room temperature. The same 42.50 µ m horizontal line segment was scanned a total amount of 64000 times. The resulting line signals were plotted below each other, creating the illusion of flow in the y–direction. Scale bar 20 µ m. Pixel size 166 nm, 256 pixels per line, pixel dwell time 4.10 µ s, 20x/0.8 objective. Illumination at 810 nm with about 83 mW of circularly polarized light on the stage. (b) Corresponding ACF, calculated by splitting the carpet into images of 256 x 256 pixels and applying the same filtering algorithm as in conventional cRICS measurements on the resulting series. For representation purposes, the G(0, 0) noise peak was removed from the plot by setting this value to G(1, 0). Although the appearance of a central ridge (ψ = 0) indicates more complex harmonic NP dynamics at the microsecond time scale than solely translational movement, the absence of noticeable diffusion over several pixel dwell times, even for the slowest scan speeds (Fig. 4.8), makes the ψ = 0 line valuable to obtain an independent calibration of the PSF. Fig. 4.14 shows G(ξ, ψ = 0), extracted from the data set from Fig. 4.7. The parameters ω0 and 〈 c〉 were fitted with the cIFM [91] with D fixed at 7 µ m2 /s, but almost identical results were found for D = 0. Averaging over three measurements at different scan speeds and calculating the standard deviation to determine the confidence intervals yields ω0 = (672 ± 8) nm and 〈 c〉 = (0.47 ± 0.08) /µ m3 . One of the fit results is plotted

in Fig. 4.14. The concentration corresponds to an average of 1.4 particles in the focal volume, but this number may not be fully reliable because of the central ridge, which is not taken into account in the theoretical model. The size of the 94


PSF, however, is in good agreement with a reference measurement with fixed blue beads excited with the same wavelength. The result after analyzing 17 subresolution 100 nm polystyrene beads is (6.5 ± 0.3) x 102 nm.

G( = 0)

1.5

1

0.5

0 -2

-1

0

r

1

2

[ m]

Figure 4.14: G(ξ, ψ = 0) cross–section from Fig 4.7, with the three central points omitted, and fit. The fitted parameter values are ω0 = 676 nm and 〈 c〉 = 0.41 /µ m3 . Fixing the height of the focal volume z0 is necessary to fit the central autocorrelation line. Based on a z–stack of the blue beads, a shape factor z0 /ω0 of 5.1 was used throughout this work. It should, however, be noted that the value of z0 does not significantly influence the ACF. For example, fixing the z0 /ω0 ratio at 3 yields a fitted ω0 value within the aforementioned confidence interval. The minor importance of z0 , combined with the extraction of ω0 from the central ridge, obviates the need for extra calibration experiments. The coherent nature of the SHG process affects the shape of the cRICS ACF compared to the fluorescence RICS ACF. The lengthy cRICS ACF [91], which was used to fit the data, can be written in a compact form as

G(ξ, ψ, ω0 , z0 , κ q , 〈 c〉 , D) =

A3 + A4 + A5 + A7 + B6 + B7 + B9 + C5 + C7 , GN

(4.1)

in which all terms in the numerator are functions of the system parameters ω0 , z0 and κ q and the sample parameters 〈 c〉 and D. G N is a normalization factor. 95


The sum (A7 + B9 + C7)/G N is equal to the fluorescence expression. The contribution of the other terms to G increases with increasing particle concentration. Consequently, when using the fluorescence expression to fit the ψ = 0 line, a significantly higher value of (865 ± 4) nm is found for ω0 . This result indicates the importance of using the cIFM for SHG active specimens. The lateral size of the PSF derived from the central line of the ACF can be employed to calculate the diffusion coefficient from the ψ 6= 0 lines. Because the rotational diffusion time is short with respect to the line scan time, the ψ 6= 0 lines are not influenced by rotational diffusion. Fixing all parameters,

except for 〈 c〉 and D, yields a diffusion coefficient of (7.5 ± 0.3) µ m2 /s, averaged over four measurements. This result corresponds to the value predicted by the Stokes–Einstein equation, which is (8 ± 2) µ m2 /s for particles with a diameter between 45.5 nm and 65.5 nm suspended in water at room temperature (viscosity 1.002 mPas [144]). The quality of the fit is illustrated by the fit residuals of Fig. 4.15. A diffusion coefficient of (12 ± 4) µ m2 /s is found upon analysis of the same data sets with the fluorescence expression and by fixing ω0 at 672 nm. In addition to substantially overestimating D, the nonrandom structure of the fit residuals, shown in the central panel of Fig. 4.15, clearly demonstrates the undesirable quality of this fit result. The fluorescence model may, however, be used to examine SHG data if ω0 is first calculated from the ψ = 0 line by means of the fluorescence expression. Even though this method yields a value of ω0 = (865 ± 4) nm, which does not correspond to the real PSF size, the fitted diffusion coefficient, (7.6 ± 0.6) µ m2 /s, closely matches the result obtained from the cIFM. Furthermore, the quality of the fit is, as illustrated in the right panel of Fig. 4.15, comparable to the SHG analysis.

96


Weighted residuals

(a)

2 0 -2 2

2

0

r

[ m]

0 -2

-2

r

[ m]

Weighted residuals

(b) 10 5 0 -5 2

2

0

r

[ m]

0 -2

-2

r

[ m]

Weighted residuals

(c)

2 0 -2

2

2

0

r

[ m]

0 -2

-2

r

[ m]

Figure 4.15: LiNbO3 cRICS fit residuals from the ACFs from Fig. 4.7 using the cIFM with (a) ω0 fixed at 672 nm and using the fluorescence model with (b) ω0 = 672 nm and with (c) ω0 = 865 nm. The corresponding diffusion coefficients averaged over 4 measurements are (7.5 ± 0.3) µ m2 /s, (12 ± 4) µ m2 /s and (7.6 ± 0.6) µ m2 /s. The reduced χ2 values are 1.3, 3.3 and 1.5, respectively.

97


One of the main advantages of using SHG active materials for mobility studies is the absence of photobleaching, as illustrated by Fig. 4.6. Consequently, cSTICS enables long–term mapping of the diffusion coefficient in cells. To check the NP uptake by the cells, we imaged cells that had been exposed to the LiNbO3 NPs for 24 h, see Fig. 4.16. The z–stack in the last panel of Fig. 4.16 shows that the NPs really are present inside the cell. A cSTICS example is presented in Fig. 4.17 and Table 4.2. We analyzed three regions inside the cell, which revealed a nonhomogeneous diffusion coefficient. The ACF for region 1 is plotted in Fig. 4.18. No central ridge is observed, which can be attributed to clustering of the nanoparticles, thereby reducing the SHG intensity dependence on the orientation of the excitation polarization plane. The corresponding diffusion coefficient is 3.8 x 10−3 µ m2 /s, which is several orders of magnitude lower than what is observed in aqueous suspension. Similar values are found for the other regions: the diffusion coefficient and standard deviation averaged over 18 regions spread over 4 cells yields D = (3.7 ± 1.5) x 10−3 µ m2 /s. Fitting again the data with the fluorescence expression and a PSF width of ω0 = 875 nm yields an almost identical result with a D value of (3.8 ± 1.8) x 10−3 µ m2 /s.

Figure 4.16: (Left) Transmission image of an A549 cell not exposed to NPs. (Center) A549 exposed for 24 hours to LiNbO3 NPs (green). (Right) Z–stack with xz and yz cross sections of a CellTrackerT M labeled A549 cell (red) exposed to LiNbO3 NPs (green). All observations are at 37 ◦ C. Scale bars 20 µ m. The small diffusion coefficient in comparison to the cRICS result cannot only be explained by clustering of the particles during the 24 h exposure time because the cluster diameter would theoretically need to be about 1000 times larger than an individual particle. Instead, the movement of most NPs must be confined to cellular organelles and the measured diffusion coefficients reflect the mobility of 98


Figure 4.17: cSTICS measurement of LiNbO3 NPs (green) in an A549 cell. The cell was kept at 37 ◦ C and 5 % CO2 . See Table 4.2 for the measured diffusion coefficients of the different regions. Scale bar 10 µ m. Table 4.2: Diffusion coefficient heterogeneity for the regions of Fig. 4.17. The errors as estimated by the fit program are much smaller than the standard deviation that can be expected when measuring the same sample multiple times. For this reason, the errors calculated during the fit analysis are not given. Since the cRICS measurements have a precision of about 5 %, one can expect a similar precision for the cSTICS experiments. Region 1 2 3

Diffusion coefficient [x 10−3 µ m2 /s] 3.8 6.7 2.6

these organelles. The diffusion coefficients we measured are in close proximity to the values found with conventional STICS [129]. In autocorrelation spectroscopy, slow diffusion processes require long measurement times. Due to the absence of bleaching of the harmonic NPs, the main limitation is the laser power, which may lead to cell damage when long exposure times are used. However, for the cSTICS experiments, the cells were exposed to the multiphoton laser for more than 15 minutes without observing a visual change in the cell morphology. 99


We measured the colocalization of the NPs with the fluorescently labeled lysosomes (N = 7) and endosomes (N = 5), see Fig. 4.19. The Manders’ coefficients were found to be (0.7 ± 0.2) and (0.6 ± 0.2), respectively. These results suggest uptake and clustering of the particles inside both cellular organelles. No directed flow of the harmonic NPs could be found within the accuracy of the cSTICS experiments, indicating the absence of active transport of the organelles. As a second test, we checked specifically for any transport of the organelles via the actin microfilaments and the microtubules by adding latrunculin and nocodazole, respectively, to the cells. Each component changes the polymerization state of the assembly that is affected, thereby severely hindering any transport along these structures [145, 146]. Although analysis of 11 regions in 4 cells treated with latrunculin – D = (1.0 ± 1.3) µ m2 /s – and 15 regions in 4 cells treated with nocodazole – D = (2.1 ± 1.6) µ m2 /s – both yield lower diffusion coefficients than untreated cells, the spread in D between different regions is too large to draw conclusions on the mechanisms involved in the NP transport.

100


)

2

G( ,

3

1

0

0 2

2

0

r

[ m]

0 -2

-2

r

[ m]

)

2

G( ,

3

1

15

0 2

2

0

r

[ m]

0 -2

-2

r

[ m]

)

2

G( ,

3

1

50

0 2

2

0

r

[ m]

0 -2

-2

r

[ m]

τ[s]

Figure 4.18: cSTICS ACF for region 1 in an A549 cell at 37 ◦ C, yielding a D value of 3.8 x 10−3 µ m2 /s. Note the absence of the central ridge.

101


(a)

(b)

Figure 4.19: Colocalization measurement between the LiNbO3 NPs and (a) the lysosomes and (b) the endosomes. The SHG signal from the NPs (green) was generated with the Mai Tai at 810 nm. The fluorescence from both the lysosome and endosome staining (red) was excited with an Ar–ion laser at 488 nm. 20x/0.8 objective. Temperature 37 ◦ C, 5 % CO2 . Scale bars 20 µ m. (a) Pixel dwell time 32.8 µ s, pixel size 249 nm. (b) Pixel dwell time 65.5 µ s, pixel size 216 nm.

102

4.4. CONCLUSIONS

4.4

Conclusions

We have delineated the cIFM conditions needed to analyze autocorrelation spectroscopy measurements with second harmonic generating light scattering harmonic NPs. The central line from the cRICS autocorrelation curve surprisingly protrudes above the rest of the surface. This central ridge was not predicted by the theory. Analyzing a cRICS data set therefore requires two steps: the central line is fitted separately and is used to extract the beam waist while the diffusion coefficient is obtained from the other lines. No additional PSF calibrations are needed for this type of experiment. The measured diffusion coefficient for 56 nm LiNbO3 NPs suspended in water at room temperature corresponds to the expected value based on the Stokes–Einstein equation. A cSTICS measurement in A549 cells revealed a much lower and heterogeneous mobility, caused by the uptake of the NPs in cell organelles, such as endosomes and lysosomes. Instead of using the complex cIFM to analyze the ACF, we have shown that for our experiments the fluorescence expression yields the same diffusion coefficient, provided that the beam waist is also measured using the fluorescence model. Further exploration is required to check whether this bypass can be generalized to other systems or samples. Regarding prospects, typical challenges with fluorescence RICS and STICS, such as photobleaching and blinking, are clearly absent in higher–harmonic generating materials. The signal–to–noise ratio may, however, be a concern when imaging small harmonic NPs. The SHG signal strength indeed declines with a decreasing size of the particles [147], scaling as the square of the NP volume. A NP with half the radius used in the current work will thus have its SHG strength reduced by a factor of 64. Consequently, the SHG signal may drop below the noise level. Increasing the illumination power is feasible only to some extent because intensities too high will negatively affect the sample. Absorption of the illumination light may lead to local heating of the sample, resulting in convection of the particle suspensions and a non–Brownian motion. Furthermore, high levels of radiation will damage a biological cell. However, it may not be necessary to increase the illumination power. Kim et al. were able to detect the second harmonic signal generated by a single 22 nm BaTiO3 NP, indicating their potential as biomarkers [147]. Depending on the properties of the sample, one might explore whether time gating can improve the signal–to–noise ratio [148]. In a more elaborate approach 103


that might be applicable to some cases, the SHG intensity may be enhanced by a factor of more than 500 by using plasmonic core–shell nanocavities, i.e. SHG nanocrystals surrounded by a metal shell [149]. Our findings to employ these NPs for autocorrelation spectroscopy studies will aid specific applications for long–term, deep tissue and organoid imaging, tissue engineering, chronic wound–healing and environmental nanoparticles exposure studies.

104

HAPTER

C

5

S TRUCTURED ILLUMINATION IN LASER SCANNING MICROSCOPY FOR MULTIPHOTON IMAGING

CHAPTER 5. STRUCTURED ILLUMINATION IN LASER...

S

ome critical considerations on resolution enhancement in structured illumination laser scanning microscopy, with the focus on multiphoton fluorescence imaging, are presented. We show that, compared to widefield

SIM, the resolution improvement is expected to be more modest. Additionally, the need for long acquisition times in laser scanning microscopy causes the technique to be prone to creating artifacts. We demonstrate the effect of stage drift on the reconstruction result.

5.1

Introduction

Two–photon microscopy modalities such as SHG imaging and 2PE imaging necessitate a high photon flux. This condition is in general met by spatially focusing a pulsed laser source in a scanning microscope, though alternative configurations have been developed, such as multipoint excitation by using a microlens array [150], line pattern illumination with a cylindrical lens [151], and temporal focusing [152]. Conventional SIM is a widefield based method, and its principle can therefore not straightforwardly be translated to a scanning system. A workaround is applying ISM instead of SIM since ISM requires scanning of the excitation spot. However, the idea of scanning SIM has been proposed by several research groups [71, 72, 153–155] and, accordingly, deserves some special attention. In this chapter, the basics of resolution in 2PE microscopy are first described. Next, the difference between a point–detector and a camera for SIM experiments is studied. A major element is post–processing of the data, which may lead to artifacts in the reconstructed image due to stage drift, as shown in the last section of this chapter.

5.2

Two–photon fluorescence excitation imaging

Because of the low emission power, 2PE is in general collected by a non– descanned detector positioned close to the sample, similar to the setup of Fig. 2.9. The measured fluorescence emission I(xL ) is quadratically dependent on the excitation intensity: 106

5.2. TWO–PHOTON FLUORESCENCE EXCITATION IMAGING

Ï

t(x) · h21 (x − xL )d2 x = t ⊗ h21 .

I(xL ) =

(5.1)

The two–photon iOTF h21 has a cut–off frequency of 4N A/λ2 , with λ2 the laser wavelength. An identical result is obtained for one–photon excitation confocal microscopy with the pinhole diameter reduced to almost zero, see Section 2.1.5. The nonlinear sample response in multiphoton microscopy thus intrinsically provides the same resolution enhancement factor, without the need for a pinhole or an ISM configuration. However, the twofold longer excitation wavelength (λ2 = 2λ) nullifies the improvement obtained. In fact, the imaging properties of a two–photon microscope are even poorer than a comparable one–photon system [156]. This conclusion can be drawn by analyzing the corresponding f2 has the same shape as the one–photon confocal OTFs. The two–photon OTF h 1

OTF but is laterally contracted by a factor of 2 due to the longer wavelength λ2 . The normalized cut–off frequency is therefore 2. Widefield imaging has the

same resolution limit, but the shape of the OTF is different. As illustrated in Fig. 5.1, two–photon microscopy is superior to widefield microscopy at spatial frequencies below about 0.43, whereas, due to the sharper decrease of the amplitude with increasing spatial frequency, the method is significantly worse at higher frequencies.

Similarly to one–photon microscopy, the imaging quality can be improved by descanning the emission signal and placing an almost closed pinhole at the conjugate focal plane. The overall OTF, shown in Fig. 5.1, is then given by the f2 ⊗ h f2 . This configuration doubles the cut–off frequency convolution product h 1

to 4, but the OTF shape is again slightly poorer than in conventional confocal microscopy. Moreover, blocking part of the already faint fluorescence signal will decrease the signal–to–noise ratio and deteriorate the image quality. Resolution enhancement in two–photon microscopy should thus be realized by alternative configurations, such as ISM or SIM. 107



1 One-photon widefield One-photon confocal Two-photon NDD Two-photon confocal

0.8 0.6 0.4 0.2 0 0

1

2

3

4

Normalized spatial frequency

Figure 5.1: Comparison of one– and two–photon OTFs. The normalized spatial frequency is expressed in units of N A/λ, with λ equal to the laser wavelength for 1PE and half the laser wavelength for 2PE. The two most–left curves cut the horizontal axis at a normalized spatial frequency of f = 2, the other two curves at f = 4. The term confocal refers to a descanned confocal setup with an almost closed pinhole. NDD = non–descanned detection.

5.3

Structured illumination in laser scanning microscopy

In imaging modalities that require a scanning laser beam, structured illumination can be achieved by temporally modulating the laser power, as illustrated in Fig. 5.2. Although this idea may appear to be equivalent to widefield SIM, the implementation is hindered by several difficulties that prevent a straightforward translation of SIM to multiphoton microscopy.

Figure 5.2: Applying structured illumination in a laser scanning microscope by means of spatiotemporal intensity modulation. A first aspect concerns the detection of the emission light. Multiphoton fluorescence is traditionally collected by a point–detector in non–descanned mode. However, as shown in this section, SIM is not compatible with point–detection, 108

5.3. STRUCTURED ILLUMINATION IN LASER SCANNING MICROSCOPY

but requires a camera instead. A second challenge is the modulation depth of the illumination pattern, which must be sufficiently high to allow for a proper reconstruction.

5.3.1

Why structured illumination microscopy with point–detection does not work

Consider the non–descanned 1PE laser scanning microscopy setup from Fig. 2.9 with a point–detector, e.g. a PMT. Following the notation and the assumptions from Sections 2.1.5 and 2.1.6, the 1D sinusoidal illumination intensity P(xL ) = ¡ ¡ ¢¢ A 1 + m sin ω0 xL + ϕ which is applied during the scan process results in a total observed fluorescence intensity equal to

Z

I(xL ) =

t(x)P(xL )h 1 (x − xL )dx Z = P(xL ) t(x)h 1 (x − xL )dx.

(5.2) (5.3)

For simplicity, a linear relationship between the illumination power and the fluorescence intensity is assumed, which limits the expression to one–photon, non–saturated fluorescence emission.

The integral is identical to the one–dimensional result obtained for conventional non–descanned imaging, see Eq. 2.14. The additional factor P(xL ) rescales the observed intensity at position xL and is operator defined. Pixel–wise calculation of I(xL )/P(xL ) in post–processing yields the exact same image as the result attained through homogeneous illumination. One can therefore immediately conclude that applying SIM to this imaging architecture does not provide information beyond the diffraction limit.

The effect of structured illumination can be shown in Fourier space as well: 109


h ³ ´i ³ ´ m m f1 (ω) e ω) = A δ(ω) + e iϕ δ(ω − ω0 ) + e− iϕ δ(ω + ω0 ) ⊗ et(ω) h I( 2 2 f1 (ω) = Aet(ω) h

m iϕ f1 (ω − ω0 ) e et(ω − ω0 ) h 2 m f1 (ω + ω0 ). + A e− iϕ et(ω + ω0 ) h 2

(5.4)

+A

(5.5)

High spatial frequencies are moved by widefield SIM into the passband of the objective, as shown by Eq. 2.23. For scanning SIM with point–detection, however, the shift of the spatial frequencies is accompanied by an equal shift of the OTF. Consequently, no resolution enhancement can be expected within the assumptions of this theory, despite claims to the contrary [157].

5.3.2

Structured illumination microscopy with camera detection

An alternative 1PE imaging architecture is presented in Fig. 5.3, in which the point–detector is replaced by a camera. All pixels of the camera integrate the emission signal during a full frame scan. The recorded image is:

0

Ï

P(xL )h 1 (x − xL )t(x)h 2 (x0 − x)dxdxL ¸ Z ·Z = P(xL )h 1 (x − xL )dxL t(x)h 2 (x0 − x)dx

(5.7)

= [((P ⊗ h 1 ) · t) ⊗ h 2 ] (x0 ).

(5.8)

I(x ) =

(5.6)

The variable x0 refers to the coordinate in the camera image. The excitation iPSF in scanning SIM, unlike in widefield SIM (Eq. 2.21), plays an important role. The convolution product with P reduces the effective pattern modulation depth P e f f at the sample plane: 110

5.3. STRUCTURED ILLUMINATION IN LASER SCANNING MICROSCOPY

Figure 5.3: Beam path laser scanning microscope with spatiotemporal structured illumination. The laser power is periodically modulated during the scan process to create an illumination pattern at the sample plane. A camera is used for fluorescence detection. Obj. = objective, DBS = dichroic beam splitter, M = emission filter.

e f P e f f (ω) = P(ω) h 1 (ω) ´ 2A ³ m m = δ(ω) + e iϕ δ(ω − ω0 ) + e− iϕ δ(ω + ω0 ) π 2 2 s Ã ! µ ¶ 2 ω |ω| −1 | ω | 1− 2 , · cos − ωc ωc ωc

(5.9)

(5.10)

with ω c = 2π f c . The inverse Fourier transform is, ignoring prefactors, equal to



P e f f (x) =

ω0  + m sin(ω0 x + ϕ) cos−1 2 ωc

π

µ

¶

 v u 2 ω0 u t1 − ω0  . −  ωc ω2c

The modulation depth m0 at the sample plane is then 111

(5.11)




m0 =

2m  −1 ω0 cos π ωc µ

¶

 v u 2 u ω ω0 t  − 1 − 02  . ωc ωc

(5.12)

The function m0 /m is plotted in Fig. 5.4. Clearly, high spatial frequencies in the illumination power pattern result in low modulation depths at the sample plane. The relationship

m0 m

(ω0 ) exactly follows the objective iOTF, Eq. 2.13.

The modulation depth reaches zero at ω0 = ω c . This outcome is expected, since any illumination pattern is low–pass filtered by the objective, regardless of the technique used to create the pattern. The effect of modulation smoothing is simulated in Fig. 5.5. 1

m' / m

0.8 0.6 0.4 0.2 0 0

0.2

0.4

0.6 0

/

0.8

1

c

Figure 5.4: Relative illumination modulation depth as a function of the relative spatial frequency of the SIM pattern. The indicated value of ω0 = 0.8ω c , 0 corresponding to a ratio m m = 0.104, is used for the simulation of Fig. 5.5. An illustrative experimental example of modulation smoothing is shown in Fig. 5.6. Even though the spatial frequency of the illumination pattern is well below the diffraction limit, the camera image cannot resolve the pattern. Modulation smoothing takes place twice in this example since the filter effect occurs each time the light travels through the objective. The modulation amplitude consequently drops below the noise level. Both a high modulation depth and a high spatial frequency of the pattern are desired to obtain the best SIM result. Gustafsson was, for a widefield SIM 112

5.4. COMBINING SIM WITH TWO–PHOTON EXCITATION MICROSCOPY

(a) Illumination power

(b) Integrated intensity at the stage

Figure 5.5: (a) Laser power as a function of the scan position for scanning SIM. The gray circle indicates the iPSF size. (b) Total intensity received at each position at the sample plane during a frame scan. The line plots show the illumination power and the integrated intensity along a single line. Simulation parameters: NA 1.4, excitation wavelength 810 nm, pixel size 10 nm, ω0 = 0.8ω c . The original modulation depth of m = 1 has decreased to m0 = 0.104.

setup, able to obtain a depth between 70 % and 90 % at a spatial frequency close to 96 % of the cut–off value [29]. The pattern was created by placing a line–patterned grating in a secondary image plane of the microscope, which is projected by the objective onto the sample. Fig. 5.4 shows in comparison that the maximum modulation depth for a scanning system is less than 1 % for ω0 = 0.96 ω c . Evidently, much lower frequencies must be used in scanning SIM,

and, consequently, no doubling of the resolution may be expected. However, a significant resolution enhancement was demonstrated at modulation depths around 30 % [153, 154].

5.4

Combining SIM with two–photon excitation microscopy

Merging the theories from Sections 5.3.2 and 5.2 is straightforward. The intensity detected by a camera pixel at position x0 for two–photon excitation is [71]: 113


Transmission Point-detector

Reflection Camera detection

Figure 5.6: Experimental evidence for modulation smoothing in point–scanning SIM. Part of a grid sample was simultaneously imaged in transmission mode with a point–detector and in reflection mode with an EMCCD camera. Experimental settings: 40x/1.1 objective, excitation wavelength 690 nm, modulation frequency 1 /µ m. More details on the setup are given in Chapter 7. The structured illumination pattern is clearly visible in the transmission image, but completely absent in the camera image. Note that the computed Fourier transform (bottom row) of the transmission signal not only contains the first order but also many higher orders which are well beyond the diffraction limit. Scale bar 20 µ m.

I(x0 ) =

Ï

P 2 (xL )h21 (x − xL )t(x)h 2 (x0 − x)dxdxL

£¡ ¢ ¤ = (P 2 ⊗ h21 ) · t ⊗ h 2 (x0 ).

The excitation pattern in Fourier space is 114

(5.13) (5.14)

5.5. STAGE DRIFT INDUCED RECONSTRUCTION ARTIFACTS

f2 . f2 · h P 1

(5.15)

f2 has a normalized As shown by the two–photon NDD curve in Fig. 5.1, the iOTF h 1

spatial cut–off frequency of 2, but has an amplitude of less than 1/7 at normalized frequencies above 1.04. Assuming that 1/7 is the detection threshold for the modulation depth of a real system, P 2 must have a frequency of less than 1.04. The maximum resolution gain that can be expected is then 1.04/2, which is about 50 %. A twofold resolution improvement, as in widefield SIM, cannot be achieved with this scanning SIM approach. The quadratic sample response to the excitation intensity must be taken into account when applying the illumination pattern. A laser power pattern P = 1 + sin(ω0 x) will lead to an excitation pattern P 2 equal to

P 2 = (1 + sin(ω0 x))2 =

(5.16) π´

3 1 + 2 sin(ω0 x) + sin 2ω0 x − . 2 2 2 ³

(5.17)

An unwanted second harmonic is introduced which could theoretically complicate the data analysis. However, if ω is sufficiently high, i.e. close to 1 or higher, the second harmonic will be below the noise level, or completely absent, respecp tively. A more elegant solution would be to apply the pattern P = 1 + sin(ω x) , which would only generate an oscillation of frequency ω. Chapter 7 provides a detailed description for installation of a scanning SIM module on a commercial microscope that can generate any desired pattern.

5.5

Stage drift induced reconstruction artifacts

Even though SIM and ISM are intrinsically the same concepts, there is an important difference in the reconstruction process. In ISM, the reconstruction, if performed in post–processing, consists of two steps: reassignment and deconvolution. In the reassignment process, the images from all detector elements 115


are compared, the optimal reassignment vectors are calculated from the data, and the images are shifted correspondingly. In general, this procedure is robust enough to not introduce artifacts. The deconvolution step is optional and can be applied to further improve the image’s appearance. Deconvolution can, however, easily lead to artifacts. In SIM, both the merging process and deconvolution must be performed in a single step. Consequently, SIM is more prone to irregularities. SIM and ISM measurements take longer than conventional imaging, which causes stage drift to become a relevant issue. In ISM, which demands a low scan speed in order for each detector element to collect a sufficient number of photons, the stage drift effect is limited since a pixel value at a certain position in the final image is determined by about 20 to 30 pixel values around this position in the raw images. A few line times are therefore sufficient to calculate a single final pixel value. In SIM, however, all (9) frames are needed to compute the final pixel value at any position, which can cause the net stage drift covered in this time to be orders of magnitude larger than in ISM. The effect of stage drift on the reconstruction process is displayed in Fig. 5.7. A sample of 128 x 128 pixels consisting of a striped fluorescent pattern was simulated [158]. A pixel represents about 200 nm. A Gaussian iPSF with a 1/e2 radius of 6 pixels was assumed. A total of 9 images were computed, each image with a different illumination pattern. Three angles ( 312π , phase shifts (0,

2π 3 ,

and

4π 3 )

7π 12 ,

and

11π 12 )

and three

were chosen. The pattern periodicity was 6 pixels

and the modulation depth was 1. Gaussian noise was added with an average of 0 and a standard deviation equal to 2 % of the maximum image value, low enough to keep all image values positive. The images were zero padded to meet the Fourier transform continuity condition. A generalized Wiener deconvolution algorithm was used to reconstruct the sample [159]. Three stage drift speeds, expressed in units of pixels per frame time, in both the horizontal and vertical direction were compared. Without stage drift, the SIM algorithm is clearly able to improve the resolution as expected. However, as the drift speed increases, artifacts become more significant. The algorithm is unable to decently recover the sample structure at a drift speed of 3 pixels per frame time, indicating the sensitivity of SIM to reconstruction artifacts and the importance of detecting stage drift [158]. 116

5.5. STAGE DRIFT INDUCED RECONSTRUCTION ARTIFACTS

Sample

Widefield imaging

SIM, no drift

SIM, drift = 1

SIM, drift = 3

Figure 5.7: Simulation of the effect of stage drift on the SIM reconstruction process. The image of a striped pattern is computed for widefield imaging and compared with the SIM result. Stage drift during the long SIM acquisition time results in reconstruction artifacts. The stage drift is expressed in units of pixels per frame time.

117


5.6

Conclusions

Implementing SIM in a laser scanning microscope with two–photon fluorescence excitation is feasible by means of spatiotemporal laser power modulation and camera detection. However, the modulation frequency must be low enough in order to have a sufficient modulation depth. The twofold resolution improvement of widefield SIM is therefore not attainable with scanning SIM. Moreover, the reconstruction quality of any SIM technique depends on, among other parameters, the stage drift. The disadvantages of scanning SIM are circumvented by combining two–photon excitation with ISM, as described in Chapter 6.

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T WO – PHOTON FLUORESCENCE EXCITATION IMAGE SCANNING MICROSCOPY

This chapter is based on Slenders E., Tcarenkova E., Tortarolo G., Castello M., vandeVen M., Koho S., Vicidomini G., Ameloot, M. “Nonlinear image scanning microscopy with an array detector”, to be submitted.

CHAPTER 6. TWO–PHOTON FLUORESCENCE EXCITATION ISM

E

xtensive scattering of the illumination light restricts the imaging depth in ISM configurations implemented with one–photon fluorescence excitation. We present an ISM implementation for resolution enhancement

in multiphoton fluorescence excitation imaging. The conventional point detector that is used in confocal microscopy is replaced by a single photon avalanche diode square array of 5 x 5 detector elements. The raw data collected by each element can be stored separately, allowing for the reconstruction to be performed in post–processing. The design offers users the flexibility to choose the pixel size and the field–of–view. Compared to confocal microscopy, we demonstrate a resolution improvement of a factor of 1.5 with beads, 1.35 for fixed cells and 1.2 at a depth of 70 µ m in a mouse brain.

6.1

Introduction

Fluorescence microscopy is extensively used in biological imaging because of the high sensitivity, the molecular specificity and the high contrast [5, 160, 161]. However, the imaging resolution is limited by diffraction. During the last decades, several methods have been developed to overcome the resolution barrier. Among others, STED [16], PALM [17] and STORM [18] have shown to yield a resolution below 35 nm. However, these methods rely on specific photophysical properties of the fluorophores used and can therefore not straightforwardly be applied to bioimaging [5, 30]. SIM encompasses a collection of super–resolution implementations that make use of patterned excitation [29]. In contrast to many other super–resolution methods, SIM does not require any special sample preparation [5]. In its original form, a striped illumination pattern with a line spacing close to the diffraction limit is projected onto the sample, thereby moving high–frequency information of the sample into the passband of the objective [29]. ISM with pixel reassignment can be considered as a special case of SIM, in which the illumination pattern is the diffraction limited PSF scanning the sample. ISM was first proposed by Sheppard [32] and later realized in a variety of implementations [74, 162–165]. In ISM, information from each scan position is collected by a two–dimensional array of detectors. The final image is all–optically or via post–processing reconstructed. Comparing the full width at half maximum of the PSF, ISM can 120


produce an image with a

p 2 improvement in resolution with respect to wide-

field microscopy [165, 166]. The same resolution can theoretically be obtained in confocal microscopy by substantially reducing the pinhole diameter [12], but at the cost of a low signal–to–noise ratio. Today, most ISM configurations are implemented with one–photon fluorescence excitation. However, extensive scattering of the illumination light in thick biological samples restricts the imaging depth. The IR radiation used in MPEM not only allows a much deeper penetration, the longer wavelength of IR illumination is also less phototoxic [37, 44, 167]. Moreover, due to the absence of out–of–focus excitation, the optical sectioning capability is intrinsically present in MPEM without the need for pinholes in the detection path [36]. We present an ISM implementation with 2PE combined with an array detector in descanned mode. This method is different from the arrangement recently proposed by Gregor et al. [161]. In their setup, the pixel reassignment process is performed all–optically by rescanning the emission signal. The natural movement of the emission beam at the non–descanned port is doubled by the rescan mirrors. The resulting beam is projected onto a camera, resulting in a single image. No further processing is needed. Rescan ISM is therefore fast and easy. However, the optimal reassignment factor may for several reasons deviate from this factor of two. Simply doubling the movement thus may not lead to the best possible image. In our approach, the reconstruction is performed in post– processing, not only offering more flexibility during the measurement, but also allowing for a more thorough reconstruction process. We compare the quality of our ISM method to a confocal setup by imaging a sample of dried fluorescent spheres and stained and fixed epithelial cells. The ISM resolution enhancement in a 3D sample is investigated using a mouse brain with neurons expressing Enhanced Yellow Fluorescent Protein (EYFP).

6.2 6.2.1

Materials and methods Setup

The ISM configuration, presented in Fig. 6.1, is identical to a conventional confocal setup, with the point–detector replaced by a 5 x 5 element array detector. 121


A Chameleon Ti:Sapphire femtosecond pulsed laser from Coherent tuned to a central wavelength of 950 nm was used for 2PE. The beam passes a lens system containing two 50 mm ThorLabs lenses placed about 100 mm apart to correct for beam divergence. The light is transmitted by a long pass 720 nm dichroic beam splitter from Semrock and is reflected by the scan mirrors. The beam is expanded by a 50 mm Leica scan lens and a 250 mm Leica tube lens before entering a Plan–Apochromat 100x/1.4-0.7 oil CS Leica objective. The fluorescent emission light is descanned by the scan mirrors, reflected by the dichroic beam splitter and focused onto the array detector using a 250 mm ThorLabs lens. A 512/40 nm Semrock emission filter was installed. Sample Objective

Scan mirrors

Dichroic beam splitter

Array detector Emission filter

Figure 6.1: Scheme of the ISM beam path.

Fluorescence detection was performed with a custom–built (SPADlab, Politecnico di Milano, Milan, Italy) 25 element array of Single–Photon Avalanche Diodes, arranged in a 5 by 5 square matrix. Each detector element is 50 x 50 µ m2 in size and is surrounded by a small dead area, resulting in an overall detector size of 350 x 350 µ m2 and a fill factor of about 50 %. The emission beam path was constructed to yield a total magnification of about 500. Consequently, the 122


diameter of the two–photon Airy disc in the image plane [168] closely matches the overall detector size. Therefore, by adding up the signal from all detector elements for each scan position, one can obtain a conventional confocal image with a virtual pinhole of about one Airy unit. The scan mirrors and the SPAD detector were controlled by using the home– built Carma software [169]. Each scan resulted in 25 images that were stored, together with the metadata, in a Matlab file (Matlab R2017b, The Mathworks, Inc., Eindhoven, The Netherlands). The larger the distance from each individual detector element to the optical axis is, the lower the signal–to–noise ratio and the larger the displacement in the field–of–view with respect to the central detector element becomes. The translative shift (δ x, δ y) between each image produced by a detector element and the image produced by the central detector element was measured by calculating the corresponding phase correlation. By applying the negative shift (−δ x, −δ y) to each image and adding up the resulting 25 images, one obtains a super–resolved ISM image. The ISM image could be calculated in the Carma software in pseudo–real–time, i.e. directly after each scan. Further post–processing, e.g. calculating the resolution improvement using Fourier Ring Correlation (FRC) analysis [170], was performed in Matlab (Matlab R2017b, The Mathworks, Inc., Eindhoven, The Netherlands). Similarly to conventional confocal imaging, our implementation of ISM offers more flexibility than the setup reported previously [161]. The user can choose the pixel dwell time, the pixel size and the field of view. Furthermore, the experimental design is less complex compared to a rescanning setup with camera detection.

6.2.2

Reconstruction with pixel reassignment

Each detector element produces an image, resulting in 25 images in total. The first step in the reconstruction algorithm is to roughly estimate the lateral shift between each image I det and the central detector element image I re f by calculating the corresponding phase correlation function C ϕ :

¡ ¢ C ϕ = F −1 F (I re f ) · F ∗ (I det ) .

123

(6.1)


The location of the maximum value of C ϕ determines the lateral shift between I det and I re f . The phase correlation curve is cropped to 11 by 11 data points, centered at the peak location. The cropped curve is fitted with a Gaussian function, with the peak location and the width in the x– and y–direction as fit parameters. In this way, the shift values can be calculated more accurately. The protocol is illustrated in Fig. 6.2.

124


Iref

Idet

Apply shift (-x, -y) Phase correlation

Fit peak with Gaussian 104 8

C

7

Peak maximum

6

at (x, y)

5 2

0

-2

y

-4

-6

2

6

4

8

10

x

Figure 6.2: Pixel reassignment protocol illustrated with fluorescent beads. Scale bars 2 µ m.

125


The next step is to apply the resulting shifts to the image I. This computation is performed in Fourier space by multiplying F (I) by a phase factor e−2π i( f x δ x+ f y δ y) , with F the Fourier transform and f x and δ x the spatial frequencies and the lateral shifts in the x–direction, respectively. Similarly, f y and δ y refer to the frequencies and the shifts in the y–direction. Note that in this way non–integer shifts can be applied and that periodic boundary conditions are implicitly assumed. In the last step, all shifted images are summed, the inverse Fourier transform is applied and the real part of the result is taken to produce the final image.

Since the setup does not make use of the rescanning principle with camera detection, the shift factors do not need to be known in advance. Instead, these values are calculated in post–processing. The optimum reassignment factor not only depends on the Stokes shift but also on the noise level [73]. Being able to compute the reassignment values after the measurement is therefore a significant advantage.

6.2.3

FRC analysis

The resolution of an optical system can be measured by using small fluorescent beads or a calibration standard. Alternatively, the resolution can directly and more conveniently be derived from any microscopy image by using FRC analysis [170]. For FRC analysis, two independent images of the same object are needed of which the similarity in the frequency space is evaluated. For the brain sample, the images were obtained by using two virtual channels: photons arriving during the first and second half of the pixel dwell time were assigned to the first and second image, respectively. If only one channel is available, the data may be split by assigning the pixels from the odd and even columns to respectively the first and second image. The rows of the resulting rectangular data sets are then averaged two by two to obtain square images. We illustrate this option with the beads and the fixed cells. 126


6.3 6.3.1

Results and discussion Alignment and magnification of the system

As a first demonstration, we imaged yellow–green carboxylate modified fluorescent spheres (FluoSpheres, ThermoFisher Scientific, USA), 45 nm in diameter, settled on a cover slip. The Carma software can calculate and plot the average intensity for each detector element during scanning, see Fig. 6.3. This function allows users to conveniently optimize the alignment until a centered Airy pattern is observed. Moreover, one can estimate and check the magnification of the system: if all pixels collect roughly the same amount of photons, the magnification is too high; if almost all signal comes from the central detector element, the magnification is too low. Ideally, one could install a zoom lens system to check which zoom produces the best image resolution. This technically challenging extension falls beyond the scope of the current work. In our setup, the intensity detected by the corner pixels is almost 80 % lower than in the center. The corresponding magnification can be estimated to be 422x, see Fig. 6.4, close to a factor of 500 that could be expected from the optical path. In the brain sample, a magnification of 494x was measured.

6.3.2

Beads

Fig. 6.5 compares for the fluorescent beads the confocal image, obtained by summing the signal from all detector elements without shifting, with ISM. The resolution improvement is clearly noticeable. Because of the high signal–to– noise ratio, FRC analysis yields a resolution enhancement of 1.5, which is about p equal to the 2 factor that is in general expected from ISM when no further processing is applied [161]. The PCR with SPAD detection is limited to a minimum of about 100 H z, i.e. the dark current PCR, and a maximum of several MH z, due to the dead time of the detector [169]. This latter constraint restricts the excitation power and consequently the applied scan speed. In ISM, however, the emission signal is distributed over a detector array, limiting the number of photons collected by each individual element. Furthermore, the probability of two–photon absorption is extremely low, resulting in a modest fluorescence intensity. The measured 127

CHAPTER 6. TWO–PHOTON FLUORESCENCE EXCITATION ISM (a)

(b)

0.35 0.3 0.25 0.2 0.15 0.1

Figure 6.3: (a) Average number of photons collected per detector element per laser position for the fluorescent beads sample. The pixel dwell time is 80 µ s, corresponding to a Photon Count Rate (PCR) of about 4.8 kH z for the central detector element and about 1 kH z for the corner elements. (b) Corresponding images recorded by three of the detector elements. Scale bars 2 µ m. PCR per detector is several kH z, see Fig. 6.3, several orders of magnitude lower than the saturation count rate, but well above the dark current PCR.

128


0.3

Total shift [ m]

0.25 0.2 0.15 0.1 0.05 0 0

50

100

150

200

250

Distance to central detector element [ m]

Figure 6.4: Total shift (x– and y–direction combined) applied during the ISM reconstruction as a function of the real distance between the detector element center and the overall detector center for the beads sample. Each data point represents one of the 25 detector elements. E.g. there are four detector elements at a distance of 75 µ m, represented by four partially overlapping data points. To obtain the total magnification, a weighted linear fit was performed with the intercept fixed at the origin and with the weights calculated by summing the photon counts of each detector element during the complete scan. The data points are colored according to the weights; from green to blue for respectively high and low weights. The weights for the two outliers in black are set to zero. The resulting fit equation is y = 0.00118x. Assuming that the optimum reassignment factor is 1/2 (see Fig. 2.15), this slope corresponds to a magnification of 1/(2 · 0.00118) = 422x.

129


(a)

(b)

1

(c)

Confocal ISM

FRC

0.8 0.6 0.4 0.2 0 0

2

4

6

8

Spatial Frequency [/ m]

Figure 6.5: Comparison of (a) confocal microscopy with (b) ISM using fluorescent beads. Scan parameters: pixel dwell time 80 µ s, pixel size 30.1 nm. A selection of the 15 x 15 µ m2 area in sample space is shown. Scale bars 2 µ m. The FRC curves are plotted in panel (c), together with the intersections with the FRC = 1/7 line [171]. The confocal microscopy image does not show spatial frequencies above 2.93 /µ m, while ISM resolves spatial frequencies up to 4.46 /µ m. The corresponding resolutions are 334 nm and 221 nm, respectively.

130


6.3.3

Fixed cells

The enhanced image resolution can also be observed in more complex and biologically relevant samples. We applied our ISM technique to a specimen of fixed human breast tumor cells, cell line MDA–MB–231, stained with an alpha– tubulin antibody and with a Star488 secondary antibody (Abberior, Germany). As demonstrated in Fig. 6.6, the maximum resolvable spatial frequency has increased with ISM by a factor of 1.35, which results in a visually significantly improved image. The lower resolution improvement compared to the beads sample can be attributed to a higher degree of scattering of the fluorescent light in this sample.

6.3.4

Mouse brain

Even in 3D samples, a small resolution enhancement can be measured. We imaged an optically cleared mouse brain, see Fig. 6.7, at a depth of 70 µ m. By applying ISM, the resolution improves by 16 % (70 nm). The lower resolution enhancement in comparison to the previous samples may partially be attributed to a lower signal–to–noise ratio. The average number of photons per excitation spot is about 0.29 per detector element per virtual channel, which is lower than the 0.44 collected for the fixed cell sample. Moreover, more intense scattering of the fluorescence signal, caused by the longer distance the light must travel in the specimen, distorts the journey of the photons from the point of creation to the cover slip. As a result, a lower number of photons will be reassigned to the correct position during the reconstruction process. Consequently, a broader emission PSF can be measured, see Section 6.3.1, and the imaging performance deviates from the optimal values found in the beads sample. A better quality could be obtained by decreasing the zoom factor or, equivalently, increasing the detector size. Alternatively, one could add more detector elements, but at the cost of a lower scan speed.

131


(a)

(b)

1

(c)

Confocal ISM

FRC

0.8 0.6 0.4 0.2 0 0

1

2

3

4

5


Figure 6.6: Comparison of (a) confocal microscopy with (b) ISM using fixed cells. Scan parameters: pixel dwell time 50 µ s, pixel size 50 nm. Scale bars 20 µ m. The insets show the indicated lower left region of the cell with a higher digital zoom. The FRC curves are plotted in panel (c), together with the intersections with the FRC = 1/7 line. The confocal microscopy image does not show spatial frequencies above 2.44 /µ m, while ISM resolves spatial frequencies up to 3.30 /µ m. The corresponding resolutions are 410 nm and 303 nm respectively.

132


(a)

(b) (c)

(c)

1 Confocal ISM

FRC

0.8 0.6 0.4 0.2 0 0

2

4

6

8

10


Figure 6.7: Comparison of (a) confocal microscopy with (b) ISM in a mouse brain with neurons expressing EYFP. The sample was optically cleared to reduce scattering of the fluorescent light. The insets show a portion of the image with a higher digital zoom. Scan parameters: pixel dwell 100 µ s, pixel size 50.1 nm. Two virtual channels of 50 µ s each were used. Scale bars 20 µ m. FRC analysis, panel (c), yields a maximal resolvable spatial frequency of 2.06 /µ m for the confocal setup and 2.44 /µ m for ISM, corresponding to a resolution of 486 nm and 410 nm, respectively. Since the contrast in the sample is rather low, several white arrows are drawn to highlight structures that are visually sharper in the ISM image compared to the confocal image. The yellow arrow points to a ring structure of about 450 nm in diameter that is only visible in the ISM image.

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6.4

Conclusions

A new ISM method that is compatible with multiphoton fluorescence excitation is presented. By implementing an array detector consisting of 25 SPAD detector elements in a descanned detection configuration, we demonstrated a resolution improvement of up to a factor of 1.5 in 2D samples and of 1.2 in 3D samples compared to conventional confocal microscopy. Avoiding camera detection in non–descanned mode gives the user the flexibility to choose the pixel size and the field–of–view. By storing the raw data, the reconstruction can be performed in post–processing, producing the optimal final image. The main limitation for the frame rate is not the movement by the scan mirrors, but the PCR, which is rather low with two–photon excitation. However, we have shown that, on average, even less than one photon per detector element per laser position is sufficient for a proper reconstructed image.

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I MAGE SCANNING MICROSCOPY IN NON – DESCANNED DETECTION FOR IMPROVED NONLINEAR EXCITATION IMAGING WITH A COMMERCIAL LASER SCANNING MICROSCOPE

CHAPTER 7. IMAGE SCANNING MICROSCOPY IN NDD...

T

he technique of combining resolution enhancement through ISM and nonlinear excitation imaging with a commercial laser scanning microscope is explored. We add a laser power control unit to the excitation

path of a commercial system and replace the non–descanned PMT box by a camera. Although the same setup can be used for both scanning SIM and ISM,

we focus mainly on the latter technique since ISM does not rely on a complex theoretical model for the pixel reassignment process. Preliminary data is presented to show the potential of the proposed setup, with specific attention to resolution enhancement in SHG microscopy.

7.1

Introduction

While an unlimited resolution is theoretically attainable through nonlinear fluorescence SIM [30], the resolution is in practice restricted by the signal– to–noise ratio and, more importantly, by photobleaching of the sample [69]. This limitation is absent in label–free SHG imaging. Extending the theory of SIM to coherent imaging modalities, such as SHG imaging, is, however, not straightforward. A proper theory must start from the amplitude fields produced by each scatterer in the sample, taking into account the Gouy phase factor. The squared modulus of the total amplitude then provides the intensity observed at a certain position in the detection plane. This approach was introduced in Chapter 2, Eq. 2.30, and used to derive the ACF for fluctuation imaging analysis with harmonic NPs in Chapter 3. Devising an analytical expression was feasible thanks to the statistics involved in the random motion of the particles. For super–resolution microscopy of nonrandom samples, however, the variable of interest is not the overall particle concentration, nor the diffusion coefficient. Instead, the unknown is the raw function c(x, t), which defines the location of every higher harmonic generating particle in the sample. The function c(x, t) could be viewed as a spatially distributed sum of Dirac delta functions, but a more accurate theory should also describe the phase information contained in the sample. The complexity of searching for a coherence SIM theory may be circumvented in several ways. A first simple solution would be to assume that the SHG signal is completely incoherent and to apply the corresponding algorithms [161]. Another 136

7.2. EXPERIMENTAL SETUP

option is to use oblique illumination. This technique, described in Section 2.1.3, is, in fact, equivalent to SIM and allows for a twofold better resolution [172– 175]. Nonetheless, oblique illumination and SIM are widefield methods and are therefore difficult to apply to SHG imaging. Fluorescence ISM, combined with pixel reassignment in post–processing, does not necessarily rely on a theoretical model describing the imaging process. The field–of–view shifts between the detector elements are simply derived from the raw data and undone in post–processing. While this method, used in Chapter 6 for 2PE, can straightforwardly be applied to SHG microscopy, we propose a different setup in this chapter. Instead of relying on a custom–built design, we explore the possibility for an add–on module to a commercial laser scanning microscope. A laser power controlling Pockels cell is added to the excitation beam path of a Zeiss LSM510 META and the non–descanned detector system is replaced by a camera. The main benefit of this approach is that the body of the commercial CLSM remains untouched and, consequently, the instrument can still be used as a conventional confocal microscope. A second important advantage of using a camera is its better performance at a high photon flux. While a SPAD detector has a maximum PCR of several MH z, see Chapter 6, each pixel of the camera can collect a much higher number of photons during a pixel dwell time because of the single read–out process. Preliminary images made by the proposed setup are shown as a proof of concept.

7.2

Experimental setup

The proposed setup is sketched in Fig. 7.1. A Pockels cell modulator [176] (M350– 80–LA–02–BK, ConOptics, Acal BFi, Zaventem, Belgium), placed after the Acousto–Optic Modulator (AOM), controls the illumination power from the Mai Tai DeepSee two–photon excitation laser. The Pockels cell contains a Potassium Dideuterium Phosphate (KD*P) crystal which rotates the polarization plane of the incident light over an angle controlled by the electric field amplitude applied to the crystal. The input laser light is horizontally polarized. An output polarizer, pre–aligned to the crystal axis, transmits the vertical component of the rotated electric field. The output power is therefore controlled by the applied voltage, as demonstrated by the calibration data in Fig. 7.2. The high voltage is produced 137


by a linear amplifier (Model 302RM, ConOptics, Acal BFi, Zaventem, Belgium) which sums two signals: a bias voltage which controls the quiescent operating point of the modulator and a differential signal which regulates relative voltage adjustments.

EMCCD Emission filter PC

Lenses NDD port Optocoupler

DAQ

AOM

Zeiss LSM 510

Zeiss PC

Amplifier

Mai Tai DeepSee

Zeiss module

Pockels cell HWP

Figure 7.1: Pockels cell setup for controlling the laser power during the scan process. NDD = non–descanned detection. Zeiss module refers to all electronics controlling the CLSM and sending the trigger signals. See the main text and the list of abbreviations at the beginning of this work for a detailed explanation.

The differential signal consists of a discrete series of voltage values generated at a maximum sample rate of 2 MH z by the analog output port of a Data– Acquisition (DAQ) device (USB DAQmx 6351, National Instruments, Austin, Texas, USA). The voltage values are calculated by a LabVIEW program (National Instruments, Austin, Texas, USA) based on the desired illumination pattern and subsequently transmitted to the internal memory of the DAQ device. All values for a single scan line are sequentially sent to the amplifier upon receiving a trigger signal. The trigger ensures a microsecond accurate synchronization between the movement of the scan mirrors and the laser power. 138

7.2. EXPERIMENTAL SETUP

3.5

Output power [mW]

3 2.5 2 1.5 1 0.5 0 -500

-250

0

250

500

Applied voltage [V]

Figure 7.2: The Pockels cell output power as a function of the applied voltage. About 4 mWof Mai Tai power at 810 nm was incident on the modulator. The data follow a sine pattern (continuous line) with a minimum and maximum transmission power around −380 V and 110 V , respectively. If a linear relationship between the input voltage and the output power is desirable, a bias voltage of about −135 V can be applied (dashed line) with a differential voltage of ±65 V (gray area).

An optocoupler system is placed in between the line trigger output port of the Zeiss communication module and the DAQ device. The system contains a 4N25V optocoupler (Vishay Intertechnology, Malvern, Pennsylvania, USA) to galvanically isolate our electronics from the Zeiss microscope. In addition, a Schmitt–trigger inverter (SN74AC14, Texas Instruments, Dallas, Texas, USA) is installed to alter the output to a standard Transistor–Transistor Logic (TTL) signal of 0 V as the default value and a +5 V pulse as the trigger signal. The electronics circuit of the optocoupler with the Schmitt trigger inverter is drawn in Fig 7.3. The laser light that passes through the Pockels cell module is vertically polarized. Since the Zeiss LSM 510 microscope requires a horizontally polarized input, a HWP, oriented at an angle of 45 ◦ between the main axis of the HWP and the optical table, is placed directly after the Pockels cell. The microscope is controlled with the standard Zeiss computer and functions completely independent of the added modules. The default PMT system at the non–descanned port of the microscope is replaced 139

CHAPTER 7. IMAGE SCANNING MICROSCOPY IN NDD... +5 V DC

6 5 4

1.1 k

0.1 F

0.5 M 10 k

2k

4N25V optocoupler

100

1 2 3

270

Line trigger from Zeiss module

1 2 3 4 5 6 7

14 13 12 11 To DAQmx 10 9 8

SN74AC14 Hex inverter Schmitt trigger

Figure 7.3: Optocoupler system with an inverter Schmitt trigger. The output of this circuit is a short TTL pulse at the start of each scan line.

by an Electron–Multiplying Charge–Coupled Device (EMCCD) (Andor iXon+ DU-888, Andor Technology, Belfast, Northern Ireland). The second harmonic or 2PE signal is focused onto the camera by an f = 3 mm lens. Environmental light is blocked by a black cloth covering the setup and a BP400 − 410 nm filter is installed in front of the camera. The camera is triggered by a line pulse from the optocoupler protected Zeiss electronics trigger output and integrates the signal during a predefined time span. Thereafter, the full image is transferred to the same computer controlling the DAQ device and the camera waits for a new line trigger. All triggers received by the camera during the integration time, if any, are ignored.

7.3

Using the setup for SIM and ISM

Any illumination pattern can be loaded into the LabVIEW program controlling the DAQ device. An esthetically nice, but otherwise inconsequential proof of this possibility is shown at the beginning of this thesis. The image of an old Carl Zeiss microscope was bleached into a sample of immobile rhodamine–B molecules. The Mai Tai laser was set to 810 nm at an average power of about 50 mW. A 40x/1.1 W objective was used and the pixel dwell time was set to 51.2 µ s. The pattern was subsequently imaged in a confocal configuration with 140

7.3. USING THE SETUP FOR SIM AND ISM

a 543 HeNe laser and the same objective. Pixel–wise control over the illumination power makes both scanning SIM and ISM feasible. The first method requires a series of harmonic patterns, each with a different orientation and/or phase. The laser power at each position P(x, y) is given by

¡ ¡ ¢¢ P(x, y) = A 1 + m cos 2π f 0 cos(θ )x + 2π f 0 sin(θ )y + ϕ ,

(7.1)

with A the power offset and f 0 , θ and ϕ the spatial frequency, the orientation and the offset of the pattern, respectively. A preliminary and illustrative example with a fluorescent sample is depicted in Fig. 7.4. Note that for real SIM experiments, the pattern frequency must be about four times higher than the value used for this figure. SIM has several limitations: stage drift (see Section 5.5) and modulation smoothing (see Section 5.3.2) complicate the experiments, and the technique is sensitive to artifacts. Moreover, even in the absence of these limitations, the SIM reconstruction algorithm requires a theoretical model of the system’s OTF. The theory for both linear and non–linear fluorescence is readily available [70]. The coherent nature of some imaging modalities, such as SHG microscopy, though, severely impedes drafting a proper model. Incoherent ISM, on the contrary, does not necessarily rely on a theoretical model. In Chapter 6, before summation, the images from each detector element were simply shifted in both directions over a distance that best suits the data. The same approach could be explored for SHG imaging, in which the theoretical shifts may be different due to the coherence of the signal. If the camera has a sufficiently high frame rate, a full image can be recorded for each position of the laser beam, as sketched in Fig. 7.5. The same 4–dimensional data set as in descanned ISM is obtained. The advantage of this configuration is that no Pockels cell is needed. However, long acquisition times are required. E.g. the Andor iXon camera described in Section 7.2 has a maximum frame rate 141


Figure 7.4: (a) Rhodamine–B calibration pattern imaged with homogeneous illumination. The sample was kindly provided by mr. Thijs Vandenryt and consists of several fluorescent rectangles with different sizes. The pattern was made using electron beam lithography in which the Rhodamine–B powder was mixed with the electron–sensitive resist. Two–photon excitation at 780 nm, 20x/0.75 objective, pixel dwell time 3.20 µ s, EMCCD camera detection, cooled to −60 ◦ C, exposure time 7.9 s, vertical shift speed 12.9 µ s, pixel readout rate 1 MH z, EM gain level 2, preamplifier gain 5x. (b) The same pattern imaged with structured illumination. Pixel dwell time 6.40 µ s, camera exposure time 15.73 s, EM gain level 50, preamplifier gain 5x. Pattern frequency 0.5 /µ m. All other settings are identical to the left image. The sample was removed from and put back onto the stage between both measurements, which explains the different orientations.

of 26 H z for a full frame readout, and 93 H z for a 512x512 pixel area readout. At the former frame rate, collecting all images takes more than 11 hours. Even at the latter frequency, though, almost 3 hours are needed. A million frame per second camera could evidently solve the time issue, but this approach is also extremely ineffective from a data size point–of–view. A camera image is about 1 MB in size. A series of 512 x 512 images then takes more than 260 GB of space. Furthermore, if we consider the emission signal, illustrated by the blue color, covering a moving square area of only 10 x 10 pixels, more than 90 % of the camera is recording noise. Correspondingly, about 236 GB of the storage space is wasted. This method is clearly not feasible to use. 142

7.3. USING THE SETUP FOR SIM AND ISM

Figure 7.5: Possible setup for ISM in non–descanned detection with an EMCCD. A full camera readout is performed at each position of the laser beam, resulting in a total of N 2 images, with N the number of pixels in a single line of the camera (512 or 1024).

A significant improvement can be expected when the Pockels cell is used to create an on/off pattern. The idea is shown in Fig. 7.6. During a frame scan, the laser is periodically turned on and off to illuminate specific locations in the sample. The camera integrates the signal, registering a series of non–overlapping fluorescence emission or scattered SHG patterns. Several frame scans with shifted motifs are needed until the full field–of–view has been covered. The number of scans and camera images is equal. This arrangement circumvents the problem of data storage since e.g. for a 4 x 4 pattern periodicity (n = 4) only 16 images are needed. With a camera frame rate of 26 H z, a measurement takes less than a second. This theoretical limit may not be reached, though, due to constraints on the scan mirror movement and the number of photons produced in a pixel dwell time. Nevertheless, an exposure time in the order of a few seconds is still a huge gain compared to the setup idea from Fig. 7.5. A preliminary experimental example of grid ISM with a fluorescent sample is shown in Fig. 7.7. The same setup can be employed to study SHG ISM.

143


Figure 7.6: More efficient setup for ISM in non–descanned detection with an EMCCD. A full camera readout is performed after a frame scan. A total amount of n2 frame scans is performed and an equal number of frames is recorded, n being the distance in pixels between two closest illuminated positions, n ¿ N.

Figure 7.7: First frame in a grid ISM series of the rhodamine–B calibration sample. Mai Tai laser at 810 nm, on/off pattern periodicity 23 pixels, camera temperature −70 ◦ C, exposure time 7.9 s, vertical shift speed 6.5 µ s, pixel readout rate 1 MH z, baseline offset −200, preamplifier gain 5x.

144

7.4. CONCLUSIONS

7.4

Conclusions

We demonstrated that the Pockels cell module is able to generate any desired illumination pattern. Our camera setup can be implemented in a commercial laser scanning microscope and can be used for both scanning SIM and ISM in non–descanned detection. The on/off pattern generated by the Pockels cell eliminates the requirement for a high frame rate camera and limits the number of images needed.

145

HAPTER

C

8

D YNAMICS OF THE PHOSPHOLIPID SHELL OF MICROBUBBLES : A FLUORESCENCE PHOTOSELECTION AND SPECTRAL PHASOR APPROACH

This chapter is based on Slenders E., Seneca S., Pramanik S. K., Smisdom N., Adriaensens P., vandeVen M., Ethirajan A., Ameloot M. “Dynamics of the phospholipid shell of microbubbles: a fluorescence photoselection and spectral phasor approach”, Chemical Communications, 54 (18), 2018.

CHAPTER 8. DYNAMICS OF THE PHOSPHOLIPID SHELL...

W

e explored the dynamic organization of the 1,2–dipalmitoyl–sn– glycero–3–phosphocholine lipid shell of perfluorobutane gas–filled microbubbles by steady–state fluorescence techniques. Linearly po-

larized two–photon excitation fluorescence microscopy of Laurdan stained microbubble shells indicates that the Laurdan chromophore in the lipid monolayer is surprisingly oriented mainly parallel to the shell surface. This remarkable outcome was seen in microbubbles at room temperature and at 42 ◦ C. We monitored the changing photoselection effect and emission spectrum of a shrinking microbubble, showing that in a time span of 30 minutes to several hours, some lipid shells undergo a dramatic transition to a more rigid structure. Our method allows rapid screening of lipid bubble structures over time for a variety of biomedical applications, such as bioimaging, drug delivery, and theranostics.

8.1

Introduction

Microbubbles are particles between 0.1 and 100 µ m in diameter comprising a gas core that is encapsulated by a stabilizing surfactant shell [61]. These spherical structures find numerous applications, including gas delivery, controlled release of a therapeutic payload for targeted therapy, contrast enhancement in ultrasound imaging, personal care products, aerated food, and foamed construction materials [59, 60, 177–183]. Containers with a lipid monolayer shell are also used as a bioprinting tool for the fabrication of living tissues through scaffold cell seeding [184]. In all these applications, knowledge of the organization and stability of the monolayer shell is crucial. These properties are highly influenced by the composition of the particle. Previously, lipids, lipid mixtures, polymer surfactants, and proteins, or combinations of these ingredients, have been used to design improved stability against rupture, enhanced circulation time in the body, stability against gas dissolution, and target specificity [185–188]. The choice of lipid or lipid mixture, but also of the encapsulated gas, influences the temperature–dependent organization of these lipids [189] and allows to tune the rigidity of the shell [190]. A fast and sensitive method is needed to characterize the shell structure of individual microbubbles, i.e. to obtain information on the shell rigidity and the lipid organization. Here, we describe a non–invasive optical method based on 148

8.1. INTRODUCTION

linearly polarized two–photon illumination of Laurdan stained microbubbles. The fluorescence intensity of Laurdan can be linked to the orientation of the chromophore with respect to the polarization orientation of the incident light, as illustrated in Fig. 8.1. The brightest emission signal is obtained when the absorption transition dipole of the chromophore is aligned parallel to the polarization direction of the excitation light. For increasing angles θ between the chromophore dipole and the polarization direction, the fluorescence intensity will decrease and ultimately vanish for θ = 90 ◦ . The intensity distribution across the shell surface of a microbubble therefore provides information on the orientation of the chromophore. This photoselection effect follows a cos2 θ relationship for 1PE and a more pronounced cos4 θ angular dependence for 2PE [191, 192]. (a)

(b)

Polarization plane of incident light

Figure 8.1: (a) Model of the Laurdan molecule. The green ellipse marks the naphthalene chromophore. The black arrow indicates the orientation of both the absorption and emission dipole moment [193, 194]. The red and blue color represent respectively oxygen and nitrogen atoms. (b) The fluorescence intensity as a function of the angle θ between the Laurdan dipole moment and the polarization plane of the incident light, indicated by the red arrow. The brightness of the green ellipse reflects the fluorescence intensity. In addition, the Laurdan fluorescence emission spectrum depends on the polarity of its immediate environment [195, 196]. In case of phospholipid vesicles in water, the Laurdan emission spectrum maximum exhibits a large red Stokes 149


shift of 50 nm – from 440 nm to 490 nm – when going from the gel to the liquid crystalline lipid phase. This pronounced spectral shift originates from a higher degree of dipolar relaxation of water molecules above the phase transition compared to the gel phase, since more water molecules are surrounding the Laurdan probe in the former situation [197, 198]. Consequently, the fluorescence emission spectrum of Laurdan provides information on the local organization of the lipids, as demonstrated in bilayers by a plethora of researchers [192, 195– 197, 199–208]. Spectral changes can be conveniently quantified with the Generalized Polarization (GP) approach. For an idealized instrument, the GP is defined as [195]

GP =

IB − IR , IB + IR

(8.1)

with I B and I R the Laurdan fluorescence intensity in the blue (440 nm) and green (490 nm) channel, respectively. GP values range from +1 when the Laurdan molecules are mainly emitting in the blue wavelength range to −1 for a red–shifted spectrum with the Laurdan located in a highly polar environment. For GP imaging, the microscopy setup must be calibrated at sample temperature with a reference spectrum. Here, we combine imaging of the GP of Laurdan stained microbubbles with fluorescence intensity measurements at different orientations of the linear excitation polarization. We apply this approach to study the lipid shell structure of 1,2–dipalmitoyl–sn–glycero–3–phosphocholine (DPPC) microbubbles, filled with the non–toxic, inert Perfluorobutane (PFB) gas. Using DPPC, Zuo [209] showed that the monolayer and bilayer phase behavior was similar. We measure the local effective lateral layer rigidity based on 2PE fluorescence imaging with two–channel GP detection and determine the Laurdan chromophore orientation with respect to the shell surface. Dynamic changes in the microbubble shell structure are recorded in time series spanning several hours. Experiments are conducted at room temperature and close to the phase transition temperature of DPPC in vesicles (41.4 ◦ C [210]), to mimic physiological pyrexia conditions. 150


8.2 8.2.1

Materials and methods Laurdan fluorescence

Calibration of GP measurements with the microscopy setup is done by measuring the steady–state fluorescence spectrum of Laurdan in Dimethyl Sulfoxide (DMSO) and comparing this reference result with the GP calculated in the two–channel microscopy setup using the same sample. Discrepancies caused by different sensitivities of the two detectors, the filter properties or any other optical effect are taken into account by computing a correction factor for the lipid measurements. Section 8.2.4 further elaborates on this calculation. Steady–state fluorescence spectra were obtained by an L–format Horiba Fluorolog Tau–3 photon counting spectrofluorimeter (Acal BFi, Eindhoven, The Netherlands). The temperature was controlled by a circulating refrigerated water bath (Neslab RTE–100, ThermoFisher-Scientific, Ghent, Belgium) and unless otherwise indicated, kept at 25 ◦ C in a stoppered fused silica cuvette with internal miniature calibrated NTC temperature probe. Quinine sulphate system spectral sensitivity calibration was carried out according to the NIST protocol [211, 212]. For Laurdan in DMSO, excitation was performed with a 450 W Xe arc lamp at 378 nm and the spectra were recorded in the range of 380 nm to 700 nm. The excitation and emission slit widths were 5 nm, the step size was 1 nm, the integration time was 1 s / step. The photon counting detector was operating in the linear response range. Spectra were blank corrected i.e. subtracting the contribution of DMSO without Laurdan. Each sample was measured at least in triplicate and averaged. Blank corrected concentrations were checked with similar settings and scan speed on a dual beam LS–45 spectrometer (Perkin Elmer, Waltham, MA, USA). The Laurdan fluorescence spectrum in DMSO is shown in Fig. 8.2. Optical arrangement and emission path filter choice and specification as well as detector gain influences the microscope dependent G correction factor for GP calculation. The factor is determined by measuring the GP of a Laurdan containing DMSO sample in the linear concentration–dependent detection response range [67] and comparing this result with a reference value as measured with a steady–state spectrofluorimeter. Calibration samples must have been 151


1

Intensity [a.u.]

0.8 0.6 0.4 0.2 0 300

400

500

600

700

Wavelength [nm]

Figure 8.2: Corrected Laurdan fluorescence spectrum in DMSO at 25 ◦ C. The colored regions correspond to the wavelength ranges of the blue and green channel filters of the microscopy setup. The red lines indicate 440 nm and 490 nm, used for the GP reference calculation.

sufficiently temperature equilibrated and must have the same temperature as the samples under investigation. Illustrating the use of different microscope measurements and filter choice conditions, GP reference values of 0.006 [213] and 0.207 [214] can be found in the literature. A second concern of the calibration is the storage method and handling of the hygroscopic DMSO. 0.1

0 (a)

(b) -0.05

0.05

GP

GP

-0.1 0

-0.15 -0.05

-0.2 GP = 0.00282 * T - 0.09875

-0.1 15

GP = -0.00483 * conc - 0.03152

-0.25 20

25

30

35

40

45

50

55

0

10

20

30

40

Concentration H2O [mM]

Temperature [°C]

Figure 8.3: (a) Laurdan in DMSO calibration for various temperatures. (b) Laurdan in DMSO calibration at 25 ◦ C for various amounts of water added. Small quantities of water present in the hygroscopic DMSO significantly influence the obtained correction factor. Therefore, we measured the temperature dependent reference GP, resulting in the left panel of Fig. 8.3. Good agreement exists with Fig. S3 in Kaiser et 152


al. [215]. Upon further examination, the literature reference value of 0.207 could be understood assuming the use of rather old color glass filters with limited transmission and a sloping broad and partially overlapping spectral bandpass [214, 216–218]. Once steep cut–on optical interference based emission filters with a limited spectral bandwidth of (10 ± 1) nm or (12 ± 1) nm [213, 219] became commercially available, instrument optical characteristics improved. The reported 0.006 value at room temperature for the correction factor was found to correspond with our photon counting spectrofluorimeter data within the tolerances as provided by the filter manufacturer [213]. Technological improvements have recently realized wider optical passband interference filters with a guaranteed transmission efficiency of 95 % or more. Spiking the chromophore solution with small quantities of ultrapure Milli–Q water showed a visually nearly imperceptible redshift. However, as demonstrated in panel (b) of Fig. 8.3, the retrieved GP is highly influenced by the presence of small quantities of water.

8.2.2

Microbubble preparation

DPPC with a 16 carbon tail length was purchased from Avanti Polar Lipids (Alabaster, AL, USA). Spectroscopic grade chloroform (assay 99.3 % stabilized with about 0.6 % ethanol) was obtained from VWR (Haasrode, Belgium). HEPES buffer (pH 7.4) consisting of 10 mM HEPES from Alfa Aesar (assay 99 %) and 150 mM NaCl from Sigma Aldrich (assay > 99.5 %) was used to hydrate the lipid film. PFB gas was obtained from F2 Chemical Ltd (Lea Lane, Lea Town, UK). Laurdan (6-Dodecanoyl-N,N-dimethyl-2-naphthylamine) and anhydrous DMSO (> 99.9 %) were purchased from Sigma Aldrich (Diegem, Belgium). DMSO was kept in the dark under vacuum before use, handled in a dry nitrogen gas filled glove box and was regularly spectroscopically checked using Laurdan for any presence of water. Deionized water obtained from a Sartorius Stedim biotech machine was used throughout the experiments. For the microbubble preparation, in order to avoid debris (unwanted lipid aggregates), a two–step sonication method was developed: in the first step, indirect sonication (using Cup Horn sonicator 450 W digital sonifier, Branson, Danbury, USA) was applied to generate larger PFB-filled microbubbles in a closed vial 153


enclosing the formulation. Subsequently, in the second step, using direct sonication (probe sonicator 450 W digital sonifier, Branson, Danbury, USA) the larger microbubbles (> 50 µ m) were broken down into smaller ones (< 50 µ m) in an open vial. Briefly, the formulation protocol used was the following: DPPC lipid was first dissolved in chloroform (10 mg/mL) in a scintillation vial, blown dry with a mild flow of nitrogen (2 bar) in a closed vial, and further dried overnight under vacuum. The lipid film was then hydrated to 5 mM with HEPES buffer, swirled and sonicated at 60 H z in a VWR ultrasonic cleaner for 120 s at room temperature (21 ◦ C) to detach the lipid, as well as to promote its dispersion. Next, the vial was incubated for 90 min in an oven (Binder, Model BD 56, Tuttlingen, Germany) at sufficiently high temperature – around 20 ◦ C above the main phase transition temperature of DPPC (T m,DPPC = 41.4 ◦ C). Thereafter, a mild stream (1 bar) of PFB gas (F2 Chemicals Ltd, Preston, UK) was applied for 150 s, followed by indirect sonication in a closed vial using the Cup Horn sonicator (employing an amplitude of 70 %) for 90 s ensuring the efficient encapsulation of PFB gas in larger microbubbles. Then, the larger microbubbles were broken down into smaller ones (< 50 µ m) in an open vial by the probe sonicator employing a 14 ” tip and an amplitude of 35 % for 30 s. The sonication frequency of the cup horn sonicator and the probe sonicator is 20 kH z. Finally, the Laurdan (0.5 mM solution in DMSO) was added to the microbubble sample in a 1:500 molar ratio and incubated for 30 min at room temperature. All microbubble samples were washed before imaging or spectroscopic measurements to remove excess probe and debris. To this extent, the microbubble solution was diluted with buffer solution (5x), shaken for a few seconds, and centrifuged for 2 min (using the refrigerated centrifuge Sigma 3–30K and rotor number 12154H) at 300 r pm (RCF = 8 g). Subsequently, the preparation was left for settling for around 3 min during which the floatation of microbubbles on top of the solution occurred. This procedure was repeated three times. After each centrifugation step, the subnatant was removed and fresh HEPES buffer (pH 7.4) was added to the microbubble sample. Afterwards, the preparations were immediately inspected with respect to microbubble morphology, dispersity, and colloidal stability using an Axiovert 40 MAT optical microscope (Carl Zeiss, 154


Oberkochen, Germany). Clean preparations were stored in the dark and at 4 ◦ C until further use.

8.2.3

Microscopy imaging

Microscopy images were obtained with a Zeiss LSM510 META (Carl Zeiss Microscopy GmbH, Jena, Germany) confocal microscope system mounted on an inverted Axiovert 200 M. Unless mentioned otherwise, imaging was performed with a 40x/1.1 water immersion objective (LD C-Apochromat 40x/1.1 W Korr UV-VIS-IR, Carl Zeiss). 7 µL of the sample suspension was poured into a spacer (Grace Bio-Labs SecureSeal imaging spacer, diameter 9 mm, height 0.12 mm) mounted on a microscope slide. A cover slip (thickness #1.5) was pressed onto the spacer. The complete assembly was positioned on the thermostated microscope stage. Measurements were collected on temperature equilibrated samples. Due to the large diameter, most microbubbles were lying still during the acquisition time of an image, which took typically about 15 s. If the microbubble had moved during acquisition, another image was taken. For the long time series measurement, refocusing during the imaging process was necessary to correct for axial drift. 2PE was performed with a femtosecond pulsed laser (Mai Tai DeepSee, Spectra– Physics Inc., Santa Clara, CA, USA) tuned to a central wavelength of 780 nm. Incident laser power at the sample was kept sufficiently low to avoid heating effects or other imaging–induced artifacts such as photobleaching. For photoselection measurements with a rotating excitation polarization plane, LSM510 emission signals were detected with an analog PMT in non–descanned, transmission mode after passing through a condenser lens, a 470 nm beam splitter and a bandpass filter BP475 − 565 nm. The sample temperature was controlled using a cage incubator built around the microscope stage and a temperature controller (Tempcontrol 37-2 digital, PeCon GmbH, Erbach, Germany). Mechanical stability of the microscope setup was ensured by prior incubator warmup. The temperature at the sample position was checked with a calibrated NTC sensor. A homebuilt polarization device containing a rotatable HWP and QWP was installed under the objective. The orientation of the HWP was automatically 155


adjusted with stepper motors (Trinamic PD-110-42, Hamburg, Germany) before the start of each image scan to make a series of images with different orientations of the linearly polarized laser light. For GP imaging, the polarization device was exchanged for a short pass 725 nm dichroic beam splitter under the objective to measure the signal in backward mode. The emission signal was split by a 470 nm beam splitter and detected with two analog PMTs. As indicated in Fig. 8.2, BP405 − 455 nm and BP475 − 565 nm emission bandpass filters were used for the blue and the green channels, respectively. The transmission signal was simultaneously detected in forward mode after passing through a condenser lens.

8.2.4

GP analysis protocol

The GP is defined as [196, 197, 199, 200, 220–223]

GP =

IB − IR , IB + IR

(8.2)

where I B and I R are the fluorescence intensity at 440 nm and 490 nm respectively. Limiting values are +1 (highest GP) and -1 (lowest GP). High GP values in a lipid environment correspond to a rigid, ordered shell phase. Low GP values indicate a more fluid, disordered phase. Each step in the GP protocol is illustrated by a panel of Fig. 8.4. Analysis of the acquired microscopy data was performed with in–house developed Matlab scripts (Matlab R2017b, The Mathworks, Inc., Eindhoven, The Netherlands). Microbubble microscopy images in the transmission, blue and green channels are shown in panels (a)–(c). First, the dark current signal was subtracted from each pixel value. From both images, the GP was calculated pixel–wise, panel (d), using the formula

GP =

IB − G IR , IB + G IR 156

(8.3)


Transmission channel (a)

Blue channel with dark current subtraction (Ib)

Green channel with dark current subtraction (Ig)

(b)

(c)

GP = (Ib - G Ig) / (Ib + G Ig) (d)

GP with mask - cropped (g)

Ib + Ig (e)

Threshold based mask (f)

GP histogram + Gaussian fit (h)

Phasor plot (i)

Figure 8.4: GP analysis protocol illustrated with a DPPC–PFB microbubble at 42 ◦ C.

157


with I B and I R the fluorescence intensity, i.e. the pixel value, in the blue (405455 nm) and green (475-565 nm) channel, respectively. The parameter G is a correction factor [213] used to calibrate the instrumental spectral response since the absolute GP value is strongly affected by instrument specific factors. This

G factor also compensates for the effect of using bandpass filters instead of measuring at single peak wavelengths [195]. Calibration experiments were performed by comparing microscopy images of Laurdan in the reference solution DMSO with steady–state fluorescence spectra of the same sample recorded on a thermostated Fluorolog Tau–3 photon counting spectrofluorimeter. Applying Eq. 8.2 to the measured spectrum at room temperature (21 ◦ C) yields a GP value of Laurdan in DMSO of 0.068. The G factor for the microscopy setup is then calculated by plugging in this reference value in the following formula:

G=

I B (1 − GP) . I R (1 + GP)

(8.4)

I B and I R are the average intensity values measured with the fluorescence microscope in the blue and green channel, respectively. For optimal signal–to–background, the sum of the fluorescence signal in the blue and the green channel, panel (e), was used to create a mask, panel (f), by setting pixel values above a user defined threshold to 1 and background pixels to 0. A smoother mask was created by a median filter. This filter was then applied to the GP image, panel (g), removing the background signal from the microbubble shell. A histogram of the remaining GP values was calculated, panel (h). Instead of solely evaluating the peak location by fitting the top of the histogram with a Gaussian function, as shown with the black line, we used the phasor calculation [205, 223]. This method does not only analyze the histogram peak but, instead, all bins are taken into account. The result is a single point in Fourier space, panel (i). 158


Phasor calculation produces a coordinate set (G, S) in two dimensions by applying the following transformation:

G

=

S

=

#(GPP ) cos (2π nGP/L) , #(GP ) P #(GPP ) sin (2π nGP/L) , #(GP )

P

(8.5) (8.6)

where #(GP) is the bin height in the histogram with center value GP, n is the number of the harmonic, set to 1 for the first order phasor used here, and L is the difference between the maximum and minimum GP value possible, i.e. 2. Summation runs over all GP bins. The presented protocol is a novel way for mapping the shell structure of lipid microbubbles. Instead of calculating the phasor coordinates based on a complete spectrum [205, 223–225], our implementation only requires the measurement of the fluorescence intensity based image in two optical channels. The shape of the resulting GP histogram obtained over the monolayer related pixels is analyzed with the phasor calculation. The phasor approach is appealing since it is a model–free transformation that produces a single coordinate in Fourier space. Interpretation of the data and comparison of several conditions becomes convenient and intuitive. Data points located in the lower left quadrant of the phasor plot correspond to the least rigid and most water molecule accessible shell structure. By rotating counterclockwise, one enters regions with a higher and more ordered shell structure and reduced access of water molecules to the chromophore. The width of the GP distribution can be derived from the distance to the origin; the higher the modulus (S 2 + G 2 ), i.e. the distance from the center, the narrower the GP distribution [221]. The phasor approach is illustrated in Fig. 8.5.

8.3

Results and discussion

Fig. 8.6 provides an overview of the microbubble imaging and GP analysis results. The majority of the microbubbles exhibit an intensity distribution similar to the first row of Fig. 8.6, i.e. with the Top (T) and Bottom (B) part brighter than the 159


Figure 8.5: Illustration of the phasor approach.

Left (L) and Right (R) side. Since the illumination light is horizontally polarized, these images indicate that the absorption dipole of the chromophoric moiety of Laurdan is, surprisingly, mainly aligned with the microbubble shell surface. This result is in stark contrast to earlier observations of Laurdan stained lipid bilayers made by others on giant unilamellar vesicles [200, 201, 203] where the polarization dependence of the fluorescence of Laurdan is rotated over 90 ◦ with respect to our observations and has maximal intensity at the L and R sides. Rotating the polarization direction of the incident laser light confirms the orientation of the absorption dipole with respect to the shell surface, see Fig. 8.7. In some Laurdan stained microbubbles, however, the photoselection effect creates a brighter L and R side compared to the T and B side, as illustrated in the 160


second row of Fig. 8.6. In these cases, the chromophore dipoles are apparently oriented perpendicularly to the shell surface, pointing radially. We observed this behavior both at 25 ◦ C and at 42 ◦ C. Microbubbles with a clear T–B photoselection pattern systematically have a lower average GP than bubbles with a clear L–R pattern, as shown in the last column of Fig. 8.6. In the T–B case, the GP values are highly negative. In contrast, in the L–R case, these are closer to zero or positive. Clearly, the L–R fluorescence intensity pattern and the high GP values in the second row in Fig. 8.6 demonstrate that the lipid shell structure of some microbubbles can differ significantly from other microbubbles within the ensemble. Moreover, a microbubble containing simultaneously both the low and the high GP phase was found, as shown in Fig. 8.8. To determine whether a microbubble shell may evolve from one state to the other, we imaged individual microbubbles in a time series spanning several hours. For each pair of blue and green channel images, the GP values were computed pixel–wise and plotted in a histogram. We evaluated each histogram with the first–order phasor calculation [223, 225]. The resulting phasor plot is shown in the left panel of Fig. 8.9. A video of the measurement can be found at

http://www.rsc.org/suppdata/c8/cc/c8cc01012a/c8cc01012a2.mp4.

161


Figure 8.6: Photoselection and GP observed in Laurdan stained DPPC–PFB microbubbles imaged with 2PE laser scanning microscopy. From left to right, column 1 (a, e, i, m): transmission images. Column 2 (b, f, j, n): blue Laurdan fluorescence emission channel. Column 3 (c, g, k, o): green Laurdan fluorescence emission channel. Right column (d, h, l, p): GP calculated pixel wise from the blue and green images. Most transmission images show multiple microbubbles. However, because of the optical sectioning effect intrinsically present in 2PE microscopy, only the sections of the microbubbles that are in focus are clearly visible in the blue and green fluorescence channels. Top and third row images show bright T and B shell regions, while the L and R side emit less fluorescence. The apparent shell thickness is influenced by the photoselection effect, creating the illusion of thicker T–B shell segments compared to the L and R sides, top row. The second and fourth row exhibit an opposite pattern. GP values are indicated by the upper right color bar. The excitation polarization is horizontal, as indicated by the white arrows. Illumination wavelength is 780 nm. Scale bars are 50 µ m and hold for the first three columns. The microbubbles in the GP panels are zoomed in. Brightness and contrast are individually adjusted for all images for visualization purposes. 162


Figure 8.7: Excitation polarization dependence of the fluorescence of Laurdan in the equatorial plane of a DPPC–PFB microbubble at 25 ◦ C. White arrows indicate the plane of excitation polarization which is varied in steps of 18 ◦ . Emission bandpass filter 475 − 565 nm. Zeiss Plan–Apochromate 20x/0.75 objective. The scale bar in the upper left image represents 50 µ m.

Figure 8.8: From left to right: transmission image, blue fluorescence channel, green fluorescence channel, GP image and GP histogram of a DPPC–PFB microbubble at 42 ◦ C showing phase separation. The scale bar represents 20 µ m. The L side of the microbubble has a positive GP, indicating a local rigid domain in an otherwise negative GP shell.

163


1

1

25 °C 42 °C

2

S

S

3

0

Time [h]

4

0

1

-1 -1

-1 -1

0

0

1

0

1

G

G

Figure 8.9: (Left) Phasor plot of the shell dynamics at 25 ◦ C of a single Laurdan stained DPPC–PFB gas–filled microbubble collected over a time interval of almost five hours. From each pair of blue and green channel fluorescence images, a histogram of GP values is calculated and analyzed with the phasor method, resulting in a pair of (G, S) coordinates for each time point. Data points are colored according to the progress in time using the color bar on the right. (Right) Phasor plot of 11 DPPC–PFB microbubbles at 25 ◦ C and 10 microbubbles at 42 ◦ C. Three classes of microbubbles can be found using a hierarchical cluster algorithm in Matlab. The first class, class I, represented by the squares, corresponds to lipid shells with negative GP values and a T–B photoselection effect. Shell structures that became more rigid after the shrinking process constitute a second group, class II, with much higher GP values, indicated by the positions of the triangular data points, and an L–R fluorescence intensity pattern under horizontally polarized laser light. The diamond shape (center right) refers to a microbubble in a third group, class III, undergoing the transition from the first to the second class during the shrinking process. The lower left quadrant of the plot corresponds to a low overall GP, close to −1, as indicated by the red colored circle segments. Data points located counterclockwise from this quadrant have continuously increasing GP values up to +1 in the upper left quadrant, as illustrated with the color gradient in the circles. The larger the distance from the center of the circle, the narrower the GP distribution.

164


At the start of the time lapse measurement, the microbubble has a T–B photoselection effect and a negative GP, similarly to the first row of Fig. 8.6. The corresponding histogram leads to a data point in the lower left quadrant of the phasor plot. During the first 90 min, consecutive images all yield similar (G, S) locations. Then, the microbubble starts shrinking, as shown in panel (a) of Fig. 8.10. The angular intensity distribution rotates 90

◦

and the blue

channel fluorescence becomes brighter than the green channel signal. In the phasor plot, the data points move progressively counterclockwise ending up in the upper left quadrant almost 3 hours after the start of the shrinking process. The microbubble shrinks about 35 % in diameter, which corresponds to a reduction in the surface area of about 58 %. It can be concluded from the right panel of Fig. 8.10 that the transition is accompanied by large fluctuations in the fluorescence intensity. Shedding sections visible at a given image scan have disappeared in the next scan 2 min later. These ubiquitous shedding shell sections display a high GP and may be related to reported zippering effect resulting in bilayer structures [226–231]. During the last 40 min of the measurement, the bubble is in a stable configuration, with no significant change in radius or phasor coordinates. Shedding events disappeared simultaneously. 60

2 (b)

Normalized intensity [a.u.]

(a)

Diameter [ m]

55

50

45

40

35

1.5

1

0.5

0 0

1

2

3

4

5

Time [hours]

0

1

2

3

4

5

Time [hours]

Figure 8.10: (a) Microbubble diameter as a function of time for the shrinking microbubble in Fig. 8.9, measured by manually selecting the white microbubble border in each frame of the transmission channel. (b) Corresponding fluorescence intensity in the blue and green channel, normalized to the average intensity per pixel for the first time point.

Additional representative cases are plotted in the right panel of Fig. 8.9. The 165


phasor calculation of 21 individual microbubbles at a single time point shows two main classes of shell rigidity with different fluorescence intensity patterns and one microbubble undergoing the transition towards the more rigid shell class. The observed T–B photoselection and the corresponding GP images can be explained by several models. Unlike for most lipid bilayers, where the dipole moments of the Laurdan chromophores are mainly oriented perpendicularly to the membrane surface, aligned with the lipid chains, the Laurdan chromophore moiety in microbubbles is preferentially oriented parallel to the shell surface. A similar result was obtained by Bagatolli et al. on giant liposomes composed of the polar lipid fraction E from the thermoacidophilic archaebacterial Sulfolobus acidocaldarius [232]. Bagatolli et al. concluded that the most plausible configuration for the observed Laurdan photoselection effect in the archaebacteria is that the chromophoric naphthalene ring is located in the lipid polar headgroup region with the absorption dipole essentially aligned parallel to the membrane surface, while the lauroyl tail is parallel to the lipid hydrocarbon chain, pointing radially. In this way, the polar carbonyl group is close to the water environment and the apolar acyl chain is surrounded by the hydrophobic lipid tails. The possibility for this L–shape conformation of Laurdan has been theoretically confirmed in DPPC vesicles in the liquid crystalline state [204] and for DOPC lipid bilayers [193]. In addition, the low GP values indicate a strong dipolar relaxation effect, confirming the close proximity of water molecules surrounding the Laurdan chromophore [195]. Alternatively, the lipid tails may be oriented nearly parallel to the shell surface instead of pointing towards the center of the microbubbles. This configuration seems feasible since the PFB gas is lipophobic [233] and the lipid density in the shell may not be high enough to force the lipid tails to point radially inwards. In this situation, the Laurdan molecules will adopt an elongated configuration and will be aligned with the shell surface with the carbonyl group pointing towards the water environment. As a result, a T–B photoselection effect combined with a negative GP can be expected. A similar surmised tail model was found by the group of Roke for sodium dodecyl sulfate at the oil–in–water droplet liquid/liquid interface [234]. 166


The temporal evolution of the microbubble can be explained in the context of PFB gas diffusion. Dependent on the diameter, the initial PFB gas content and the density of the lipid shell surrounding the gas bubble, the PFB gas may diffuse at different rates from the microbubble core to the medium environment. A deflating microbubble will shrink and the increasing lipid density may change the lipid organization in the shell. The observed Laurdan photoselection effects and the GP values indicate that after the shrinking process, fewer water molecules are surrounding the chromophores, which are then oriented perpendicularly to the shell surface. We present a possible model to explain this behavior. Upon shrinking of the microbubble, the lipid to gas ratio increases. Assuming not all of the excess lipids will be shed from the bubble shell in the form of vesicles or lipid aggregates, the lipid concentration per unit area will rise and will force the molecules to reorganize from a loosely covered shell to a more densely packed configuration [235]. The lipid heads will move closer to each other, pushing the hydrophobic tails into the gas core. Consequently, the Laurdan molecules will also move inwards and will adopt the elongated conformer configuration [204], due to the increased density of the lipid tails. The naphthalene groups can populate the phospholipid glycerol region [236], with the long naphthalene axis parallel to the shell normal. The carbonyl groups will reside below the hydrophobic–hydrophilic interface [204]. GP values will turn positive when the number of water molecules surrounding the Laurdan naphthalene groups decreases. A changing orientation of the chromophore moiety results in an L–R photoselection intensity pattern upon horizontally polarized illumination. Fig. 8.8 indicates that this process may start locally in a small segment of the bubble. It cannot be excluded, however, that this peculiar arrangement resulted from a merger of two neighboring microbubbles. Alternatively, the whole shell structure may simultaneously, but gradually, undergo the transition, as observed in the time series measurement presented in Fig. 8.9. Fig. 8.11 provides an overview of the proposed models. Our model for the Laurdan position and orientation in the shrunken microbubble is comparable to the expected behavior of Laurdan in a lipid bilayer in the gel phase [204]. Furthermore, the positive GP values found in DPPC vesicles below 167


Figure 8.11: 3D view of a microbubble with the focal plane indicated. The cross section panels show in detail the proposed configurations for the Laurdan and DPPC molecules across the shell surface, both for a large microbubble with a T–B photoselection pattern and a smaller microbubble with an L–R fluorescence intensity pattern. The arrows indicate the polarization plane of the incident light. In model I and model II, the Laurdan chromophores are aligned with the shell surface and consequently the T and B part of the microbubble will produce the most intense fluorescence signal. In the smaller microbubble, the lipid density has increased, and therefore the lipid tails must be pointing radially, despite the lipophobicity of the PFB gas. Consequently, the Laurdan molecules will adopt the elongated shape and most of the fluorescent light will be produced by the L and R side of the bubble, see the L–R model.

the phase transition temperature [197, 203] are close to our observations of the shrunken microbubbles, both at room temperature and at 42 ◦ C. However, it cannot be concluded that the lipid structure in a gas–filled, shrunken microbubble is similar to the organization of a bilayer. Photoselection and GP measurements on Laurdan stained giant unilamellar vesicles showed a temperature driven change in GP values upon going through the phospholipid main phase transition, while the angular distribution of the fluorescence intensity did not change [237]. In contrast, we observed a temperature dependence of neither the GP values nor the photoselection effect. Instead, we measured a transition in which the shell rigidity increases and the angular intensity distribution switches from T–B to L–R. The simultaneous shrinkage of the microbubble suggests that this transition can be induced by diffusion of the PFB gas and increased lipid density. 168

8.4. CONCLUSIONS

Our observations would benefit from detailed calculations on the interactions between PFB gas and lipids – as lipid tail cooperativity may be influenced by PFB gas [238–240] – which is outside the scope of the present work.

8.4

Conclusions

In conclusion, the lipid organization of the lipid shell of microbubbles was investigated by a microfluorimetric approach using the lipid probe Laurdan which is sensitive to water molecule proximity. By changing the excitation polarization direction, we have shown that the Laurdan chromophore is surprisingly oriented mainly parallel to the shell surface in gas–filled DPPC–PFB microbubbles. The negative GP values indicate a low shell rigidity, implying a high penetration of water molecules. However, some microbubbles revealed a 90 ◦ rotated intensity pattern, combined with higher GP values, indicating a restricted penetration of water molecules. We observed this effect both at 25 ◦ C and at 42 ◦ C. We demonstrated with a time series measurement that this complex behavior relates to shrinking of the microbubbles, induced by PFB gas diffusing into the surrounding air saturated medium. Enhanced resolution microscopy techniques, such as SIM [63] and single molecule techniques [38, 241], may be helpful as a future guideline to check the effect of possible dye clustering on the observed GP values. This requires that proper laser excitation is available for the Laurdan dyes and that probe concentrations are validated for absence or presence of concentration quenching. This fast and sensitive linearly polarized illumination approach as described will aid selection and sorting of lipid shell encapsulated gas–filled microbubbles. The non–invasive optical methods presented here provide a useful extension to the Spectral Imaging Toolbox provided by Aron et al. [222] for the characterization of individual microbubbles. This extension opens the path for screening and sorting through the use of phasor plots of individual microbubble shells and sections thereof, or through a photoselection analysis. This may contribute to designing microbubbles with a shell rigidity optimized for specific (bio–)engineering applications.

169

HAPTER

C

9

C ONCLUSIONS AND OUTLOOK

CHAPTER 9. CONCLUSIONS AND OUTLOOK

T

he microscope image is the interference effect of a diffraction phenomenon. Often summarized with this sentence, Abbe’s theory provides a mathematical framework for describing the optical image formation process. A

direct consequence of the theory is the resolution limit, which played a central role in this work. A conventional optical microscope cannot resolve structures in the specimen smaller than the Abbe limit, which is typically about 250 nm. We explored two ways to deal with this law of microscopy. A first approach was to search for a method that circumvents the diffraction limit. Secondly, we used a priori sample information to extract subdiffraction information from a diffraction limited system. More specifically, the diffusion properties of nanometer–sized particles and the orientation of fluorescent molecules in a lipid shell were studied. In this chapter, we describe to which extent the aims formulated in Chapter 1 have been realized. The main conclusions discussed in the previous chapters are briefly recapitulated, and we present some ideas for follow–up work.

9.1

Correlation spectroscopy with harmonic nanoparticles

As a consequence of Abbe’s diffraction limit, light waves focused by a lens do not converge into an infinitesimally small point but, instead, they constitute a micrometer–sized focal volume. Probing the emission intensity produced by fluorescent nanoparticles diffusing through this focal volume with methods such as FCS, RICS, and STICS allows extracting information on the mobility of the particles. Fluorescence–based methods have, however, several disadvantages, of which photobleaching is the main issue in long–term studies. In contrast, the signal produced by higher harmonic generating materials is extremely stable, though it necessitates a different model to analyze the correlation spectroscopy data because of the coherent nature of SHG and THG. Although the mathematics involved in coherent imaging is significantly more complex than in fluorescence imaging, we have in Chapter 3 been able to analytically derive the expressions for the coherent counterparts of FCS, TICS, RICS and STICS. Our cIFM converges, as expected, to the fluorescence expressions in the low concen172

9.1. CORRELATION SPECTROSCOPY WITH HARMONIC...

tration limit. When the average number of particles residing simultaneously in the focal volume increases to more than one, the effect of coherence can be noticed. The cIFM method was used in Chapter 4 to analyze diffusion experiments with SHG active LiNbO3 and BaTiO3 nanoparticles. cRICS measurements in aqueous suspensions surprisingly showed a ridge in the ψ = 0 line of the ACF superimposed on top of an otherwise normal looking function. The presence of this ridge is not predicted by the cIFM. In our model, the signal generated by each NP is assumed to be solely dependent on its relative position in the sample with respect to the illumination focal volume. The influence of the orientation of the NP, comparable to the photoselection effect in a fluorescent molecule, is not taken into account. The faster time scale of rotational diffusion compared to translational diffusion suggests that the observed ridge is the result of a Brownian motion induced changing orientation of the NP while illuminated by the laser beam. FCS has already decades ago been used to examine the rotational diffusion of fluorescent molecules [242, 243]. Adding the effect of rotational diffusion to the cIFM and theoretically checking the presence of a central ridge would be an interesting follow–up study. If Brownian rotational motion turns out not to explain the ridge, further research would be needed to check whether light–matter interactions, e.g. optical trapping, can cause this behavior. While the central ridge could not be used in the process of fitting the diffusion coefficient, the remainder of the cRICS ACF displayed the expected behavior and the measured diffusion coefficient matches the theoretical value when the cIFM is used. We showed that employing the fluorescence expression to analyze the same lines will produce poor fit residuals and a wrong diffusion coefficient. If, however, the PSF width is extracted from the ψ = 0 line with the fluorescence formula, and the remaining data is fitted with the same expression, the correct diffusion coefficient is found for our samples. This outcome raises the question whether the cIFM could in more situations be replaced with the simpler fluorescence model. E.g. could a suspension containing multiple species, each having a different diffusion coefficient, be analyzed with the multicomponent fluorescence model, provided the proper PSF width? On the one hand, due to the 173


coherence in SHG, the ACF of a multicomponent sample cannot be assumed to simply be the sum of the individual ACFs. On the other hand, if the coherence in the signal influences the ACF in the same way as a different PSF would, the effect of coherence may be neglected, in a similar fashion as we illustrated for one–component samples. The answer to this question is unknown today, but certainly not unimportant. When investigating NP uptake by live cells, for example, two components can be present. Some NPs may be freely diffusing in the cytosol, while others are taken up by the slower and directionally moving cell organelles. Being able to separate the components would allow obtaining a more accurate description of the behavior of the NPs in a cell. Measuring the diffusion coefficient of LiNbO3 nanoparticles in live cells was possible by means of a cSTICS experiment. By imaging 200 frames and analyzing regions of 64 x 64 pixels, we were able to locally probe the heterogeneous diffusion coefficient, which turned out to be more than 103 times lower than in suspension. This value indicated that the NPs were not freely diffusing in the cytosol. Colocalization with stained lysosomes and endosomes showed uptake of the NPs by these cell organelles. The same 20x/0.8 objective as in the cRICS measurements was used. Future experiments with a higher NA objective and a smaller pixel size could reveal whether direct flow is present in the movement of the lysosomes and endosomes, and could therefore quantify the transport of the cell organelles along the actin microfilaments and the microtubules.

9.2

Resolution enhancement in multiphoton imaging

Widefield SIM is difficult to combine with multiphoton microscopy because of the requirement of an extremely high photon flux. As described in Chapter 5, modulating the laser power to generate a SIM pattern while scanning theoretically provides a resolution enhancement, but is not feasible due to modulation smoothing. ISM, in contrast, is definitely a workable solution. We showed in Chapter 6 a significant resolution improvement with fluorescent beads and with stained fixed MDA–MB–231 cells. The large penetration depth of the IR excitation radiation makes deep tissue imaging possible. Using ISM, we obtained a 174

9.3. COMBINING CORRELATION SPECTROSCOPY AND ISM

16 % resolution enhancement in a mouse brain at a depth of 70 µ m compared to confocal microscopy. This relatively modest improvement can partially be attributed to a low signal–to–noise ratio, which may be increased by cooling the detector or using lock–in detection, and partially to a higher degree of scattering of the emission light compared to a 2D specimen, even though the sample had been optically cleared. In addition, the pixel reassignment algorithm may not have found the optimal shift values as a result of the low PCR. A more sophisticated algorithm might be able to produce a better resolution image from the same data set. Being able to store the unprocessed data is therefore a huge advantage compared to the all–optical reconstruction strategy. The approach explored in Chapter 7, with camera detection implemented at the non–descanned port of a commercial CLSM, holds the same advantage, but further research is needed to apply this technique to 2PE or SHG. Secondly, ISM has the flexibility to be combined with other imaging techniques, such as RICS (see Section 9.3), fluorescence lifetime imaging [244] and STED microscopy. STED microscopy, in particular, could benefit from an array detector since ISM could account for part of the resolution enhancement and, consequently, a less intense STED beam is required to obtain the same resolution as in a conventional STED setup.

9.3

Combining correlation spectroscopy and ISM

The two main topics of this thesis, autocorrelation spectroscopy and resolution enhancement via ISM, can be elegantly connected through ISM–RICS, a RICS measurement with the optical design of ISM. Instead of integrating the emission signal with a point–detector in descanned mode for 1PE or in non–descanned mode for 2PE, employing the detector array of an ISM setup may have several advantages. For sufficiently low diffusion coefficients, recording RICS images and reassigning the pixels based on a calibration measurement is similar to p a conventional RICS experiment with a 2 smaller focal volume. Probing a smaller volume increases the relative intensity fluctuations, which should result in a more accurate value for the fitted diffusion coefficient. Moreover, a smaller PSF allows to measure the diffusion properties locally and to create high–resolution diffusion maps [245]. Alternatively, a global analysis of the 175


signal from all detector elements could be performed, e.g. by calculating the cross–correlations between all combinations of two detector elements. A better defined ACF can be expected due to a large number of detector elements. For the latter strategy, however, a new theoretical model is needed, since each element has a different detection PSF. The cross–correlation thus solely arises from the intersection of each pair of focal volumes. In 2PE microscopy, a second obstacle is the low number of detected photons. E.g. for the current uncooled prototype system described in Chapter 6, about 11 photons per excitation spot were on average collected by the ISM detector in the fixed cell sample. These 11 photons are distributed over 25 detector elements, meaning that most elements do not observe any photon during a pixel dwell time. The use of a detector array is thus limited by the signal–to–noise ratio, which itself is limited by both the design characteristics and photobleaching. The long–term stability of the SHG and THG signal makes ISM–cRICS a promising tool. Depending on the number of detector elements, the illumination power could be significantly increased until a sufficient PCR is obtained. While the experimental aspect of ISM–cRICS may be more convenient than in ISM–RICS, the challenge concerning the analysis of coherent signals remains. To calculate the higher harmonic intensity as a function of the position in the image plane, a drastically more complex model, compared to the cIFM, is needed. Based on the results of Chapters 3 and 4, one can be optimistic, though, since this issue may be circumvented. For low enough particle concentrations, the SHG signal can be treated as a simpler incoherent signal. The ACF of a high concentration system can be made incoherent–like by adjusting the PSF size in the model. The same approach could be tested for cCS and cSTICS. The global analysis approach is in particular crucial in cCS, since the steady laser beam in this technique makes pixel reassignment impractical.

9.4

Microbubble shell characterization

The lipid shell of DPPC–PFB microbubbles stained with Laurdan was studied in Chapter 8 by using the fluorescence photoselection effect and the GP. Most microbubbles surprisingly showed more intense T–B shell segments compared to 176

9.4. MICROBUBBLE SHELL CHARACTERIZATION

the L and R sides, both at room temperature and at 42 ◦ C. A quantitative analysis of these shells with the GP technique revealed a high penetration of water molecules, indicating a low shell rigidity. Some microbubbles, however, showed a completely opposite behavior: brighter T–B shell segments and a high GP. The higher shell rigidity of these microbubbles indicates a different organization of the lipid molecules in the shell. A microbubble can undergo a transition from the first to the second class upon gas–leakage induced shrinking. The higher GP of class II microbubbles suggests an improvement in stability against rupture and longer circulation times in the human body. These hypotheses, as well as the acoustic response of the microbubbles, must be evaluated in future research. In a next phase, the most stable microbubbles can be stained with a self–quenching dye to check their performance in acousto–optic imaging. This hybrid technique would enable deep tissue imaging, combined with the specificity of fluorescence.

177

PPENDIX

A

A

D ERIVATION OF THE COHERENT INTENSITY FLUCTUATION MODEL FOR AUTOCORRELATION IMAGING SPECTROSCOPY WITH HIGHER HARMONIC GENERATING POINT SCATTERERS

This appendix is based on the Supporting Information of Slenders E., vandeVen M., Hooyberghs J., Ameloot M. “Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating point scatterers – a comprehensive theoretical study”, Physical Chemistry Chemical Physics, 17, 2015.

APPENDIX A. DERIVATION OF THE CIFM

T

he first and second section of this appendix contain the full derivation of the general cIFM for three and two dimensional diffusion, respectively. Section 3 describes the earlier published fIFM. The fourth section uses

the cIFM to derive the ACF for cSTICS, cRICS, cTICS and cCS. The low and high particle concentration limit of our model is derived in Section 5 and compared to the fIFM. In Section 6, the fit simulations for the parameter retrieval are explained in more detail. A summary and a convenient overview of the used symbols and typical values for these quantities are listed at the end of this appendix.

A.1

Derivation of the cIFM

In autocorrelation spectroscopy, the intensity of the scattered or emitted light measured at the points (r 0 , t) in space and time is correlated with the intensity at the points (r 0 + ρ , t + τ). More specifically, the ACF G(ρ , τ) is defined as:

G(ρ , τ) = =

〈δ I q (r 0 , t)δ I q (r 0 + ρ , t + τ)〉

(A.1)

〈 I q (r 0 , t)〉2 〈 I q (r 0 , t)I q (r 0 + ρ , t + τ)〉 − 〈 I q (r 0 , t)〉2 〈 I q (r 0 , t)〉2

,

(A.2)

where 〈 · 〉 is the average intensity, calculated over all measured points in space (r 0 ) and time (t). The total intensity I q (r 0 , t) is proportional to the squared modulus of the total field amplitude, which is expressed as the complex sum of the signals coming from the particles [90]:

¯2 ¯ ¯ ¯Z ¯ ¯ ( q) ¯2 ¯¯ I q (r 0 , t) = ¯χ ¯ ¯ A q (r − r 0 )c(r, t)dV ¯¯ .

(A.3)

Here, χ( q) is the electric susceptibility of the scatterer material and c(r, t) is the particle concentration, which can be represented as a sum of Dirac delta 180

A.1. DERIVATION OF THE CIFM

functions. A q (r) combines the illumination point spread function and the Gouy shift κ q :

£ ¤ A q (r) = A ∗q (r) cos(κ q z) − i sin(κ q z) ,

(A.4)

p p with A ∗q a 3D Gaussian function with a lateral width ω0 / q and a height z0 / q :

Ã

A ∗q (r) = A q0 exp −

x 2 + y2 ω20 /q

!

Ã

exp −

z2 z02 /q

!

.

(A.5)

Eq. (A.3) can thus be rewritten as

¶2 ¯ ¯ µZ ¯ ( q) ¯2 ∗ A q (r − r 0 ) cos(κ q (z − z0 ))c(r, t)dV + I q (r 0 , t) = ¯χ ¯ ¶2 ¯ ¯ µZ ¯ ( q) ¯2 A ∗q (r − r 0 ) sin(κ q (z − z0 ))c(r, t)dV . ¯χ ¯

First we calculate term 1 in the numerator of Eq. (A.2): 181

(A.6)


term1 = 〈 I q (r 0 , t)I q (r 0 + ρ , t + τ)〉 ¯ ¯ ZZZZ ¯ ( q) ¯4 =〈 ¯χ ¯ A ∗q (r 1 − r 0 ) cos(κ q (z1 − z0 ))c (r 1 , t) A ∗q (r 2 − r 0 ) cos(κ q (z2 − z0 ))c (r 2 , t) A ∗q (r 3 − r 0 − ρ ) cos (κ q (z3 − z0 − ρ z ))c (r 3 , t + τ) A ∗q (r 4 − r 0 − ρ ) cos (κ q (z4 − z0 − ρ z ))c (r 4 , t + τ) dV1 dV2 dV3 dV4 〉 ¯ ¯4 ZZZZ ¯ ¯ + 〈 ¯χ( q) ¯ A ∗q (r 1 − r 0 ) cos(κ q (z1 − z0 ))c (r 1 , t) A ∗q (r 2 − r 0 ) cos(κ q (z2 − z0 ))c (r 2 , t) A ∗q (r 3 − r 0 − ρ ) sin (κ q (z3 − z0 − ρ z ))c (r 3 , t + τ) A ∗q (r 4 − r 0 − ρ ) sin (κ q (z4 − z0 − ρ z ))c (r 4 , t + τ) dV1 dV2 dV3 dV4 〉 ¯ ZZZZ ¯ ¯ ( q) ¯4 + 〈 ¯χ ¯ A ∗q (r 1 − r 0 ) sin(κ q (z1 − z0 ))c (r 1 , t) A ∗q (r 2 − r 0 ) sin(κ q (z2 − z0 ))c (r 2 , t) A ∗q (r 3 − r 0 − ρ ) cos (κ q (z3 − z0 − ρ z ))c (r 3 , t + τ) A ∗q (r 4 − r 0 − ρ ) cos (κ q (z4 − z0 − ρ z ))c (r 4 , t + τ) dV1 dV2 dV3 dV4 〉 ¯ ¯4 ZZZZ ¯ ¯ + 〈 ¯χ( q) ¯ A ∗q (r 1 − r 0 ) sin(κ q (z1 − z0 ))c (r 1 , t) A ∗q (r 2 − r 0 ) sin(κ q (z2 − z0 ))c (r 2 , t) A ∗q (r 3 − r 0 − ρ ) sin (κ q (z3 − z0 − ρ z ))c (r 3 , t + τ) A ∗q (r 4 − r 0 − ρ ) sin (κ q (z4 − z0 − ρ z ))c (r 4 , t + τ) dV1 dV2 dV3 dV4 〉.

For better readability, we will from this point on only note the first term of the sum. We will refer to the three other terms as “3 similar terms containing cos*cos*sin*sin, sin*sin*cos*cos and sin*sin*sin*sin".

The average is calculated over r 0 and/or t while the integration variables are r 1 , ..., r 4 . The order of computation can thus be reversed: 182


¯ ¯ ZZZZ ¯ ( q) ¯4 〈 cos (κ q (z1 − z0 )) cos (κ q (z2 − z0 )) term1 = ¯χ ¯

cos (κ q (z3 − z0 − ρ z )) cos (κ q (z4 − z0 − ρ z )) A ∗q (r 1 − r 0 )A ∗q (r 2 − r 0 )A ∗q (r 3 − r 0 − ρ )A ∗q (r 4 − r 0 − ρ ) c (r 1 , t) c (r 2 , t) c (r 3 , t + τ) c (r 4 , t + τ) 〉 dV1 dV2 dV3 dV4 + 3 similar terms containing cos*cos*sin*sin, sin*sin*cos*cos and sin*sin*sin*sin.

(A.7)

The averaging can be simplified using the following substitutions:

r ∗1 = r 1 − r 0

(A.8)

r ∗2 = r 2 − r 0

(A.9)

r ∗3 = r 3 − r 0 − ρ

(A.10)

r ∗4 = r 4 − r 0 − ρ

(A.11)

This results in:

〈 cos(κ q z1∗ ) cos(κ q z2∗ ) cos(κ q z3∗ ) cos(κ q z4∗ )A ∗q (r ∗1 )A ∗q (r ∗2 )A ∗q (r ∗3 )A ∗q (r ∗4 ) ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ c r ∗1 + r 0 , t c r ∗2 + r 0 , t c r ∗3 + r 0 + ρ , t + τ c r ∗4 + r 0 + ρ , t + τ 〉

(A.12)

This coordinate transformation is nothing more than the movement of the sample seen from the (steady) laser beam. Now the focal volume function and the cosine functions are constants for the averaging process: 183


¯ ¯4 ZZZZ ¯ ¯ term1 = ¯χ( q) ¯ cos (κ q z1∗ ) cos (κ q z2∗ ) cos (κ q z3∗ ) cos (κ q z4∗ ) ¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ 〈 c r ∗1 + r 0 , t c r ∗2 + r 0 , t c r ∗3 + r 0 + ρ , t + τ c r ∗4 + r 0 + ρ , t + τ 〉

A ∗q (r ∗1 )A ∗q (r ∗2 )A ∗q (r ∗3 )A ∗q (r ∗4 )dV1∗ dV2∗ dV3∗ dV4∗ + 3 similar terms containing cos*cos*sin*sin, sin*sin*cos*cos and sin*sin*sin*sin.

(A.13)

From now on, we will use the following short–hand notation for the concentration differences:

δ c i = δ c(r ∗i + r 0 , t) δ c iρτ = δ c(r ∗i + r 0 + ρ , t + τ)

(A.14) (A.15)

the average can then be rewritten as follows:

¡ ¢ ¡ ¢ ¡ ¢ ¡ ¢ 〈 c r ∗1 + r 0 , t c r ∗2 + r 0 , t c r ∗3 + r 0 + ρ , t + τ c r ∗4 + r 0 + ρ , t + τ 〉 ¡ ¢¡ ¢ =〈 ( c¯ + δ c 1 ) ( c¯ + δ c 2 ) c¯ + δ c 3ρτ c¯ + δ c 4ρτ 〉

= c¯4 + ¡ ¢ c¯3 〈δ c 1 〉 + 〈δ c 2 〉 + 〈δ c 3ρτ 〉 + 〈δ c 4ρτ 〉 + ¡ ¢ c¯2 〈δ c 1 δ c 2 〉 + 〈δ c 1 δ c 3ρτ 〉 + 〈δ c 1 δ c 4ρτ 〉 + 〈δ c 2 δ c 3ρτ 〉 + 〈δ c 2 δ c 4ρτ 〉 + 〈δ c 3ρτ δ c 4ρτ 〉 + ¡ ¢ c¯ 〈δ c 1 δ c 2 δ c 3ρτ 〉 + 〈δ c 1 δ c 2 δ c 4ρτ 〉 + 〈δ c 1 δ c 3ρτ δ c 4ρτ 〉 + 〈δ c 2 δ c 3ρτ δ c 4ρτ 〉 + 〈δ c 1 δ c 2 δ c 3ρτ δ c 4ρτ 〉 .

(A.16)

The propagator function, denoted by

µ ¶ kρ k2 P(ρ , τ) = exp − , 4D τ (4πD τ)3/2

1

184

(A.17)


defines the probability density that a randomly diffusing particle with diffusion coefficient D will be found at position ρ at time τ when it was at position 0 at time 0. Combining this with the Palmer formalism [95], we can come up with expressions for the terms in Eq. (A.16).

• All terms with c¯3 are zero due to the randomness of the diffusion process: there is an equal probability of having a positive or a negative δ c. • 〈δ c 1 δ c 2 〉 = c¯δ(r ∗2 − r ∗1 ) ∗ ∗ ¯ • 〈δ c i δ c jρτ 〉 = cP(r j + ρ − r i , τ)

• 〈δ c 3ρτ δ c 4ρτ 〉 = c¯δ(r ∗4 − r ∗3 ) • 〈δ c i δ c j δ c kρτ 〉 = c¯δ(r ∗j − r ∗i )P(r ∗k + ρ − r ∗i , τ) • 〈δ c i δ c jρτ δ c kρτ 〉 = c¯δ(r ∗k − r ∗j )P(r ∗k + ρ − r ∗i , τ) • 〈δ c 1 δ c 2 δ c 3ρτ δ c 40ρτ 〉 = c¯δ(r ∗2 − r ∗1 )δ(r ∗4 − r ∗3 )P(r ∗3 + ρ − r ∗1 , τ) + c¯2 P(r ∗4 + ρ − r ∗2 , τ)P(r ∗3 + ρ − r ∗1 , τ) + c¯2 P(r ∗4 + ρ − r ∗1 , τ)P(r ∗3 + ρ − r ∗2 , τ) + c¯2 δ(r ∗4 − r ∗3 )δ(r ∗2 − r ∗1 )

The following short–hand notation for the propagator is used:

P i j,ρτ =P(r ∗i + ρ − r ∗j , τ)

Eq. (A.13) can then be written as: 185

(A.18)


¯ ¯ ZZZZ ¡ ¢ ¯ ( q) ¯4 term1 = ¯χ ¯ [ c¯4 + c¯3 2δ(r ∗1 − r ∗2 ) + 4P31,ρτ ¡ ¢ + c¯2 4δ(r ∗1 − r ∗2 )P31,ρτ + 2P31,ρτ P42,ρτ + δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )

+ c¯δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )P31,ρτ ]

4 Y

i =1

cos(κ q z∗i )A ∗q (r ∗i )dVi∗

¯ ¯ ZZZZ ¡ ¢ ¯ ( q ) ¯4 + 2 ¯χ ¯ [ c¯4 + c¯3 δ(r ∗1 − r ∗2 ) + δ(r ∗3 − r ∗4 ) + 4P31,ρτ

+ c¯2 (2δ(r ∗1 − r ∗2 )P31,ρτ + 2δ(r ∗3 − r ∗4 )P31,ρτ + 2P31,ρτ P42,ρτ + δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )) + c¯δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )P31,ρτ ] cos(κ q z1∗ ) cos(κ q z2∗ ) sin(κ q z3∗ ) sin(κ q z4∗ )

4 Y

A ∗i dVi∗

i =1

¯ ¯4 ZZZZ ¡ ¢ ¯ ¯ + ¯χ( q) ¯ [ c¯4 + c¯3 2δ(r ∗1 − r ∗2 ) + 4P31,ρτ ¡ ¢ + c¯2 4δ(r ∗1 − r ∗2 )P31,ρτ + 2P31,ρτ P42,ρτ + δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )

+ c¯δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )P31,ρτ ]

4 Y

i =1

sin(κ q z∗i )A ∗q (r ∗i )dVi∗ .

(A.19)

To be able to refer to a specific term in this equation, we will adopt the following notation: all terms of the first integrand will get the label A, the second integrand ¯ ¯4 B and the last integrand C. E.g. term C3 = 4 ¯χ( q) ¯ 〈 c〉3 P31,ρτ . In total, there are 7 A–terms, 9 B–terms and 7 C–terms.

Before solving the integral, it is worth calculating the normalization factor 〈 I q (r 0 , t)〉2 :

186


¯ ¯2 Ï ¯ ¯ 〈 I q (r 0 , t)〉 =〈 ¯χ( q) ¯ A ∗q (r 1 − r 0 )A ∗q (r 2 − r 0 )

c (r 1 , t) c (r 2 , t) cos (κ q (z1 − z0 )) cos (κ q (z2 − z0 ))dV1 dV2 〉+ ¯ ¯2 Ï ¯ ¯ 〈 ¯χ( q) ¯ A ∗q (r 1 − r 0 )A ∗q (r 2 − r 0 ) c (r 1 , t) c (r 2 , t) sin (κ q (z1 − z0 )) sin (κ q (z2 − z0 ))dV1 dV2 〉 ¯ ¯ Ï ¯ ( q) ¯2 = ¯χ ¯ cos (κ q z1∗ ) cos (κ q z2∗ )A ∗q (r ∗1 )A ∗q (r ∗2 ) ¢ ¡ ¢ ¡ 〈 c r ∗1 + r 0 , t c r ∗2 + r 0 , t 〉 dV1∗ dV2∗ + ¯ ¯ Ï ¯ ( q) ¯2 sin (κ q z1∗ ) sin (κ q z2∗ )A ∗q (r ∗1 )A ∗q (r ∗2 ) ¯χ ¯ ¢ ¡ ¢ ¡ 〈 c r ∗1 + r 0 , t c r ∗2 + r 0 , t 〉 dV1∗ dV2∗ .

(A.20)

The average of the product of two concentrations is equal to c¯2 + c¯δ(r ∗2 − r ∗1 ). Eq. A.20 then simplifies to:

¯ ¯2 Ï ¯ ¯ 〈 I q (r 0 , t)〉 = ¯χ( q) ¯ c¯2 cos (κ q z1∗ ) cos (κ q z2∗ )A ∗q (r ∗1 )A ∗q (r ∗2 )dV1∗ dV2∗ ¯ ¯ Z ³ ´2 ¯ ( q) ¯2 + ¯χ ¯ c¯ cos2 (κ q z1∗ ) A ∗q (r ∗1 ) dV1∗ Ï ¯ ¯ ¯ ( q) ¯2 2 ¯ + ¯χ ¯ c sin (κ q z1∗ ) sin (κ q z2∗ )A ∗q (r ∗1 )A ∗q (r ∗2 )dV1∗ dV2∗ ¯ ¯2 Z ³ ´2 ¯ ¯ (A.21) + ¯χ( q) ¯ c¯ sin2 (κ q z1∗ ) A ∗q (r ∗1 ) dV1∗ .

The third term is an integration of the product of an odd function with a Gaussian over a symmetric interval, and is therefore zero. The cos2 and sin2 of the second and fourth term can be combined into one term, but in this case it is easier to calculate them separately. Define first the following short–hand notations: 187


Ac i =A ∗q (r ∗i ) cos(κ q z∗i )

(A.22)

As i =A ∗q (r ∗i ) sin(κ q z∗i )

(A.23)

dVi∗jk...

=dVi∗ dV j∗ dVk∗ ...

(A.24)

term 2 =〈 I q (r 0 , t)〉2 ¯2 Ï ¯2 Z ¯ ¯ ¯ ¯ ¯ ¯ ∗ =[〈 c〉2 ¯χ( q) ¯ Ac 1 Ac 2 dV12 + 〈 c〉 ¯χ( q) ¯ (Ac 1 )2 dV1∗ ¯ ¯ Z ¯ ( q ) ¯2 + 〈 c 〉 ¯χ ¯ (As 1 )2 dV1∗ ]2 (A.25) ¯ ¯4 ZZZZ ¯ ¯ ∗ =〈 c〉4 ¯χ( q) ¯ Ac 1 Ac 2 Ac 3 Ac 4 dV1234 ¯4 Ï ¯4 Ï ¯ ¯ 2 2 ∗ ∗ 2 ¯ ( q) ¯ 2 ¯ ( q) ¯ + 〈 c 〉 ¯χ ¯ (Ac 1 ) (Ac 2 ) dV12 + 〈 c〉 ¯χ ¯ (As 1 )2 (As 2 )2 dV12 ¯ ¯4 ZZZZ ¯ ¯ ∗ + 2〈 c〉3 ¯χ( q) ¯ Ac 1 Ac 2 Ac 3 Ac 4 δ(r ∗1 − r ∗2 )dV1234 ¯ ¯4 ZZZZ ¯ ¯ ∗ + 2〈 c〉3 ¯χ( q) ¯ Ac 1 Ac 2 As 3 As 4 δ(r ∗3 − r ∗4 )dV1234 ¯ ¯4 ZZZZ 2 ¯ ( q) ¯ ∗ + 2〈 c〉 ¯χ ¯ Ac 1 Ac 2 As 3 As 4 δ(r ∗1 − r ∗2 )δ(r ∗3 − r ∗4 )dV1234 . (A.26)

Each of the 6 terms in this equation has a counterpart in (A.19), so when calculating the difference (i.e. the numerator of (A.2)), these terms disappear. Table A.1 lists an overview of these terms. Table A.1: Terms in Eq. A.26 with their respective counterpart in Eq. A.19. Term from Eq. A.26

Term from Eq. A.19

1

A1

2

A6

3

C6

4

A2

5

B3

6

B8

Integrand ¯ ¯4 〈 c〉4 ¯χ( q) ¯ Ac 1 Ac 2 Ac 3 Ac 4 ¯ ¯4 〈 c〉2 ¯χ( q) ¯ (Ac 1 )2 (Ac 2 )2 ¯ ¯4 〈 c〉2 ¯χ( q) ¯ (As 1 )2 (As 2 )2 ¯ ¯4 2〈 c〉3 ¯χ( q) ¯ Ac 1 Ac 2 Ac 3 Ac 4 δ(r 3 − r 4 ) ¯ ¯4 2〈 c〉3 ¯χ( q) ¯ Ac 1 Ac 2 As 3 As 4 δ(r 3 − r 4 ) ¯ ¯4 2〈 c〉2 ¯χ( q) ¯ Ac 1 Ac 2 As 3 As 4 δ(r 1 − r 2 )δ(r 3 − r 4 )

188


Several integrands of Eq. A.19 are odd functions, and are therefore zero after integrating: B1, B2, B4, B5, C1, C2, C3 and C4. Together with the six terms that have a counterpart, only 9 terms remain:

G(ρ , τ) ∼ 〈 I q (r 0 , t)I q (r 0 + ρ , t + τ)〉 − 〈 I q (r 0 , t)〉2 ∼ A3 + A4 + A5 + A7 + B6 + B7 + B9 + C5 + C7

(A.27) (A.28)

To express these terms in a more convenient format, the following notation is used:

Aw(n) =nqD τ + ω20

(A.29)

Az(n) =nqD τ + z02

(A.30)

N=

¯ 0 ω20 π3/2 cz q 3/ 2

¯ ef f = cV

(A.31)

with Ve f f the so–called effective focal volume. Table A.2 shows some typical values for these parameters. Table A.2: Typical values for some parameters. Parameter n q N

Typical values 2, 4, 8/3 2 (SHG), 3 (THG) [0.01, 100]

Notice also that each term contains a factor A 4q0 |χ( q) |4 , but since these are also present in the denominator of Eq. A.2 they do not influence the normalized autocorrelation function and are therefore omitted. The integrals were evaluated with Maple 18. This script is available upon request. The final result for the general cIFM is: 189


Ã

A3 =4N

3

ω20

!Ã

!

z0

p 2Aw(2) 2 2Az(2) ! Ã κ2q z02 Az(4) q(ρ 2x + ρ 2y ) qρ 2z − − · exp − 2Aw(2) 2Az(2) 2qAz(2) Ã Ã 2 ! Ã !! 2 4 −κ q z0 z0 κ q ρ z · cos + exp Az(2) 2qAz(2)

Ã

A 4 =4 N

2

ω20

!Ã

(A.32)

!

z0

(A.33) p 3 Aw(8/3) 4 3 Az(8/3) Ã ! 2 q(ρ 2x + ρ 2y ) κ2q z02 Az(4) 2 qρ 2z · exp − − − 3 Aw(8/3) 3 Az(8/3) 3 qAz(8/3) " Ã 2 ! Ã 2 2 !Ã Ã 2 ! Ã !!# z0 κ q ( Az(4) − z02 ) −2 z04 κ2q 2 z0 κ q ρ z 4 z0 κ q ρ z · 2 cos + exp − cos + exp 3 Az(8/3) 3 qAz(8/3) 3 Az(8/3) 3 qAz(8/3)

ω40

Ã

A5 =2N 2

!Ã

z02

!

(2Aw(2))2 8Az(2) Ã ! q(ρ 2x + ρ 2y ) z02 κ2q (Az(2) − z02 ) qρ 2z · exp − − − Aw(2) Az(2) qAz(2) Ã Ã 2 ! Ã !! 2 κ2q z04 z0 κ q ρ z + exp − · cos Az(2) 2qAz(2)

³ ´   ! q ρ 2x + ρ 2y qρ 2z z0  A7 =N exp − − p 4Aw(4) 16 Az(4) Aw(4) Az(4) " Ã 2 2 ! Ã 2 !# z0 κ q Az(8) z0 ρ z κ q · 4 exp − cos 4qAz(4) Az(4) " Ã 2 2 ! Ã 2 ! Ã 2 2! # z0 κ q (Az(4) − z02 ) z0 κ q 2z0 ρ z κ q + exp − cos + exp − +2 qAz(4) Az(4) q Ã

ω20

(A.34)

!Ã

190

(A.35)


Ã

B6 =4N

2

B7 =4N

2

ω20

!Ã

!

z0

p 3Aw(8/3) 8 3Az(8/3) Ã ! 2q(ρ 2x + ρ 2y ) z02 κ2q Az(4) 2qρ 2z · exp − − − 3Aw(8/3) 3Az(8/3) 3qAz(8/3) ! Ã 2 2 !# " Ã 2 z0 κ q (Az(4) − z02 ) 2z0 κ q ρ z − 2 exp − · 4 cos 3Az(8/3) 3qAz(8/3) "Ã Ã 2 ! Ã !!# 4 2 2z0 κ q 4z0 κ q ρ z · cos + exp − 3Az(8/3) 3qAz(8/3)

Ã

ω40

!Ã

z02

!

(2Aw(2))2 8Az(2) ¡ ¢! Ã Ã 2 ! q(ρ 2x + ρ 2y ) κ2q z02 Az(2) − z02 z0 ρ z κ q qρ 2z 2 · exp − − − sin Aw(2) Az(2) qAz(2) Az(2)

! ! Ã q(ρ 2x + ρ 2y ) qρ 2z z0 B9 =2N exp − − p 4Aw(4) 16 Az(4) Aw(4) Az(4) " Ã 2 2 !Ã Ã ! Ã 2 !!# 2 2 4 z0 κ q (Az(4) − z0 ) κ q z0 2z0 ρ z κ q · 2 − exp − exp − + cos qAz(4) qAz(4) Az(4) ω20

Ã

Ã

C5 =2N

2

ω40

(A.36)

(A.37)

!Ã

!Ã

z02

(A.38)

!

(2Aw(2))2 8Az(2) ¡ ¢! Ã q(ρ 2x + ρ 2y ) z02 κ2q Az(2) − z02 qρ 2z − − · exp − Aw(2) Az(2) qAz(2) Ã Ã 2 ! Ã !! 2 z04 κ2q z0 ρ z κ q · cos − exp − Az(2) 2qAz(2) 191

(A.39)


! ! Ã q(ρ 2x + ρ 2y ) qρ 2z z0 C7 =N − exp − p 4Aw(4) 16 Az(4) Aw(4) Az(4) " Ã 2 2 ! Ã 2 ! Ã 2 2 !# 2 z0 κ q (Az(4) − z0 ) z0 κ q 2z0 ρ z κ q · 2 + exp − cos + exp − qAz(4) Az(4) q " Ã 2 2 ! Ã 2 !# z0 κ q Az(8) z κq ρ z −4 exp − cos 0 4qAz(4) Az(4) Ã

ω20

!Ã

(A.40)

The final step is the calculation of the normalization factor, i.e. the denominator of Eq. A.2. Instead of writing out the quadratic form into a sum with quadruple integrals, it is more convenient to calculate 〈 I q (r 0 , t)〉 directly, and taking the square afterwards. The result is:

Ã 2 2 !!2 z0 κ q N 2 . G N = 〈 I q (r 0 , t)〉 = p + N exp − 2q 2 2 Ã

2

(A.41)

Note that when κ q = 0, there is a perfect symmetry between the radial components (x and y) and the axial component (z). E.g. in term A3 the sum of the cosine and the exponential term cancels out with with the factor 1/2 between the second brackets, leaving a z0 factor that is perfectly analogous to the ω0 factor in front. This is to be expected since the (Gouy) phase shift is the only factor that creates an asymmetry in the equations. A4, A5 and A7 behave in a similar way, the B and C terms all go to zero. The spatial evolution of G is plotted in Figure A.1 for κ q = 0 and typical other parameter values. 192

A.2. THE TWO DIMENSIONAL CIFM

Figure A.1: Plots of the ACF with respect to the lateral spatial shift ρ x and ρ y in a cSTICS simulation for time lags τ = 1 s (a)–(b), τ = 10 s (c)–(d), τ = 30 s (e)–(f). The parameter values are ω0 = 2.7 µ m, z0 = 54 µ m, N = 10, D = 0.5 µ m2 /s and κ q = 0. The left panels show 3D plots of the temporal evolution of the SHG ACF. In the right panels the ACF cross section ρ y = 0 is plotted, as well as a comparison with the fluorescence ACF.

A.2

The two dimensional cIFM

Each term of the general cIFM is written in such a way that one can easily see from which integration each factor is coming. This makes it convenient to obtain the 2D formulas: one can simply remove all factors in brackets and all terms in exponentials that contain z0 . This results in the following outcome: 193


Ã

A3 =4N

3

A4 =4N

2

ω20

!

Ã

exp −

2Aw(2) ω20

Ã

!

3Aw(8/3) ω40

Ã

A5 =2N 2

q(ρ 2x + ρ 2y )

(A.42)

2Aw(2)

Ã

exp − !

!

2q(ρ 2x + ρ 2y )

!

3Aw(8/3) q(ρ 2x + ρ 2y )

Ã

(A.43)

!

exp − Aw(2) (2Aw(2))2 ³ ´  Ã ! q ρ 2x + ρ 2y ω20  A7 =N exp − 4Aw(4) Aw(4)

(A.44)

(A.45)

Note that N is here the 2D focal volume:

N=

One of the 3 factors

c¯ω20 π

(A.46)

q

p 2 in the denominator of Eq. A.41 is coming from the z

integration. Leaving this out results in the 2D normalization factor:

N GN = + N2 2 µ

¶2

.

(A.47)

Note that this result differs from the expressions in Gassin’s work [116]. When taking the limit for N ¿ 1, we retrieve as expected both for 3D and 2D diffusion the fluorescence equations (see below), while the cited reference does not show this limiting behavior. Note also that when the diffusion plane is parallel to the light beam, one does have to take into account the phase shift κ q .

A.3

The general fIFM

We will compare the autocorrelation spectroscopy expressions of the following sections with the corresponding fluorescence expressions. These have been noted 194

A.4. INTENSITY FLUCTUATION AUTOCORRELATION SPECTROSCOPY

in earlier publications [65, 121]. Fluorescence emission is a stochastic process, leading to a different intensity fluctuation model. The general form is:

³ ´   2 q ρ 2x + ρ 2y ω20 z0 qρ z . G(ρ , τ) = exp − − p Aw(4) Az(4) N Aw(4) Az(4)

(A.48)

This formula applies both to 1PE (q = 1) and 2PE (q = 2).

A.4

Intensity fluctuation autocorrelation spectroscopy

In this section we describe how ρ and τ in the general cIFM must be adapted for each specific autocorrelation spectroscopy type.

A.4.1

cSTICS

Several images are recorded sequentially in a cSTICS type measurement. Each of these images is considered to be taken instantaneously. The resulting data set is then correlated both in space and time. The general cIFM must be adapted for the discrete raster of pixels: ρ = (ρ x , ρ y , ρ z ) = (δ r ξ, δ r ψ, δ sφ) with δ r and δ s the pixel size in the lateral and axial direction and ξ, ψ and φ the pixel number in the x–, y–, and z–direction, respectively. These substitutions have to be made in Eq. A.33–A.41 for 3D diffusion and in Eq. A.42–A.47 for 2D diffusion. The variable τ is the time difference between the recording of the two images containing the two pixels that are correlated.

A.4.2

cRICS

When all pixels are scanned sequentially in a raster pattern, there is a definite relation between the spatial and temporal part of the equation. G(ρ , τ) becomes now G(ρ (τ)) with τ(ρ ) = ρ x τ x + ρ y τ y + ρ z τ z = ρ · τ and τ a vector containing respectively the pixel dwell time, line scan time and frame time. Note that τ has units of time while τ has units of time per distance. To summarize, Eq. A.33– A.41 and A.42–A.47 remain valid, but one must use the substitution τ = ρ · τ in Eq. A.29 and A.30. 195


A.4.3

cTICS and cCS

In cCS, which is the most simple form of autocorrelation spectroscopy, a steady beam detects a fluctuating intensity purely caused by the movement of particles into and out of the focal volume. The calculated temporal correlation can thus be fitted by simply putting ρ = 0 in Eq. A.33–A.41 and A.42–A.47 for 3D and 2D diffusion respectively. The same formula applies to cTICS, where all pixels in a set of images are correlated in time.

Ã

A3 =4N

3

A4 =4N

2

A5 =2N

2

ω20

!Ã

!

z0

Ã

κ2q z02 Az(4)

!

exp − p 2Aw(2) 2 2Az(2) 2qAz(2) Ã Ã !! 2 4 −κ q z0 · 1 + exp 2qAz(2)

ω20

Ã

!Ã

!

z0

Ã

κ2q z02 Az(4)

(A.49)

!

exp − p 3Aw(8/3) 4 3Az(8/3) 3qAz(8/3) " Ã 2 2 !Ã Ã !!# 2 z0 κ q (Az(4) − z0 ) −2z04 κ2q · 2 + exp − 1 + exp 3qAz(8/3) 3qAz(8/3)

ω40

Ã

!Ã

z02

(2Aw(2))2 8Az(2) Ã Ã !!2 κ2q z04 · 1 + exp − 2qAz(2)

Ã

ω20

!

Ã

exp −

z02 κ2q (Az(2) − z02 )

!Ã

qAz(2)

(A.50)

!

(A.51)

! z0 A7 =N (A.52) p 4Aw(4) 16 Az(4) Ã Ã 2 2 ! Ã 2 2 ! Ã 2 2! ! z0 κ q Az(8) z0 κ q (Az(4) − z02 ) z0 κ q · 4 exp − + exp − + exp − +2 4qAz(4) qAz(4) q

196

A.4. INTENSITY FLUCTUATION AUTOCORRELATION SPECTROSCOPY

ω20

Ã

B6 =4N

2

B7 =4N

2

!Ã

!

z0

Ã

z02 κ2q Az(4)

!

exp − p 3Aw(8/3) 8 3Az(8/3) 3qAz(8/3) " Ã 2 2 !Ã Ã !!# 2 z0 κ q (Az(4) − z0 ) 2z04 κ2q · 4 − 2 exp − 1 + exp − 3qAz(8/3) 3qAz(8/3)

ω40

Ã

!Ã

z02

(A.53)

!

(A.54)

(2Aw(2))2 8Az(2) ¡ ¢! Ã Ã 2 ! q(ρ 2x + ρ 2y ) κ2q z02 Az(2) − z02 z0 ρ z κ q qρ 2z 2 · exp − − − sin Aw(2) Az(2) qAz(2) Az(2)

ω20

Ã

B9 =2N

!Ã

4Aw(4) Ã

"

· 2 − exp −

C5 =2N

(A.55)

z02 κ2q (Az(4) − z02 )

ω40

Ã 2

!

z0 p 16 Az(4)

!Ã

qAz(4)

!Ã

z02

!

Ã

exp −

Ã

C7 =N

ω20

!Ã

4Aw(4) Ã Ã

· 2 + exp −

z0 p 16 Az(4)

!

qAz(4)

!#

+1

¡ ¢! z02 κ2q Az(2) − z02

exp − (2Aw(2))2 8Az(2) Ã Ã 2 ! Ã !!2 z04 κ2q z0 ρ z κ q · cos − exp − Az(2) 2qAz(2)

Ã

κ2q z04

(A.56)

qAz(2)

!

z02 κ2q (Az(4) − z02 ) qAz(4)

(A.57) !

Ã

+ exp −

Ã 2 2 !!2 z0 κ q N 2 G N = p + N exp − 2q 2 2

z02 κ2q q

!

Ã

− 4 exp −

z02 κ2q Az(8)

!!

4qAz(4)

Ã

(A.58)

197


For 2D diffusion, the same substitution must be made in Eq. A.42–A.47:

Ã

A3 = 4N

3

A4 = 4N

2

A5 = 2N

2

!

(A.59)

2Aw(2) Ã

ω20

!

(A.60)

3Aw(8/3) Ã

Ã

A7 = N

ω20

ω40

!

(A.61)

(2Aw(2))2 ! ω20

(A.62)

4Aw(4) µ ¶2 N 2 +N GN = 2

A.4.4

(A.63)

Diffusion with flow

When the particles exhibit a net flow v = (v x , v y , v z ), each component of ρ in the exponents of the ACFs must be adjusted. For cSTICS and cRICS type measurements, one must make three substitutions in Eq. A.33–A.41 and A.42– A.47 for 3D and 2D diffusion respectively: ρ x → ρ x − v x τ, ρ y → ρ y − v y τ and ρ z → ρ z − v z τ. The same equations can be used for 3D and 2D cTICS and cCS

experiments with flow using the following substitutions: ρ x → v x τ, ρ y → v y τ and ρ z → v z τ. Note that due to the symmetry between v x and v y in the obtained

formula, it is only possible to fit the magnitude of the lateral flow in cTICS and cCS, but not the direction.

A.5

The limiting behavior of the general cIFM

The following two sections describe the behavior of our model in the limit of a low and high particle concentration. The results are compared to the fluorescence model.

A.5.1

The cIFM in the low particle concentration limit

When N ¿ 1, the only terms that remain in the general cIFM (Eq. A.33–A.41) are the ones containing the smallest power of N, i.e. A7, B9 and C7. Therefore 198

A.5. THE LIMITING BEHAVIOR OF THE GENERAL CIFM

the autocorrelation function simplifies to:

G=

A7 + B9 + C7 0

GN

,

(A.64)

with

0

GN =

N2 . 8

(A.65)

The result is:



³ ´ q ρ 2x + ρ 2y

 qρ 2z  8 exp − − G(ρ , τ) = p Aw(4) Az(4) N 2 8Aw(4) Az(4) ³ ´   2 2 2 q ρ + ρ x y qρ z 1 . = exp − − s 2 ³ ´ 4qD τ 4qD τ + ω0 4qD τ + z02 4 qD τ N ω2 + 1 +1 0 z02 ω20 z0 N

(A.66)

Note that the phase factor κ q is not present anymore in the equation; when there is most of the time not more than one particle in the focal volume (N ¿ 1), the phase information becomes unimportant. Eq. A.66 is the exact same equation as obtained for the fIFM. This means that our cIFM converges to the fluorescence model for low particle concentrations. For q = 1, ρ x = δ r ξ − v x τ, ρ y = δ r ψ − v y τ and ρ z = v z τ, the STICS autocorrelation function for one–photon fluorescence with flow is obtained. When using the substitution τ = ρ · τ, we get the fluorescence RICS expression. Similarly, the two–photon equations are found for q = 2. A.5.1.1

Special case: a steady laser beam

When the laser is not scanning, one can derive the autocorrelation function G(τ) by substituting ρ = 0 in Eq. A.66. This results in: 199


G(τ) = N

³

4 qD τ ω20

+1

1 s ´ 4qD τ z02

.

(A.67)

+1

This is again equal to the one and two–photon fluorescence expression for q = 1 and q = 2 respectively.

A.5.2

The limit for large N

When N À 1 the only term in the sum that remains is A3:

G=

A3 00

GN

,

(A.68)

with

Ã 00

4

G N = N exp − A.5.2.1

z02 κ2q q

!

.

(A.69)

Special case: a steady laser beam and κ q = 0

For a non–scanning system with κ q = 0 and q = 1, this simplifies to: p 2 G(τ) = N ³

1+

2D τ ω20

´

1 s 1+

2D τ

.

(A.70)

z02

This is equal to the fluorescence equation (index F) when using the following substitutions:

p N = 2 NF

(A.71)

D =2D F

(A.72)

200

A.6. PARAMETER RETRIEVAL IN DATA FITTING

A.6

Parameter retrieval in data fitting

Several ACF fit simulations were performed to check the influence of noise on the parameter recovery. All simulations started from the theoretical temporal ACF with typical values for the laser beam properties: ω0 = 0.32 µ m and z0 = 0.982 µ m. The temporal shifts were chosen between 10−5 s and 1 s in 500 logarithmically divided steps. Random noise was added to this curve according to the following empirical formula [246]:

σ(τ) =

a −0.35 ·τ · Gaussian(0, 1), N

(A.73)

where a is the noise factor that was linearly varied between 0 and 0.05 in 21 steps and the Gaussian function is a random number generator that produces Gaussian distributed numbers with mean 0 and standard deviation 1. This curve was then fitted with the lsqnonlin function in Matlab, where the solution space was restricted to positive numbers. The start values for the parameters were picked randomly between 0.1 and 10 times the exact value:

P ST ART = P E X ACT · 102·rand ()−1 ,

(A.74)

where the rand() function produces random, linearly distributed numbers between 0 and 1. The fitted values were then stored and the process was repeated 1000 times for each of the 21 noise levels. An example of an ACF fit is plotted in Figure A.2 and 2D histograms of the recovered values are shown in Figure A.3. 201


Autocorrelation

25 Simulated data Fitted ACF

20 15 10 5 0 −5 10

−3

−1

10 10 Temporal shift [s]

Figure A.2: Computer simulation of the temporal ACF with noise and the fitted curve. The exact parameter values are c = 0.505/µ m3 , which is equal to N = 0.1 /µ m3 , D = 0.1 µ m2 /s, κ q = 2.49 /µ m and a = 0.005. The fit parameters are D and c.

0.6

0.16

Fitted c [/µm3]

Fitted D [µm2/s]

0.18

0.14 0.12 0.1

0.55 0.5 0.45

0.08

0.4

0.06 0

0.01

0.02

0.03

0.04

0.05

0

a

0.01

0.02

0.03

0.04

0.05

a

Figure A.3: 2D histograms of the 21x1000 fits for the parameters described in Figure A.2. The color represents the number of fits that ended up in that voxel: white means up to 103 fits, and this exponent decreases as the color gets darker. In this example, there is only one minimum in the fit space for noiseless curves. As a gets bigger, the resulting c and D values are more spread out, but the symmetry indicates that one can average over multiple data sets to obtain an accurate result.

Similar plots were made for several combinations of parameter values. The concentration was varied between N = 0.1 and N = 10, the diffusion coefficient between D = 0.01 µ m2 /s and D = 10 µ m2 /s and the phase shift between κ q = 0.249 /µ m and κ q = 24.9 /µ m. All histograms show a similar behavior as in Figure A.3. 202

A.7. SUMMARY 500 (a)

(b)

20 15 10

(c)

0.8

Fitted κq [/µm]

25

Fitted c [/µm3]

Fitted D [µm2/s]

30

0.6 0.4

400 300 200 100

5 0

0.01 0.02 0.03 0.04 0.05 a

0

0.01 0.02 0.03 0.04 0.05 a

0

0.01 0.02 0.03 0.04 0.05 a

Figure A.4: Histograms of the fit results with the same parameter values as in Figure A.3, but with κ q as an additional fit parameter. Plots (a) and (c) are zoomed in for better viewing. Fitting c, D and κ q results in parasitic local minima in the fit space, even when a = 0. It is therefore an unreliable procedure to measure D and c, even when averaging over multiple data sets. Moreover, the fitted κ q values can be overestimated by a factor of 100.

When κ q is left as a fit parameter, however, the solution space can contain local minima around other points than the exact values. It is especially difficult to obtain reliable values for κ q , as shown in Figure A.4. It is therefore recommended to estimate κ q based on the experiment optics and fix this parameter during the fit analysis. The Gouy phase anomaly can be estimated by expressing the phase shift of a focused Gaussian beam as a function of the z position [247]:

Ã φ = atan

!

λ πω20

z ,

(A.75)

with λ the laser wavelength. To obtain κ q , a first order approximation can be made at the focal plane z = 0:

κq =

A.7

λ πω20

.

(A.76)

Summary

Table A.3 gives a convenient overview of the formula that must be used to describe the ACF in each specific case. 203

204

Scan type 3D cSTICS with flow

G (A3 + A4 + ... + C7)/G N

Eq. A.33–A.41

N A.31

3D cSTICS without flow

(A3 + A4 + ... + C7)/G N

A.33–A.41

A.31

2D cSTICS with flow

(A3 + A4 + A5 + A7)/G N

A.42–A.47

A.46

2D cSTICS without flow

(A3 + A4 + A5 + A7)/G N

A.42–A.47

A.46

3D cRICS with flow

(A3 + A4 + ... + C7)/G N

A.33–A.41

A.31

3D cRICS without flow

(A3 + A4 + ... + C7)/G N

A.33–A.41

A.31

2D cRICS with flow

(A3 + A4 + A5 + A7)/G N

A.42–A.47

A.46

2D cRICS without flow

(A3 + A4 + A5 + A7)/G N

A.42–A.47

A.46

3D cTICS/cCS with flow

(A3 + A4 + ... + C7)/G N

A.33–A.41

A.31

3D cTICS/cCS without flow

(A3 + A4 + ... + C7)/G N

A.50–A.58

A.31

2D cTICS/cCS with flow

(A3 + A4 + A5 + A7)/G N

A.42–A.47

A.46

2D cTICS/cCS without flow

(A3 + A4 + A5 + A7)/G N

A.59–A.63

A.46

τ and ρ τ (δ r ξ − v x τ, δ r ψ − v y τ, δ sφ − v z τ) τ (δ r ξ, δ r ψ, δ sφ) τ (δ r ξ − v x τ, δ r ψ − v y τ) τ (δ r ξ, δ r ψ) (δ r ξ, δ r ψ, δ sφ) · (τ x , τ y , τ z ) (δ r ξ − v x τ, δ r ψ − v y τ, δ sφ − v z τ) (δ r ξ, δ r ψ, δ sφ) · (τ x , τ y , τ z ) (δ r ξ, δ r ψ, δ sφ) (δ r ξ, δ r ψ) · (τ x , τ y ) (δ r ξ − v x τ, δ r ψ − v y τ) (δ r ξ, δ r ψ) · (τ x , τ y ) (δ r ξ, δ r ψ) τ (v x τ, v y τ, v z τ) τ τ (v x τ, v y τ) τ -


Table A.3: Summary of the derived ACFs. The first column lists the experiment type. The second and third column state the corresponding ACF, in which the given definitions of N, τ and ρ must be used.

A.8. LIST OF SYMBOLS

A.8

List of symbols

Table A.4 provides a list of the symbols used in the above derivation and the summary. Note that the ACF is a dimensionless function, making it irrelevant which units are used to express the quantities. Table A.4: List of symbols. † A numerical value is not given for this parameter because this quantity is removed from the autocorrelation function after normalization. Symbol ρ τ

G(ρ , τ) I(r, t) q χ A q (r)

c(r, t) N κq P(ρ , τ)

ω0 , z 0

vx , v y , vz δr , δs ξ, ψ, φ

Meaning Spatial difference between two points in space and time Temporal difference between two points in space and time Autocorrelation function Measured higher harmonic light intensity when the laser beam is at position r at time t Number indicating the order of the higher harmonic Electrical susceptibility tensor Electric field amplitude of light scattered by a particle at position r Concentration of the SHG/THG producing particles at position r at time t Average number of particles in the focal volume Gouy phase factor Propagator function, i.e. the probability density of finding a particle at position r + ρ at time t + τ when it was at position r at time t Respectively width and depth of the Gaussian focal volume, i.e. 1/e2 values of the illumination intensity Flow speed in the x–, y– and z–direction, respectively Pixel size in the lateral and z–direction, respectively Pixel number in the x–, y– and z–direction, respectively

205

Typical value 0 − 1000 µ m 0 − 10000 s 0 − 1000 †

2, 3 † †

1 − 10000 /µ m3 0.01 − 100 0 − 5 [radians]/µ m ≥0

0.1 − 10 µ m

0 − 1000 µ m/s 10 − 1000 nm 1 − 1024

S UMMARY

ptical microscopes are omnipresent in biomedical research, helping to answer questions in the life sciences by visualizing biological structures on the micrometer scale. Diffraction of the light involved in the formation of the image does, however, pose a limit to the size of the structures that can be resolved. The resolution in optical microscopy is limited to about 250 nm. Studying the mechanisms of life on a molecular scale is therefore not feasible.

O

Another obstacle in optical microscopy is the difficulty for light to penetrate deeply in three–dimensional samples. A solution is to employ two–photon microscopy. In a two–photon process, such as two–photon fluorescence or second harmonic generation (SHG), two or more photons interact semi–simultaneously with the sample to generate one photon with more energy than each of the individual incoming photons. The light generated by the sample thus has a shorter wavelength than the illumination light. Using infrared radiation for illuminating the sample allows a much deeper penetration, up to about 100 µm, but the long wavelength also negatively affects the resolution. Several imaging techniques have been developed over the past decades to circumvent the diffraction limit. One of the methods, called image scanning microscopy (ISM) with pixel reassignment, is able to improve the resolution by a factor of about 1.4. ISM can be viewed as an extension of conventional confocal laser scanning microscopy in which the pinhole and the point–detector are removed and an array detector is placed in the image plane. Although several implementations of ISM have been realized by other research groups, the combination of ISM with multiphoton processes has not yet been well developed. Hence, one of the main goals of this work was the realization of multiphoton ISM. We have built an ISM setup with a multiphoton fluorescence excitation laser. Although we can show a resolution improvement in both two– and three– dimensional samples, the effect is less pronounced in the latter case. This result can be caused by a higher degree of scattering of the fluorescence, leading to a lower signal–to–noise ratio. As a consequence, the reconstruction algorithm may 207

SUMMARY

not produce the optimal image. In future work, other reconstruction algorithms and their performance on images with a low signal–to–noise ratio should be tested. Subdiffraction information cannot only be obtained by modifying the imaging setup, but also by inventively utilizing a diffraction limited system. Fluorescence intensity fluctuation imaging is a collection of ensemble–based microscopy methods that can measure the diffusion properties of nanometer–sized particles in suspension or in more complex environments. In these techniques, the random nature of the movement of fluorescent particles into and out of the focal volume is exploited to measure the mobility of the particles. The fluorescence trace over space and/or time is fitted to a theoretical model, yielding the average diffusion coefficient and the directed flow velocity. The technique is well established for fluorescent samples, but applying the technique to SHG active materials would allow to perform label–free fluctuation imaging. Unlike fluorescence, though, SHG is a coherent process. As a result, a new model was required for the study of the mobility of SHG active nanoparticles. We have developed a theoretical model for measuring the diffusion and flow properties of SHG active nanoparticles based on intensity fluctuation imaging. The model was successfully applied in experiments in suspension and in live cells. Typical challenges with fluorescence, such as photobleaching, blinking and saturation, are absent in SHG materials, allowing for stable, long–term measurements. Our findings can be employed in future research, such as environmental nanoparticle exposure studies. A penetration depth of more than 100 µm is feasible by using ultrasound imaging. Microbubbles, i.e. micrometer–sized gas bubbles with a stabilizing surfactant shell, can be used for contrast enhancement in ultrasound imaging. Employing microbubbles demands a method to characterize the shell properties of individual gas bubbles. We demonstrated a technique based on staining of the shell with the fluorescent probe Laurdan and measuring of both the fluorescence spectrum and the photoselection effect. These data allow determining the rigidity and the molecular organization of the shell. Future research is needed to investigate which shell characteristics are best suited to be applied to ultrasound imaging. In summary, we presented in this work (i) a method for resolution enhancement in optical imaging, (ii) a framework for measuring microbubble characteristics for contrast enhancement in ultrasound imaging and (iii) a protocol for label–free measurement of diffusion characteristics of nanoparticles. We believe that our results will offer new opportunities for further research on both a fundamental and an applied level.

208

N EDERLANDSTALIGE SAMENVATTING

ptische microscopen zijn alomtegenwoordig in biomedisch onderzoek. Ze helpen in de levenswetenschappen om vragen te beantwoorden door biologische structuren op micrometerschaal te visualiseren. Diffractie van het licht dat betrokken is bij de beeldvorming stelt echter een limiet op de grootte van de structuren die opgelost kunnen worden. De resolutie in optische microscopie is beperkt tot ongeveer 250 nm. De mechanismen van het leven onderzoeken op moleculaire schaal is dus niet mogelijk.

O

Een andere hindernis in optische microscopie is de moeilijkheid die licht ondervindt om diep door te dringen in driedimensionale stalen. Een oplossing hiervoor is gebruikmaken van multifotonmicroscopie. Bij een tweefotonenproces, zoals tweefotonenfluorescentie of opwekking van de tweede harmonische (second harmonic generation, SHG), interageren twee fotonen semisimultaan met het staal en produceren daarbij één foton met meer energie dan elk van de individuele fotonen had. Het licht gegenereerd door het staal heeft dus een kortere golflengte dan dat van de belichting. Door infrarode straling te gebruiken om het staal te belichten, kan men veel dieper, tot ongeveer 100 µm diep, doordringen. De lange belichtingsgolflengte heeft echter ook een negatief effect op de resolutie. Verschillende beeldvormingstechnieken werden gedurende de voorbije decennia ontwikkeld om de diffractielimiet te omzeilen. Eén van die methoden, image scanning–microscopie (ISM) genaamd, is in staat om de resolutie met een factor van ongeveer 1.4 te verbeteren. ISM kan gezien worden als een uitbreiding op conventionele confocale laserscannende microscopie waarbij de pinhole en de puntdetector verwijderd worden en een detector bestaande uit een matrix van verschillende detectorelementen geplaatst wordt in het beeldvlak. Ondanks het feit dat verschillende implementaties van ISM gerealiseerd zijn door andere onderzoeksgroepen, is de combinatie van ISM met multifotonprocessen nooit ten volle ontwikkeld. Eén van de hoofddoelstellingen van deze thesis was dan ook de realisatie van multifoton–ISM. 209

NEDERLANDSTALIGE SAMENVATTING

We hebben een ISM–opstelling gebouwd waarbij een multifotonfluorescentie– excitatielaser werd gebruikt. Hoewel we een resolutieverbetering in zowel twee– als driedimensionale stalen kunnen aantonen, is het effect minder uitgesproken in het laatste geval. Dit resultaat kan het gevolg zijn van een hogere graad van verstrooiing van de fluorescentie, met een lagere signaal–ruisverhouding tot gevolg. Hierdoor kan het reconstructiealgoritme mogelijk niet het optimale beeld produceren. In de toekomst zullen andere reconstructiealgoritmes en hun prestaties op beelden met een lage signaal–ruisverhouding getest moeten worden. Subdiffractie–informatie kan niet alleen verkregen worden door de microscopieopstelling aan te passen, maar ook door inventief gebruik te maken van een diffractiegelimiteerd systeem. Beeldvorming van de fluorescentie– intensiteitsfluctuaties is een verzameling van ensemble–gebaseerde microscopiemethoden die de diffusie–eigenschappen van deeltjes met nanometergrootte, bv. in suspensie, kunnen meten. Bij deze technieken wordt gebruik gemaakt van het willekeurige karakter van de beweging van de deeltjes in en uit het focale volume om de mobiliteit van de deeltjes te meten. Het fluorescentiepatroon in functie van de ruimte en de tijd wordt gefit aan een theoretisch model, waaruit de diffusiecoëfficiënt en de gerichte stromingssnelheid bepaald kunnen worden. Deze techniek is goed gekend voor fluorescente stalen maar veel minder voor SHG–actieve materialen, terwijl deze laatste juist als voordeel hebben dat ze labelvrij en voor een lange tijd gevolgd kunnen worden. In tegenstelling tot fluorescentie is SHG echter een coherent proces. Dit vereiste bijgevolg een nieuw model om de data te kunnen fitten. We hebben een theoretisch model ontwikkeld om de diffusie– en stromingseigenschappen van SHG–actieve nanodeeltjes te meten door de intensiteitsfluctuaties in beeld te brengen. Dit model is succesvol toegepast in experimenten in suspensie en in levende cellen. Typische uitdagingen die fluorescentie met zich meebrengt, zoals photobleaching, blinking en saturatie, zijn afwezig bij SHG, waardoor stabiele, langdurige experimenten mogelijk zijn. Onze bevindingen zijn zinvol voor toekomstig onderzoek, bv. voor studies waarbij het effect van blootstelling aan nanodeeltjes wordt onderzocht. Een penetratiediepte van meer dan 100 µm is mogelijk door gebruik te maken van ultrasone echografieën. Microbubbels kunnen hierbij aangewend worden om bijkomend contrast te geven. Microbubbels zijn gasbellen met een grootte tussen 0.1 µm en 100 µm die gestabiliseerd worden door een schil van amfifiele moleculen. Het gebruik van deze gasbellen vereist een methode om de schileigenschappen van individuele gasbellen te karakteriseren. Wij hebben aangetoond dat het kleuren van de schil met de fluorescente indicator Laurdan 210

en het opmeten van zowel het fluorescentiespectrum als het fotoselectie–effect toelaat om de rigiditeit en de moleculaire organisatie van de schil te bepalen. Bijkomend onderzoek is nodig om na te gaan welke schilkarakteristieken het best geschikt zijn om te gebruiken in contrastvloeistof voor echografieën. Samengevat, in dit werk hebben wij (i) een techniek voor resolutieverbetering in optische beeldvorming voorgesteld, (ii) een methode voor het bepalen van de schileigenschappen van microbubbels voor echografieën ontwikkeld en (iii) een protocol voor het labelvrij bepalen van diffusie–eigenschappen van nanodeeltjes uitgewerkt. Wij zijn ervan overtuigd dat onze resultaten mogelijkheden bieden voor verder onderzoek, zowel op een fundamenteel als een meer toegepast vlak.

211

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Publications in international journals Slenders E., Bové H., Urbain M., Mugnier Y., Sonay A. Y., Pantazis P., Bonacina L., Vanden Berghe P., vandeVen M., Ameloot M. “Image correlation spectroscopy with second harmonic generating nanoparticles in suspension and in cells”, The Journal of Physical Chemistry Letters, 9, 2018. Collins J. T., Zheng X., Braz N. V. S., Slenders E., Zu S., Vandenbosch G. A. E., Moshchalkov V. V., Fang Z., Ameloot M., Warburton P. A., Valev V. K. “Enantiomorphing chiral plasmonic nanostructures: a counterintuitive sign reversal of the nonlinear circular dichroism”, Advanced Optical Materials, 2018, 2018. Slenders E., Seneca S., Pramanik S. K., Smisdom N., Adriaensens P., vandeVen M., Ethirajan A., Ameloot M. “Dynamics of the phospholipid shell of microbubbles: a fluorescence photoselection and spectral phasor approach”, Chemical Communications, 54 (38), 2018. Coninx L., Thoonen A., Slenders E., Morin E., Arnauts N., De Beeck M. O., Kohler A., Ruytinx J., Colpaert J. V. “The SIZRT1 gene encodes a plasma membrane–located ZIP (Zrt–, Irt–like protein) transporter in the ectomycorrhizal fungus suillus luteus”, Frontiers in Microbiology, 8, 2017. Donders R., Sanen K., Paesen R., Slenders E., Gyselaers W., Stinissen P., Ameloot M., Hellings N. “Label–free imaging of umbilical cord tissue morphology and explant–derived cells”, Stem Cells International, 2016, 2016. Bové H., Steuwe C., Fron E., Slenders E., D’Haen J., Fujita Y., Uji-i H., vandeVen M., Roeffaers M., Ameloot M. “Biocompatible label–free detection of carbon black particles by femtosecond pulsed laser microscopy”, Nano Letters, 16 (5), 2016. 231

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Slenders E., vandeVen M., Hooyberghs J., Ameloot M. “Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating point scatterers – a comprehensive theoretical study”, Physical Chemistry Chemical Physics, 17, 2015. Losada-Perez P., Mertens N., de Medio–Vasconcelos B., Slenders E., Leys J., Peeters M., van Grinsven B., Gruber J., Glorieux C., Pfeiffer H., Wagner P., Thoen J. “Phase transitions of binary lipid mixtures: a combined study by adiabatic scanning calorimetry and quartz crystal microbalance with dissipation monitoring”, Advances in Condensed Matter Physics, 2015, 2015. Kouyate M., Flores-Cuautle J. J. A., Slenders E., Sermeus J., Verstraeten B., Ramirez B. M. L. G., Martinez E. S. M., Kubicar L., Vretenar V., Hudec J., Glorieux C. “Study of thermophysical properties of silver nanofluids by ISS–HD, hot ball and IPPE techniques”, International Journal of Thermophysics, 36 (10–11), 2015. Leys J., Losada–Perez P., Slenders E., Glorieux C., Thoen J. “Investigation of the melting behavior of the reference materials biphenyl and phenyl salicylate by a new type adiabatic scanning calorimeter”, Thermochimica Acta, 582, 2014.

Poster presentations Slenders E., vandeVen M., Ameloot M. “Raster image correlation spectroscopy with Second Harmonic Generating nanoparticles”, Belgian Physical Society Conference, Antwerp, Belgium, September 10th, 2017. Slenders E., Seneca S., Pramanik S. K., Smisdom N., Ameloot M., Ethirajan A., vandeVen M. “Characterization of lipid organization and rigidity in gas– filled microbubbles using optical microscopy”, Methods and Applications in Fluorescence, Bruges, Belgium, September 10th, 2017. Slenders E., Seneca S., Pramanik S. K., Smisdom N., Ameloot M., Ethirajan A., vandeVen M. “Characterization of lipid organization and rigidity in gas–filled microbubbles using optical microscopy”, Royal Belgian Society of Microscopy, Antwerp, Belgium, September 7th, 2017. Slenders E., vandeVen M., Ameloot M. “Image processing in super-resolution two-photon point scanning structured illumination microscopy”, Focus on Microscopy, Bordeaux, France, April 9th, 2017. Slenders E., Pramanik S. K., vandeVen M., Ethirajan A., Ameloot M. “Highly unusual fluorescent probe orientation in embedded lipid encapsulated microbub232

bles”, Royal Belgian Society for Microscopy, Brussels, Belgium, September 8th, 2016. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating nanoparticles”, Annual Scientific Meeting IAP, Hasselt, Belgium, September 11th, 2015. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “A theoretical study of coherence image correlation spectroscopy of higher harmonic generating point scatterers”, Econos Workshop on Non-Linear Imaging and Microscopy in Biology and Materials Science, Leuven, Belgium, April 12th, 2015. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “A theoretical study of coherence image correlation spectroscopy of higher harmonic generating point scatterers”, Focus on Microscopy, Göttingen, Germany, March 29th, 2015. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “Coherence correlation spectroscopy of higher harmonic generating point scatterers – a theoretical study”, µFiBR 2014 symposium, Diepenbeek, Belgium, October 3rd, 2014. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “Coherence correlation spectroscopy of higher harmonic generating point scatterers – a theoretical study”, Dutch Biophysics Meeting, Veldhoven, the Netherlands, September 29th, 2014.

Oral presentations Slenders E., Tcarenkova E., Tortarolo G., Castello M., vandeVen M., Koho S., Vicidomini G., Ameloot, M. “Image scanning microscopy – juggling with pixels for lateral resolution enhancement”, NanoMacro Microscopy Workshop, Diepenbeek, Belgium, September 6th, 2018. Slenders E., Seneca S., Pramanik S. K., Smisdom N., Adriaensens P., vandeVen M., Ethirajan A., Ameloot M. “Characterization of the phospholipid shell of microbubbles using fluorescence microscopy”, Belgian Physical Society Conference, Antwerp, Belgium, September 10th, 2017. Slenders E., vandeVen M., Hooyberghs J., M. Ameloot. “Coherent intensity fluctuation model for autocorrelation imaging spectroscopy with higher harmonic generating nanoparticles”, Annual Scientific Meeting IAP, Hasselt, Belgium, September 11th, 2015. 233

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Bursaries FWO Travel Grant for attending the EuroScience Open Forum 2018, Toulouse, France, from July 9th, 2018 to July 13th, 2018. FWO Travel Grant for a long stay abroad. Visit to Istituto Italiano di Tecnologia (IIT), Genova, Italy, from June 3rd, 2017 to August 13th, 2017. Travel Grant provided by Deutscher Akademischer Austauschdienst (DAAD) to attend the 4th International Summer School Modern Computational Science – Optimization at the University of Oldenburg, Germany, from August 19th, 2012 to August 31st, 2012.

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ysica. De studie van het allerkleinste tot het allergrootste. Ontstaan uit een mengsel van nieuwsgierigheid en logica, van theorie en experiment, van filosofie en praktische toepasbaarheid. Mijn passie voor de fysica vindt haar oorsprong in het vak Wetenschappelijk Werk op de middelbare school. Het is mede dankzij de lessen van mevr. Schraepen in het tweede jaar secundair onderwijs dat ik het jaar erna koos voor de richting Wetenschappen waarbij ik in het bijzonder uitkeek naar de lessen fysica. Hoewel ik een kleine explosie op z’n tijd wel kon waarderen, had ik, meer dan veel medeleerlingen, ook een sterke interesse in de minder spectaculaire en vaak ook meer theoretische onderwerpen.

F

Tien jaar geleden ben ik gestart met de opleiding Fysica aan de UHasselt. Het is hier dat ik voor het eerst kennis maakte met verscheidene takken van de natuurkunde, zoals kwantummechanica, relativiteit en biofysica. Niet alle leerstof was even eenvoudig of intuïtief maar het was juist door die vakken dat ik zeker wist de juiste richting gekozen te hebben. Bovendien zorgde de kleine maar heel toffe groep medestudenten voor een aangename sfeer. In het bijzonder wil ik Jeroen, Michiel, Peter, Alexandra en Sidney vermelden omwille van de drie fijne jaren die we samen beleefd hebben. De kleinschaligheid van de UHasselt kwam ook het contact tussen de studenten en het personeel ten goede. Er zijn verschillende proffen en assistenten – een bijzondere vermelding voor Mieke is hier op haar plaats – aan wie ik goede herinneringen bewaar omwille van de gedrevenheid waarmee ze lesgaven. Na de bacheloropleiding ging ik naar de KU Leuven waar ik een specialisatie moest kiezen voor de masterjaren. Ik heb lang getwijfeld tussen Kernfysica, Theoretische Fysica en mijn uiteindelijke keuze, Fysica van de Zachte Materie. Het interdisciplinaire karakter en de mogelijkheid om veel computationele vakken op te nemen gaven hierin de doorslag. Ik ben prof. Christ Glorieux heel dankbaar voor de kansen die ik toen bij hem gekregen heb. Niet alleen doceerde hij verschillende vakken, hij moedigde me ook aan om een summer school te doen in het buitenland en hij gaf me de mogelijkheid om mijn masterthesis in zijn labo 235

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te doen. Samen met dr. Jan Leys en prof. Jan Thoen hielp hij me bovendien twee keer om een doctoraatsbeurs aan te vragen. Omdat geen van beide aanvragen goedgekeurd werd, moest ik jammer genoeg al een half jaar na het behalen van mijn masterdiploma de groep verlaten. Toch kan ik terugblikken op een mooie tijd waarin naast het werk ook aandacht was voor andere activiteiten, zoals de game–avond, de voetbalmiddagen en het kerstfeestje. De ontgoocheling om niet te kunnen starten aan de KU Leuven was snel vergeten toen ik eind 2013 telefoon kreeg van prof. Marcel Ameloot. Ik mocht aan de UHasselt beginnen met een doctoraat in Geavanceerde Optische Microscopie. Marcel heeft me in de loop der jaren verdacht veel benadrukt dat ik niet enkel gekozen werd omdat ik de enige Nederlandstalige sollicitant was en daardoor gemakkelijk ingezet kon worden voor onderwijstaken. Waarom dan wel precies is me nooit helemaal duidelijk geworden. De vacature waarop ik gesolliciteerd had, ging over microscopie, resolutieverbetering en labelvrije beeldvorming. Voor de rest was het zeer vaag geformuleerd. Nu begrijp ik dat dat was onder het motto “het heeft geen zin om een gedetailleerde projectomschrijving te geven want een doctoraat loopt toch een andere kant op”. Het voordeel daarvan was dat ik in mijn eerste jaar de tijd kreeg om mij in te werken en voor een stuk zelf mijn pad uit te stippelen. Marcel, ik wil u bedanken voor de grote vrijheid die ik – naar mijn aanvoelen – van u gekregen heb. Uiteraard waren er regelmatig vergaderingen en e–mailupdates maar toch heb ik altijd heel zelfstandig mogen werken. Die vrijheid is niet vanzelfsprekend en heb ik dan ook sterk gewaardeerd. Inhoudelijk bestond mijn doctoraat uit een verzameling van verschillende projecten waarbij een gemeenschappelijke noemer soms moeilijker te vinden leek dan een krimpende microbubbel. Marcel, u weet dat ik over het ene project al iets enthousiaster was dan over het andere. Toch ben ik tevreden met de grote afwisseling die daardoor in het werk zat. In het bijzonder heb ik de mogelijkheid om zowel theoretisch als experimenteel werk te doen erg kunnen smaken. Marcel, bedankt voor de bijna vijf jaar dat ik deel mocht zijn van de Biofysicagroep. Uw zinvolle suggesties en oprechte feedback hebben de kwaliteit van dit werk zeker verhoogd. Prof. Luc Michiels, copromotor van mijn doctoraat, en de andere leden van mijn doctoraatscommissie, prof. Jef Hooyberghs en prof. Martin vandeVen, hebben via de jaarlijkse evaluatievergaderingen ook bijgedragen aan mijn onderzoek en wil ik bij deze dan ook bedanken. Luc, uw steevast positieve ingesteldheid was voor mij een extra stimulans om telkens weer goedgezind het volgende jaar te starten. Jef, de vele vragen die u stelde en de talrijke voorstellen die u deed tijdens de vergaderingen getuigden van een gemeende interesse in 236

mijn werk. Bovendien heeft u meegewerkt aan de theorie die uiteindelijk tot mijn eerste publicatie heeft geleid. Martin, uw belangrijke bijdrage mag niet onderschat worden. Met onder andere computersimulaties, experimenten en veel opzoekwerk in de literatuur heeft u een grote impact gehad op dit werk. Het tempo waarop u artikels kunt lezen en onthouden is indrukwekkend. Niet alleen weet u enorm veel over (bio)fysica, ook uw algemene kennis, gaande van het Chinese schrift via de dialecten van Limburg tot de trekroutes van vogels, is fenomenaal. Naast de leden van de doctoraatscommissie ben ik ook de externe jury bestaande uit prof. Pieter Vanden Berghe, M.E.R. Luigi Bonacina en prof. Kevin Braeckmans dankbaar voor het kritisch nalezen van mijn thesis. Pieter, bedankt voor alle keren dat ik bij u in het labo mocht komen meten, voor uw feedback op het manuscript waaraan u hebt meegewerkt en voor de interessante discussies die we verschillende keren gehad hebben. Luigi, I still remember the first time we met, at a conference in Maastricht. I had a question about the nonlinear correlation spectroscopy paper. You took your time to kindly explain this subject and you brought me into contact with your coworkers. Thank you for contributing to this project. Kevin, wij hebben elkaar de voorbije jaren niet zo heel vaak ontmoet, maar uiteraard heb ik uw gedetailleerde feedback op mijn werk even sterk gewaardeerd. Bedankt. Toen ik mijn doctoraat begon in 2014, was de biofysicagroep nog best groot. Met Nick, Kristof, Rik, Kathleen, Sarah, Rozhin, Daniel en Hannelore had ik een heleboel collega’s die me hielpen om vlot te kunnen starten. Rik, jij hebt me de ins and outs van de confocale microscoop geleerd. Als fysicus/ingenieur was jouw achtergrond heel gelijkaardig aan die van mij en heel anders dan die van zowat alle andere doctoraatsstudenten op BIOMED. Het was dan ook een geruststelling om van jou te horen dat het normaal is dat het wat tijd vraagt om aan die biomedische omgeving gewoon te worden. Hoewel ik na bijna vijf jaar nog altijd geregeld merk dat mijn basiskennis over cellen en weefsels wel heel basis is, heb ik toch heel wat opgestoken van jou, onder andere door te mogen meewerken aan het spieronderzoek bij MS– en diabetespatiënten. Kristof and Daniel, I had the privilege to go with you to the FLIM meeting in Saarbrücken, my first conference as a PhD student. For some reason you thought that me ordering there a hot chocolate milk with whipped cream was hilarious. I still don’t fully understand why that was funny, but I do know that with you two around things don’t get boring easily. Sarah and Rozhin, with you it was easier to have a serious conversation. Thank you for introducing me into the world of nanoparticles and RICS. Kathleen, jij had het talent om de sowieso al overvoltijdse job van doctoraatsstudent nog te combineren met die van professioneel organisator, consultant en psycholoog. Ik geef toe dat 237

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het nogal gemakkelijk was om die taken aan jou uit te besteden maar het moet gezegd dat je dat uitstekend deed. Je bekommerde je om iedereen, je organiseerde teambuildingactiviteiten en je stelde regelmatig voor om samen iets te gaan doen: de jeneverfeesten, naar het EK voetbal kijken, Winterland,... Ook al ben je al een tijdje weg van BIOMED, het blijft fijn om regelmatig contact te houden. Nick, jij bent pas in de tweede helft van mijn doctoraat een voltijdse collega geworden maar in die periode heb ik wel veel van je geleerd. Veel wetenschappelijke zaken, nog meer niet–wetenschappelijke zaken. Tot die eerste categorie behoren onder andere verschillende microscopietechnieken en -systemen en Matlabtricks. Je voorliefde voor woordspelingen, nu zit ik bij de tweede categorie, is ondertussen legendarisch. Veel woordgrapjes waren goed, sommige waren minder goed, zowat allemaal hadden ze bij mij tijd nodig om door te dringen. Toch ga ik dat wel missen, net zoals de slechte geur van warme chocolademelk uit de automaat, die gaat waar jij gaat (de geur, niet de automaat). Als ik nog een tip mag geven voor de toekomst: leg de lat iets hoger bij het kiezen van een hotel. Hannelore, jij bent de enige met wie ik bijna letterlijk van de eerste tot de laatste dag van mijn doctoraat het bureau gedeeld heb. Jouw inzet en gedrevenheid zijn bewonderenswaardig, jouw CV is indrukwekkend. Je hebt me ook geholpen met ‘mijn’ celexperimenten en je gaf me zo nu en dan een spoedcursus biologie. Toch nam je naast al dat werk nog de moeite en de tijd om de hele biofysicagroep te bevoorraden met grote hoeveelheden (zelfgemaakte) cake, taart en snoep. Bovendien hield je ons op de hoogte van het bovengrondse reilen en zeilen op BIOMED. Als je wat te vertellen had, had ik altijd wel de intentie om actief te luisteren maar ik geef toe dat het er niet altijd ook effectief van kwam. Bij deze wil ik benadrukken dat ik toch heel dankbaar mag zijn jou als collega gehad te hebben. Ondertussen heb je een nieuwe positie maar gelukkig kom je nog regelmatig naar BIOMED. Als je in de nabije toekomst nog metingen komt doen en er scheelt iets met één van de microscopen, dan wil ik gerust kijken (heb je ’m?) naar het probleem. Bedankt allemaal! Sinds 2014 zijn er veel collega’s gegaan maar gelukkig zijn er ook weer anderen bijgekomen. Bart, Jelle en Veerle, strikt genomen zijn jullie geen biofysicacollega’s maar toch zijn jullie voor een stuk deel van onze groep. Bart, het was altijd fijn om jou terug te zien wanneer je tussen je werk op het VITO door nog eens een sporadisch bezoekje bracht aan BIOMED. Veel succes met het verdere verloop van je doctoraat – en met het planten van virtuele prei! Jelle, jouw komst is zeker een versterking geweest voor het Bioimaging team. Ik ben ervan overtuigd dat de nieuwe microscopen bij jou in goede handen zijn. Veerle, jij kunt als geen ander ’s ochtends goedgezind toekomen op het werk. Dat alleen al maakt van jou een fijne collega, al helpt het natuurlijk ook dat je zo nu en dan zelfgemaakte koekjes meebrengt. Uiteraard wens ik ook jou alle succes toe met je onderzoek – en met alles daarnaast. 238

Doorheen de jaren zijn er nog verschillende anderen geweest die in meer of mindere mate hebben bijgedragen tot dit werk, of – even belangrijk – tot het aangenaam invullen van de beperkte vrije tijd. Marco and Stefan, your theoretical skills are impressive. Thank you for the small discussions now and then about RICS, general physics topics, or not work–related topics. The Materials Physics group of Anitha, thank you for your collaboration in the microbubble project. Senne, ik zou in het bijzonder jou willen bedanken voor het harde werk bij het maken van de preparaten, vaak heel vroeg in de ochtend of laat in de avond. Jouw energie en passie voor wetenschappelijk onderzoek zijn vermeldenswaardig. Michel, Rik en Dorine, bedankt voor jullie hulp bij het organiseren van de practica elektromagnetisme. Tijdens de jaarlijkse fysicavoetbaltoernooitjes zorgden jullie bovendien, samen met de rest van de ‘G6 en omstreken’, telkens weer voor een geslaagde avond. My ten–week research stay in Genoa, Italy, during the summer of 2017 was definitely one of the coolest (and hottest) adventures I’ve ever experienced. Giuseppe, thank you for inviting me to your Molecular Microscopy and Spectroscopy lab at the Italian Institute of Technology. Thanks to your support and enthusiasm, I’ve been able to get really nice results in a limited amount of time. Of course, I am also very grateful and honored that you recently offered me a postdoc position. Marco and Giorgio, you were always very helpful in the lab. You showed a lot of interest in my work and I remember your excitement when we discussed the final results. Sami, I highly appreciated your support and mentorship during my stay. The phrase So, how’s it going? you very often asked upon entering the lab was a genuine expression of interest and concern. Apart from the scientific aspects, you also assisted with practical questions concerning public transport, internet, etc. and you showed me and Elena the most beautiful places in and around Genoa. Elena, enthusiastic and energetic are understatements to describe your character. You are/were a hardworking and talented PhD student. I remember several very late evenings we spent in the lab, trying to perfectionize the alignment of the microscopes. You were definitely an awesome colleague, with now and then a somewhat crazy idea, like waking up at 5:00 a.m. to go hiking. Thank you for making an already enjoyable research stay even more exciting. I wish you all the best with your PhD – and with the color of your phone! Molte grazie a tutti e a presto. Vrienden van de fysica, Peter, Michiel en Jeroen, ondanks dat we ondertussen niet meer allemaal in dezelfde tijdzone wonen, houden we toch nog regelmatig contact. Op een aantal collega’s na waren jullie zowat de enigen die de voorbije jaren konden begrijpen wat mijn werk inhield. Bedankt voor jullie interesse, voor jullie suggesties met betrekking tot mijn toekomstig verblijf in Italië en voor de nodige ontspanning tijdens de game–avonden. Jeroen, ik moet jou in het 239

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bijzonder bedanken om mijn thesis na te lezen, niet alleen op taal, maar zelfs voor een stuk ook op inhoud! Hopelijk kunnen we volgend jaar nog eens met z’n allen samenkomen. Tot slot wil ik nog mijn familie bedanken. Oma† , oma en opa† , tantes en nonkels, meter en peter, broers en zussen, de ene al iets beter dan de andere op de hoogte van wat ik eigenlijk deed als job, maar allemaal wel geïnteresseerd in mijn werk. Mama en papa, jullie moet ik in het bijzonder bedanken voor jullie steun en interesse, voor de kansen die ik gekregen heb om verder te studeren en uiteraard voor de komende reis naar Malta die jullie ons vijven, jullie zonen en dochters, cadeau gedaan hebben omdat we – geheel volgens verwachting natuurlijk – allemaal een mooi diploma gehaald hebben. Bedankt!

Eli, 31 oktober 2018

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