Apr 29, 2009 ... The Optical Transfer Function (OTF) and ..... Consider the optical system from
lecture 19, slide 16, with a pupil mask consisting of two holes, ...
Today
• Temporal and spatial coherence • Spatially incoherent imaging – The incoherent PSF – The Optical Transfer Function (OTF) and
Modulation Transfer Function (MTF)
– MTF and contrast – comparison of spatially coherent and incoherent imaging
next two weeks • Applications of the MTF • Diffractive optics and holography
MIT 2.71/2.710 04/29/09 wk12-b- 1
Temporal coherence
Michelson interferometer
If paths 1 & 2 are matched, then the recombined waveforms at the detector are correlated so they produce interference fringes. However, as the difference d2−d1 increases, the degree of correlation decreases and so does the contrast in the interference pattern.
random illumination (not single color anymore) detector
1 0.8
waveform from path 2, time delay t2=const+2d2/c
0.6
0.2
1
0
0.8
−0.2
0.6
−0.4
0.4
−0.6
0.2
E(t) [a.u.]
E(t) [a.u.]
0.4
por of e al dep e mit ted nden fiel ce d
−0.8
2
4
6
8
0
interference no interference (fields add coherently) (fields add incoherently)
−0.2
10
t [µ sec]
−0.4 −0.6 −0.8 −1 0
2
4
6
8
10
t [µ sec]
1
d2
tem
−1 0
0.9 0.8 0.7
I(d2−d1) [a.u.]
point source 1
d1
0.8
E(t) [a.u.]
MIT 2.71/2.710 04/29/09 wk12-b- 2
0.5 0.4 0.3
0.6
0.2
0.4
waveform at mirror 1,
time delay t1=const+2d1/c
0.6
0.2
0.1
0 −0.2
0 0
−0.4 −0.6 −0.8 −1 0
2
4
6 t [µ sec]
8
10
2
4
d2−d1 [µm]
6
8
10
Spatial coherence
Young interferometer 10
If holes 1 & 2 are coincident, or very closely spaced, then the recombined waveforms at the detector are correlated so they produce interference fringes. However, as the difference x2−x1 increases, the degree of correlation decreases and so does the contrast in the interference pattern.
waveform from hole 2, location x2
4
x [µm]
6
8
waveform from hole 1, location x1
x2 matched paths (equal time delay from the two holes to the detector)
1 0.9 0.8 0.7
I(x2−x1) [a.u.]
−1 0
x1
interference recorded near the bisectrix (almost matched paths)
E(x) [a.u.]
random waveform
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
2
interference no interference (fields add coherently) (fields add incoherently)
0.6 0.5 0.4 0.3 0.2 0.1 0 0
MIT 2.71/2.710 04/29/09 wk12-b- 3
2
4
x2−x1 [µm]
6
8
10
Field intensity in the coherent and incoherent cases
