Sensitive photothermal interferometric detection

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ence fringe pattern formed at a plane with a distance away from the sample, the Gaussian propagation characteristic of the probe laser beam must be taken into ...
Sensitive photothermal interferometric detection method for characterization of transparent plate samples Bincheng Lia) Department of Chemistry, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China

Yanzhuo Deng Center for Analysis and Testing, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China

Jieke Cheng Department of Chemistry, Wuhan University, Wuhan 430072, Hubei, People’s Republic of China

~Received 30 October 1995; accepted for publication 30 May 1996! In this article, a recently developed, sensitive photothermal interferometric detection technique, in which an interference fringe pattern formed by overlapping two reflected probe beams from the front and rear surfaces of the sample was used to measure the photothermal signal, and its application for characterization of transparent ~or partially transparent! plate samples were theoretically and experimentally investigated in detail. The theoretical descriptions of the intensity distribution of the interference fringe pattern and the photothermal signal with pulsed excitation were presented. Experiments were conducted with plate samples of optical glasses doped with heavy-metal ions and the results were compared with the theoretical ones. Good agreement between theoretical and experimental results demonstrated the proposed photothermal interferometric detection technique to be a sensitive photothermal method for the study of the thermophysical properties of transparent samples. Its applicability to weak absorption or spectroscopy measurement and microvolume trace analysis was also discussed. © 1996 American Institute of Physics. @S0034-6748~96!02109-0#

I. INTRODUCTION

There has been increasing interest in applications of photothermal spectroscopy technique to absorption measurement and material characterization.1–3 For transparent materials such as optical glasses, weakly absorbing gases, or liquids, thermal lensing spectroscopy~TLS!,4,5 photothermal deflection spectroscopy ~PTDS!,6,7 or photothermal phase-shift spectroscopy ~PTPS!8,9 technique has been used to measure the weak absorption or thermo-optical parameters of samples. Photothermal phase-shift spectroscopy technique was discovered by Stone,10 by Davis,11 and by Davis and Petuchowski,12 who refer to this technique as phase fluctuation optical heterodyne ~PFLOH! spectroscopy. Since then many theories and applications of this technique have been investigated.8,9,13,14 In this article we refer to this technique as photothermal interferometric detection technique. The basis of the photothermal interferometric detection technique is two-beam interference. As a laser beam ~either pulsed or cw modulated! illuminates the sample, the heating produced by the absorption of laser radiation causes a temperature rise within the sample, resulting in a change in refractive index of the measured sample due to the temperature-induced changes of electronic polarizability and/or thermal expansion of the sample.5 If one places the sample in one arm of an interferometer, a phase shift produced by the refractive index change causes a spatial shift of the interference fringe. By experimentally detecting the fringe shift with a position-sensitive detector ~PSD!, one can a!

Present address: Laboratory of Photoacoustic Sciences, Institute of Acoustics, Nanjing University, Nanjing 210093, People’s Republic of China.

Rev. Sci. Instrum. 67 (10), October 1996

determine the structural, thermal, and optical properties of the sample. Recently, a photothermal interferometric method based on the interference between the two retroreflected beams from the two surfaces of a transparent plate or thin film was developed to measure the thermal diffusivity,15,16 thickness, and sound velocity ~see Fig. 1!.17,18 The same general interferometric approach is widely used for optical nondestructive testing, refractive index and thickness measurements of thin transparent films, and monitoring the temperature of plate sample.19 Compared to other interferometric measurement techniques, this retroreflected beam interference configuration is simple and easy to align. Since both the signal and reference beams reflect from the same component ~the sample!, by carefully designing the optical arrangement ~for example, the probe beam is normally incident on the surface of the sample!, this method is relatively insensitive to environmental vibration ~including the sample translation! and air turbulence, as well as the refractive index variation in the medium surrounding the sample. The measurement sensitivity, therefore, can be improved. The photothermal interferometric detection technique employing the retroreflected beam interference possesses all the advantages mentioned above, that is, simplicity of optical arrangement, convenience of alignment, and high measurement sensitivity. Being a common photothermal measurement technique, this method can find wide applications in the characterization of transparent solid plates such as optical glasses5 or polymers,20 weak absorption or spectroscopy measurement of optically thin liquids or gases, as well as microvolume trace analyses of biological or chemical substances. But, to our knowledge, not many applications of

0034-6748/96/67(10)/3649/9/$10.00

© 1996 American Institute of Physics

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FIG. 2. Detailed illumination of the formation of an interference fringe pattern at the detection plane for an oblique incidence case. FIG. 1. Schematic diagram of proposed photothermal interferometric detection technique.

this photothermal interferometric detection method have been reported until now, especially in applications to weak absorption and spectroscopy measurement and trace analysis. In our opinion, this is mainly due to lack of detailed methodological investigation of this configuration, both theoretically and experimentally. This is the main purpose of the present article. Differing from that described by Saenger,15 in this article we use tightly focused ~other than nonfocused! laser beams as the probe and excitation beams. Therefore, our experimental scheme is spatially resolved and is capable of high resolution nondestructive evaluation ~NDE! and imaging, as well as microvolume trace analysis and as an on-column detector for high performance liquid chromatography ~HPLC! and capillary electrophoresis ~CE!. Optimum detection sensitivity is obtained by appropriately choosing the detector position at the interference fringe pattern for different incident angles of the probe beam. The proposed experimental scheme is suitable for samples with thicknesses from several micrometers to several centimeters. The main restriction of this technique deals with the necessity for the sample under study to have smooth and approximately parallel surfaces and appropriate thickness, and also to be at least partially transparent to the probe beam wavelength ~it is not necessarily transparent to the excitation beam wavelength!. Fortunately, these requirements are easy to meet for most materials of interest mentioned above. In Sec. II, we present the theoretical description of the intensity distribution of the interference fringe pattern at the detection plane, the differential detection of the optical phase shift, and the photothermal interferometric signal at pulsed excitation case. The experimental arrangement is described in Sec. III and the results and discussions are given in Sec. IV.

ure 2 shows a detailed illumination of formation of the interference fringe pattern at the detection plane by two reflected beams of a focused probe laser beam from the front and rear surfaces of the sample. Suppose that the propagation axis of the probe beam and its reflected beam from the front surface of the sample is used as the z axis, and the waist position of the probe beam is located at z50. The propagation distance of the probe beam from the waist position to the front surface of the sample is z 1 and the distance from the front surface to the detection plane is z 2 . The ~1/e 2! waist radius of the probe beam is v0 , the incident and refractive angles are u and u1 , and the refractive index and thickness of the sample are n and d, respectively. The field intensity distribution of the reflective probe beam from the front surface of the sample at the detection plane is21 E 1 ~ x,y ! 5

When deducing the intensity distribution of the interference fringe pattern formed at a plane with a distance away from the sample, the Gaussian propagation characteristic of the probe laser beam must be taken into consideration. Fig3650

Rev. Sci. Instrum., Vol. 67, No. 10, October 1996

v1

exp~ 2r 2 / v 21 !

F S

3exp 2ik z 1 1z 2 1

r2 2R 1

DG

~1!

,

where v1 is the ~1/e 2! radius of the reflected beam at the detection plane, R 1 is the curvature radius of the laser beam wave front, k52p/l is the wave number, l is the wavelength of the probe beam, R r is the reflectivity of the sample surface, C is a constant, r 5 Ax 2 1y 2 , and

v 1 5 v 0 $ 11 @~ z 1 1z 2 ! / f # 2 % 1/2,

~2!

R 1 5 ~ z 1 1z 2 ! $ 11 @ f / ~ z 1 1z 2 !# % .

~3!

2

f 5pv20/l

is the confocal distance of the probe beam. Here we have assumed that the central point of the reflected beam from the front surface of the sample at the detection plane was the origin of the x-y coordinate system, and the x axis was along the direction of the origin to the central point of the reflected beam from the rear surface. The field intensity distribution of the reflected beam from the rear surface at the detection plane is

II. THEORY A. Intensity distribution of interference fringe pattern

ACR r

E 2 ~ x,y ! 5

AC ~ 12R r ! 2 R r v2

F S

exp~ 2r 8 2 / v 22 !

3exp 2ik z 1 1z 2 12nd cos~ u 1 ! 1

r 82 2R 2

DG

,

~4! Photothermal interferometer

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where r 8 2 5 ~ x2D ! 2 1y 2 ,

~5!

D52d cos~ u ! tan~ u 1 ! ,

~6!

v 2 5 v 0 ~ 11 $ @ z 1 1z 2 12d cos2 ~ u ! /n 3cos~ u 1 !# / f % 2 ! 1/2,

~7!

R 2 5 @ z 1 1z 2 12d cos2 ~ u ! /n cos~ u 1 !#~ 1 1 $ f / @ z 1 1z 2 12d cos2 ~ u ! /n cos~ u 1 !# % 2 ! .

~8!

Here we have assumed that both surfaces have the same reflectivity R r and the sample does not absorb the probe light. The intensity distribution resulting from the interference of the two reflected probe beams, therefore, is

FS

I ~ x,y ! 5I 1 1I 2 12 AI 1 I 2 cos k 2nd cos~ u 1 ! r8 r 1 2 2R 2 2R 1 2

2

DG

~9!

,

where I 1 5CR r / v 21 •exp~ 22r 2 / v 21 ! ,

~10!

I 2 5CR r ~ 12R r ! 2 / v 22 •exp~ 22r 8 2 / v 22 ! .

~11!

Examination of Eq. ~9! indicates that a regularly spaced linear interference fringe pattern is formed at the detection plane. The constructive and destructive interference reciprocally occur along the x direction. The intensity distribution along the x axis is

FS

I ~ x ! 5I 1 ~ x ! 1I 2 ~ x ! 12 AI 1 ~ x ! I 2 ~ x ! cos k 2nd cos~ u 1 ! 1

x2 ~ x2D ! 2 2 2R 2 2R 1

DG

~12!

,

where I 1 ~ x ! 5CR r / v 21 •exp~ 22x 2 / v 21 ! ,

~13!

I 2 ~ x ! 5CR r ~ 12R r ! 2 / v 22 •exp@ 22 ~ x2D ! 2 / v 22 # .

~14!

The fringe spacing is dependent on the propagation distance from the sample to the detection plane, the sample thickness, and the incident angle. When z 1 1z 2 @ f , d@l, and the incident angle is not too small, the fringe spacing is approximately expressed as l'l ~ z 1 1z 2 ! / @ 2d cos~ u ! tan~ u 1 !# .

~15!

As the incident angle decreases, the fringe spacing increases, the linear fringe pattern is gradually distorted, and, at last, a circular fringe pattern is formed at the detection plane in the case of normal incidence ~as shown in Fig. 3, the incident angle is equal to zero!. The intensity distribution of the circular fringe pattern is I ~ r ! 5I 1 ~ r ! 1I 2 ~ r ! 12 AI 1 ~ r ! I 2 ~ r !

FS

3cos k 2nd1

r2 r2 2 2R 2 2R 1

DG

,

Rev. Sci. Instrum., Vol. 67, No. 10, October 1996

~16!

FIG. 3. Illumination of the formation of an interference fringe pattern for the case where the probe beam is normally incident on the sample surface.

where I 2 ~ r ! 5CR r ~ 12R r ! 2 / v 22 •exp~ 22r 2 / v 22 ! ,

~17!

v 2 5 v 0 $ 11 @~ z 1 1z 2 12d/n ! / f # 2 % 1/2,

~18!

R 2 5 ~ z 1 1z 2 12d/n ! $ 11 @ f / ~ z 1 1z 2 12d/n !# 2 % .

~19!

The expressions for I 1 (r), R 1 , and v1 are same as that mentioned previously. If the surfaces of the sample are not parallel but have a small angle, that is, a wedge-shaped plate sample, an approximately linear fringe pattern is formed at the detection plane, which is similar to the case of the probe beam being obliquely incident on a sample with parallel surfaces. But in this case the angle between the two surfaces must be smaller than the divergence angle of the focused probe beam; otherwise the two reflected beams do not overlap and no interference fringe pattern is formed at the far field. The normal incidence experimental scheme has the advantages that the photothermal signal is relatively insensitive to the refractive index variation in air surrounding the sample and the photoreflectence effect. Because both the reference and signal beams pass the same path outside the sample, the fringe shifts at the detection plane are only related to the optical phase shift caused by the photothermal effect inside the sample; the environmental vibration and the air turbulence have little effect on the photothermal measurement. The disadvantage of the normal incidence configuration is that the circular fringe pattern formed at the detection plane is less convenient for differential detection than the linear fringe pattern formed in the oblique incidence case. The oblique incidence configuration is used in our experimental arrangement. B. Measurement of small phase shift

Usually a typical experimental scheme for phase-shift measurement with interferometric detection is that using a detector ~for example, a photodiode! positioned behind a pinhole to measure the intensity change at the midpoint between the constructive and destructive interference to determine the fringe shift.8,12,22 Recently a position-sensitive detection method was introduced for measurement of the phase shift and higher measurement sensitivity was demonstrated.23,24 For a linear fringe pattern, a slit and a position-sensitive detector are used to measure the fringe shift caused by the phase shift, as shown in Fig. 4. We assume that the width of Photothermal interferometer

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FIG. 5. Theoretical differential output of PSD vs the slit position.

F S

2p 1 C Il a1 i 8a 5i a 1 K 1 I 0 • sin x 02 2 p l 2 FIG. 4. Measurement of fringe shift with a position-sensitive detector.

the slit is a and the fringe spacing is l. The centerline of the PSD is located at a position shown in Fig. 4. For simplicity, the intensity distribution of the interference fringe pattern is simply described by the one-dimensional sinusoidal function 1 I ~ x ! 5 I 0 @ 11C I cos~ 2 p x/l !# , 2

~20!

where C I is the intensity contrast, and I 0 is the maximum intensity. Assume that the centerline of the PSD is located at position x 0 . Then the output currents of the two cells of the PSD are given by i a 5K 1

i b 5K 1

E

x0

x 0 2a 1

E

x 0 1a 2

x0

~21!

I ~ x ! dx,

~22!

I ~ x ! dx,

H S DJ H S DJ

F S

2p 1 C II 0l a1 i a5 K 1 a 1I 01 cos x 02 2 p l 2

p a l 1

p a l 2

DG ~23!

,

F S

2p 1 C II 0l a2 cos x 01 i b5 K 1 a 2I 01 2 p l 2 3sin

DG

.

~24!

A small phase shift Df ~Df!p/2! will cause a small fringe shift at the interference pattern, resulting in changes of the output currents of the two cells of the PSD, i.e., 3652

S D

p a •D w , l 1

Rev. Sci. Instrum., Vol. 67, No. 10, October 1996

~23a!

F S

1 C Il a2 2p sin x 01 i 8b 5i b 1 K 1 I 0 • 2 p l 2 3sin

S D

DG

p a •D w . l 2

~24a!

The signal current, which is the output current of the differential amplifier, is the complementary output of the PSD

S

i5K 2 ~ i a8 2i b8 ! 5K ~ i a 2i b ! 1

I 0C Il Dw 2p

H S D F S DG S D F S D GJ D

3 sin 2sin

p 2p a1 a 1 sin x 02 l l 2

p 2p a2 a 2 sin x 01 l l 2

,

~25!

where K 2 is the gain of the differential amplifier, and K5K 1 K 2 . To obtain maximum measurement sensitivity and minimum common-mode noise output, we have i a 2i b 50,

with a 2 5a2a 1 . K 1 is a constant that depends on the sensitivity and mixing efficiency of the PSD. Substituting Eq. ~20! into Eqs. ~21! and ~22!, we have

3sin

3sin

DG

a 1 5a 2 5l/2,

~26! a5l.

~27!

That is, without the phase shift Dw, the two cells of the PSD have identical output current, and the slit width equals the fringe spacing. Figure 5 shows the differential output i versus the centerline position x 0 while i a 2i b 50 and a5l. From Fig. 5 we learn that the maximum measurement sensitivity is obtained when the centerline of the PSD is located at the constructive or destructive interference ~brightest or darkest point! position. The constructive interference position is preferable because it is more stable than the destructive interference position. At the constructive interference position, Eq. ~25! can be simply expressed as i52KC I P 0 / p •D w ,

~28!

where P 0 is the total power of the fringe used for detection. Equation ~28! shows that for a small phase shift, the differential output of the PSD is directly proportional to the phase shift. From Eq. ~28! the minimum detectable phase shift therefore is14 Photothermal interferometer

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D w min5

Ah

phnD f , CIP0

~29!

where h n is the laser photon energy of the probe beam, h is the detector quantum efficiency, and D f is the bandwidth. In fact, this ultimate sensitivity set by the photon noise limit is very difficult to achieve because of existence of noises induced by mechanical vibration, air turbulence, pointing error of the laser beam, etc. The actual performance will be very much improved if the interferometric system is insensitive to those noise sources. C. Expressions for pulsed photothermal signals

A rigorous theoretical treatment of the photothermal phase-shift signals has been given by Bonson and co-workers.8 However it is not directly usable for our experimental configuration. We present here a simple model which is adequate for our purposes. A phase shift caused by the temperature rise within the sample can be expressed as5 Dw5

2p l

E

path

ds •T ~ x,y,z,t ! ds, dT

~30!

where ds/dT is the temperature coefficient of optical path length of the sample. The integration is carried out over the path of the probe beam. For a solid sample such as optical glasses,25 ds dn 1 3 5 ~ n21 !~ 11 n ! b 1 1 n Y b ~ q 111q 12! , dT dT 4

~31!

~32!

where n is the refractive index, n is Poisson’s ratio, and b is the linear temperature coefficient of thermal expansion. Y is Young’s moludus. q 11 and q 12 are the stress-optic coefficients. dn/dT is the temperature coefficient of the refractive index. For a weakly absorbing sample with optical absorption coefficient a, the temperature distribution within the sample following the excitation by a laser pulse of the form Q(r)5I 0 exp(22r 2 / v 2p ) d (t) @d(t) is the delta function# is27 T p ~ r,t ! 5

1 2aE0 • • exp@ 22r 2 / ~ v 2p pr c v 2p 18k tht 18k tht !# ,

3exp@ 22x 20 / ~ v 2p 18k tht !# 1

E

d/cos~ u 1 !

0

exp$ 22 @ x 0 12z

D

3tan~ u 1 !# 2 / ~ v 2p 18k tht ! % dz ,

~34!

where x 0 is the relative position between the probe and excitation beams. The peak value of the photothermal signal, which occurs immediately after the excitation pulse turns off, can be obtained by setting the time t50 in Eq. ~34!. For a sample with relatively high optical absorption coefficient, the temperature gradient along the propagation direction of the excitation within the sample is no longer negligible, and the thermal conduction at the interfaces and along the propagation axis in the sample must be taken into account when solving the thermal conduction equation. This procedure is quite complicated, and only a numerical solution to this equation has been given until now. But if only the peak value of the photothermal signal is used for measurement, it is simple because the thermal conduction during the heating of the sample by the excitation pulse is negligible. For our experimental configuration the peak phase shift caused by the temperature rise within the sample is D w p max5

S

2 p ds 2 a E 0 1 1 • • • exp~ 22x 20 / v 2p ! l dT pr c v 2p a

E

d/cos~ u 1 !

0

D

3exp$ 22 @ x 0 12z tan~ u 1 !# 2 / v 2p 2 a z % dz .

~35!

Equation ~34! expresses the photothermal signal transient for a weakly absorbing material, while Eq. ~35! presents the signal peak magnitude for a material with relatively high optical absorption coefficient. Equations ~34! and ~35! show that the photothermal signal peak magnitude is related to the absorption coefficient, the temperature coefficient of the optical path length, and the signal transient is related to the thermal diffusivity of the material. By experimentally measuring the photothermal signal peak magnitude and/or transient, these parameter values can be separately determined. III. EXPERIMENTAL SETUP

~33!

where E 0 is the energy of laser pulse, and k th5K/ r c is the thermal diffusivity. K, r, and c are the thermal conductivity, density, and specific-heat capacity of the sample. vp is the radius of the excitation beam. Substituting Eq. ~33! into Eq. ~30! and taking the experimental configuration shown in Fig. 6 into consideration, we obtain the photothermal phase shift at the pulsed excitation case as Rev. Sci. Instrum., Vol. 67, No. 10, October 1996

S

1 2 p ds 2 a E 0 d • • • 2 l dT pr c v p 18k tht cos~ u 1 !

3 $ 12exp@ a d/cos~ u 1 !# % 1

while for liquid or gas samples,26 ds dn ' , dT dT

D w p5

The experimental photothermal interferometric detection configuration is illuminated in Fig. 6. A Nd:YAG frequencydoubled pulsed laser operated at 532.1 nm wavelength is used as the excitation beam, illuminating the sample from the rear surface. The pulsed duration is 8 ns and the repetition rate is 10 Hz. A 2 mW He–Ne laser at 632.8 nm wavelength is used as the probe beam. A bicell photodiode detector is used as position-sensitive detector to measure the fringe shift at the interference field. The output of the detector is fed into the input end of a boxcar averager after difPhotothermal interferometer

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ferentiation and amplification by a differential amplifier. The signal is monitored by a storage oscilloscope and the output of the boxcar averager is recorded by a recorder. After propagating through a prism and an aperture for eliminating the light at 1.06 mm wavelength, and an variable attenuator for energy adjustment, the excitation beam is focused by a spherical lens ~focal length 140 mm! onto the sample from the rear surface. A fraction of the laser energy is sampled out and monitored by an energy meter. Another small part of the excitation beam is used to trigger the boxcar averager and the storage oscilloscope. Care is taken to adjust the energy of the excitation beam illuminating the sample to prevent the occurrence of nonlinear effects.28 The probe beam is focused with a lens of 46 mm focal length onto the sample from the front surface. To maximize the interaction length of the excitation and probe beams and therefore the photothermal signal magnitude, the collinear photothermal configuration is used. The relative position of the excitation and probe beams is adjusted by carefully moving the focusing lens L1 mounted on a micrometer-driven translation stage. The probe beam ~and also the excitation beam! is incident on the sample surface with an incident angle of 16.3°; therefore, the reflected probe beams do not pass through focusing lens L2 again. A filter is used before a He–Ne laser to prevent the excitation beam to enter into the resonator of the probe laser. The reflected probe beams from the two surfaces of the sample interfere as they propagate away from the sample and an interference fringe pattern is formed at the far field. A slit with width approximately equal to the fringe spacing is used to select a suitable fringe for detection. The slit position is adjusted with a micrometer-driven translation stage to allow only one fringe to pass through the slit and be detected by a bicell detector.22,23 To gather more light at the detector, the fringe is compressed along the vertical direction by a cylindrical lens ~focal length, 40 mm!. A 632.8 nm band pass filter is placed at the front of the slit to eliminate the excitation laser light. The PSD is mounted on a micrometer-driven two-dimensional translation stage for accurate alignment. Its position is adjusted vertically and laterally to eliminate the common-mode amplitude noise and maximize the measurement sensitivity. The samples used in this experiment are a plate of optical glass doped with rare earth metal ions, with optical absorption coefficient at 532.1 nm is 90 cm21, 0.99 mm thickness, and a plate of fluoroaluminate glass doped with erbium ions, whose optical absorption coefficient at 532.1 nm is 0.39 cm21 and a thickness of 1.20 mm. IV. RESULTS AND DISCUSSION

Figure 7~a! shows the x-directional intensity distribution of the interference fringe pattern at the detection plane, recorded by a photodiode with a pinhole of 0.2 mm diameter placed in front of the detector. The sample used is the optical glass of thickness 0.99 mm. The propagation distance between the sample and the detection plane is 1.03 m. Figure 7~b! shows the theoretical results calculated from Eq. ~12!. The waist radius of the probe beam used in the calculation is 21 mm, which is determined by measuring the radius of the 3654

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FIG. 6. Experimental arrangement: YAG, Nd:YAG frequency-doubled pulsed laser; AP1, AP2, aperture; M1, M2, mirror; P, prism; BS1, BS2, beam splitter; PD, photodiode; A, attenuator; EM, energy meter; L1, L2, spherical lens; S, sample; F1, F2, filter; He–Ne, He–Ne laser; SL, slit; L3, cylindrical lens; BD, bicell photodiode detector; DA, differential amplifier; SO, storage oscilloscope; BA, boxcar averager; RE, recorder.

probe beam at the focusing lens position with a knife-edge scan technique.29 The refractive index of the sample should be 1.50. Other parameter values are same as that in Fig. 7~a!. Accounting for the inaccuracy of the parameter values used in the calculation, it is reasonable to believe that both the theoretical and experimental intensity distribution of the interference fringe patterns are in good agreement. Figure 8 illuminates the dependence of the peak magnitude of the photothermal signal on the slit position for the five fringes at the central area of the interference fringe pattern. The slit with width approximately equal to the fringe spacing is mounted on a micrometer-driven translation stage and its position is laterally moved by adjusting the micrometer. At each measurement the PSD position is adjusted to nullify the common-mode dc voltage output of the differential amplifier. The pulse energy of the excitation beam is about 10mJ. The relative position of the excitation beam to the probe beam is carefully adjusted to maximize the photothermal signal magnitude. Comparing the results with the theoretical one shown in Fig. 5, we find that because of the Gaussian intensity profile of the probe beam at the detection plane, the maximum photothermal magnitude at each fringe decreases as the fringes depart from the central region of the interference field, which is not in agreement with the theoretical results with a simple assumption of the sinusoidal intensity distribution of the interference fringe pattern, but for measurement of each fringe, both the experimental and theoretical results are quite coincident. Since the fringe located near the central region of the interference fringe pattern gives the maximum intensity and therefore the maximum photothermal signal magnitude, it is chosen for detection. The photothermal signal peak magnitude versus the relative position between the excitation and probe beams is shown in Fig. 9. The ~1/e 2! radius of the excitation beam is measured with a knife-edge scan technique to be 89 mm. The experimental results ~solid points! are compared to the theoretical prediction ~solid curve! obtained from Eq. ~35!. The position of the experimental data points are adjusted and the scaling of the height is carried out to fit the theoretical shape. Photothermal interferometer

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An examination of Fig. 9 shows that the Gaussian profile of the theoretical curve shape at the normal incidence case is distorted due to the oblique incidence beam geometry used in this experiment. The maximum photothermal magnitude is not at the position where the excitation and probe beams are coincident, it is slightly offset. Compared to that at the normal incidence beam geometry case, the half-width of the curve profile is broadened. Figure 10 shows the measured photothermal transient of the plate of fluoroaluminate glass doped with heavy-metal ions. The transient consists of a rapid rise process determined by the rate of thermalization of the deposited energy and a slow delay process controlled by the rate of thermal conduction. Our experimental system has poor mechanical stability and poor vibration isolation ability, which cause a large dc drift at the photothermal transient. To avoid the effect of the dc drift at the signal source, the ac coupling of the gated integrator is chosen. The output from the differential amplifier is coupled to the input of the gated integrator equipped with a high-pass filter. The frequency at which the response of the gated integrator is lowered by 3 dB is 16 Hz, below this frequency the response drops at the rate of 20 dB/ decade. Choosing the ac coupling causes a loss of lowfrequency information of the photothermal transient. The loss of low-frequency information has to be compensated if the photothermal transient is to be quantitatively interpreted. The compensation can be completed and the photothermal transient recovered by spectral analysis and convolution.30 An alternative solution to the dc drift problem is choosing the dc coupling input mode and applying the baselinesampling operation of the gated integrator. This method may be effective if the dc drift does not change too rapidly. This can be done by improving the mechanical stability and the vibration-isolated ability of the experimental apparatus. Besides the boxcar averager, a digital storage oscilloscope is another effective instrument for recording and processing the pulsed photothermal signal transient. The peak magnitude of the photothermal transient can be used to measure the spectroscopic data or thermo-optical parameters ~ds/dT or dn/T! of the sample. The time characteristic is useful for determining the thermal diffusivity or conductivity of the sample. An analysis of the theoretical treatment of the intensity distribution of the interference fringe pattern shows that the interference fringe pattern is dependent on the propagation distance of the probe beam from the waist position to the detection plane, independent on the relative position between the probe beam waist and the sample. The waist position may be inside or outside the sample without influencing the detection of the phase shift. Therefore, optimum spatial resolution can be obtained by carefully adjusting the waist position of the probe beam when applying for highly resolved inspection or imaging of materials. As mentioned in Sec. I, the retroreflected beam interference configuration is suitable only for samples with appropriate thickness. If the sample is too thin, no interference fringe will be formed at the detection plane. If the sample is too thick, there will be too many fringes formed at the detection plane. The optical power of each fringe is, therefore, not enough for sensitive and accurate measurement of the Rev. Sci. Instrum., Vol. 67, No. 10, October 1996

FIG. 7. ~a! Interference fringe pattern recorded at a plane with a distance of 1.03 m from the sample. Sample thickness50.99 mm; refractive index 51.50; incident angle516.3°. ~b! Theoretical interference fringe pattern calculated from Eq. ~12!. The waist radius of the probe beam is 21 mm; other parameter values are same as those in ~a!.

phase shift. Supposing that at least one fringe is formed at the interference field, from Eq. ~15! the smallest thickness of the sample should be approximately four times the waist radius of the probe beam. For a thin sample, one should focus the probe beam as tightly as possible, so that a fringe is formed at the detection plane. In general, the appropriate thickness of the sample ranges from several micrometers to several millimeters or thicker. Thinner plate samples such as optical coatings can be measured if the measurement sensitivity optimization is not required.18 If the experimental system performance is optimized and the detection limit is mainly set by the photon noise, from Eq. ~29! the minimum detectable phase shift can be further lowered by increasing the power of the probe beam arrived at the detector active area. This can be done by increasing the output power of the probe laser, or by decreasing the fringe number at the interference pattern. ~Because the total power at the interference field is determined only by the reflectivity of the sample surface and the power of the probe laser, the light power of the fringe chosen for detection increases as the fringe number decreases.! Simple numerical deduction shows that the fringe number is approximately reversely proportional to the waist radius of the focused probe beam. It seems that increasing the waist radius of the focused probe beam is useful for measuring sensitivity improvement, with a decrease in spatial resolution, because the waist size of the probe beam determines the spatially resolved ability of the photothermal interference technique. In theoretical description only the contribution of the optical phase shift caused by the temperature rise to the phoPhotothermal interferometer

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FIG. 8. Photothermal signal peak magnitude vs slit position. The solid points are the experimental results, and the solid line has been drawn to guide the eye. The slit width is 1.95 mm, which is equal to the fringe spacing. At each measurement the PSD position is adjusted to nullify the common-mode dc voltage output of the differential amplifier.

tothermal signal is taken into account. Practically in the case of collinear photothermal experimental configuration, the thermal lens effect and probe beam deflection caused by the temperature gradient within the sample,9 the photoreflectance effect caused by the surface reflectivity change,31 and the reflected probe beam deflection and divergence caused by the surface thermoelastic deformation32 all contribute to the total photothermal signal. Their contribution may increase or decrease the total photothermal signal, depending on the beam geometry and experimental scheme. Usually in a photothermal interferometric detection experiment these contributions to the total photothermal signal are negligible compared to the contribution of the phase shift caused by the temperature rise. Although in this article we mainly demonstrated the applicability of this photothermal interferometric detection technique to characterization of transparent solid plates, the most promising application of this simple interferometric configuration should be weak absorption measurement and microvolume trace analysis. In recent years, due to the rapid developments of HPLC and CE separation techniques, a number of interference methods based on transmitted-beam interference33–35 have been developed and successfully used as universal refractive index ~RI! detection for HPLC and CE

FIG. 10. Photothermal transient of a 1.20 mm fluoroaluminate glass plate. The pulsed energy of the excitation beam is about 0.3 mJ, and the ~1/e 2! radius is 73 mm.

separations. Keeping other conditions the same, the retroreflected beam interference method is potentially more sensitive than the transmitted beam interference approach because the probe beam passes twice through the detection region in the retroreflected beam configuration. By using the same experimental setup but with the 40/60 water/ethanol solution of standard pyronine G dye filled in a commercially available fused-silica tube with 1.0 mm i.d. and 1.7 mm o.d. as the sample, the weak absorption measurement ability of the proposed photothermal interference approach and its application to HPLC and CE separations were proven. With a pulse energy of about 100 mJ, the detection limit of 1.831026 absorbance was achieved even though the experimental apparatus was far from optimum.36 The measurement sensitivity will be very much improved after performance optimization of the experimental system. It is noteworthy to point out that the photothermal interferometric detection configuration described here is a common photothermal technique. Other beam geometry used in conventional photothermal experiments, such as transverse or obliquely crossed schemes, can also be employed in this photothermal interferometric detection configuration. The excitation beam can be either a pulsed or cw modulated laser beam. This technique is expected to find applications to optical or thermal characterization and highly resolved nondestructive evaluation of optical materials5 or coatings deposited on transparent substrate,37,38 weak absorption or spectroscopy measurement, as well as microvolume trace analysis. Potential application of this photothermal interference technique to detection of CE and HPLC separations is being undertaken at our laboratory. ACKNOWLEDGMENTS

The authors thank Professor Jiasheng Zhong of the Institute of Infrared Optical Materials, Wuhan University for providing the fluoroaluminate glass material. This work was supported by the National Natural Science Foundation of China. A. C. Tam, Rev. Mod. Phys. 58, 381 ~1986!. J. D. Spear and R. E. Russo, J. Appl. Phys. 70, 580 ~1991!. 3 M. Liu, M. B. Suddendorf, and M. G. Somekh, J. Appl. Phys. 76, 207 ~1994!. 1

FIG. 9. Photothermal signal peak magnitude vs relative position between the excitation and probe beams at the oblique incidence case. The incident angle is 16.3°. 3656

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T. Chen, S. J. Shein, and J. F. Scott, Phys. Rev. B 43, 615 ~1991!. M. L. Baesso, J. Shen, and R. D. Snook, J. Appl. Phys. 75, 3732 ~1994!. 6 M. Commandre and E. Pelletier, Appl. Opt. 29, 4276 ~1990!. 7 Y.-X. Nie and L. Bertrand, J. Appl. Phys. 65, 438 ~1989!. 8 B. Monson, R. Vyas, and R. Gupta, Appl. Opt. 28, 2554 ~1989!. 9 D. M. Friedrich, in Ultrasensitive Laser Spectroscopy, edited by D. S. Rliger ~Academic, New York, 1983!, p. 311. 10 J. Stone, Appl. Opt. 12, 1828 ~1975!. 11 C. C. Davis, Appl. Phys. Lett. 36, 515 ~1980!. 12 C. C. Davis and S. J. Petuchowski, Appl. Opt. 20, 2539 ~1981!. 13 W. K. Lee, A. Gungor, P.-T. Ho, and C. C. Davis, Appl. Phys. Lett. 47, 916 ~1985!. 14 D. L. Mazzoni and C. C. Davis, Appl. Opt. 30, 756 ~1991!. 15 K. L. Saenger, J. Appl. Phys. 63, 2522 ~1988!. 16 K. L. Saenger, J. Appl. Phys. 65, 1447 ~1989!. 17 O. B. Wright, T. Hyoguchi, and K. Kawashima, Jpn. J. Appl. Phys. 30, L131 ~1990!. 18 O. B. Wright, J. Appl. Phys. 71, 1617 ~1992!. 19 K. L. Saenger and S. Gupta, Appl. Opt. 30, 1221 ~1990!. 20 A. Eickmeier, T. Bahners, and E. Schollmeyer, J. Appl. Phys. 70, 5221 ~1991!. 21 A. Yariv, Quantum Electronics ~Wiley, New York, 1975!. 22 J. M. Jewell, C. Askins, and I. D. Aggarwal, Appl. Opt. 30, 3656 ~1991!. 4 5

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A. E. Bruno, B. Krattiger, M. Maystre, and H. M. Widmer, Anal. Chem. 63, 2689 ~1991!. 24 J. Vattulainen and R. Hernberg, Rev. Sci. Instrum. 64, 1451 ~1993!. 25 J. M. Jewell and I. D. Aggarwal, J. Non-Cryst. Solids 40, 61 ~1980!. 26 J. Shen, M. L. Baesso, and R. D. Snook, J. Appl. Phys. 75, 3738 ~1994!. 27 J. F. Power, Appl. Opt. 29, 52 ~1990!. 28 S. E. Bialkowski, X. Gu, P. E. Poston, and L. S. Powers, Appl. Spectrosc. 46, 1335 ~1992!. 29 B. Cannon, T. S. Gardner, and D. K. Cohen, Appl. Opt. 25, 2981 ~1986!. 30 M. A. Schweitzer and J. F. Power, Appl. Spectrosc. 48, 1076 ~1994!. 31 M. B. Suddendorf, M. Liu, and M. G. Somekh, Appl. Phys. Lett. 62, 3256 ~1992!. 32 H. Saito, M. Irikura, M. Haraguchi, and M. Fukui, Appl. Opt. 31, 2047 ~1992!. 33 B. Krattiger, A. E. Bruno, H. M. Widmer, M. Geiser, and R. Dandliker, Appl. Opt. 32, 956 ~1993!. 34 B. Krattiger, G. J. M. Bruln, and A. E. Bruno, Anal. Chem. 66, 1 ~1994!. 35 B. Krattiger, A. E. Bruno, H. M. Widmer, and R. Dandliker, Anal. Chem. 67, 124 ~1995!. 36 B. Li, Y. Deng, and J. Cheng, Talanta 43, 627 ~1996!. 37 M. Reichling, E. Welsch, A. Duparre, and E. Matthias, Opt. Eng. 33, 1334 ~1994!. 38 E. Welsch and D. Ristau, Appl. Opt. 34, 7239 ~1995!.

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