AMI. chem. 1992, 64, ia24-1a30
1824
Comparison of BaTi03 Optical Novelty Filter and Photothermal Lensing Configurations in Photothermal Experiments Shashi D. Kalaskar and Stephen E. Bialkowski’ Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300
Photorefractlve BanOsIs used as an optlcal novelty fllter to hbhlbht the hlgh rpatlal frequency components of the photothermal rlgnal. A reaMkne phase gratlng recorded In Banos acts as a matched reJectlonrpatlal fllter for the probe laser. Thk reducesthe statlonarybackgroundfrom the optical signals thereby Increasing rlgnal contrast ratlos. Rejectlon of the monolonowstatlonary slgnal providesa powerfulmeans of Improving the photothermal rlgnal. Thk paper describes the condructlon of thls novel apparatus and the experlments perfotmed In order to compare lts performance wlth photothermal lensing results. A theory that explains photothermal rlgnal fllterlng wlth BalmO, as an adaptive spatlal frequency fllter k presented. Results comparlng the optkal slgnak obtalned In a photothermal lensing experknents and those obtalned In the BanOSoptlcal novelty fllter experlments are presented. The optical novelty fllter rlgnals demonstrate a remarkable Improvement In the a n a l contrastsfor moderate photothermal-lnduced phase 8hHts.
INTRODUCTION An optical novelty filter (ONF) can be used to increase the image contrast of dynamic phase altering signals.’ The first demonstration of optical tracking novelty filtering by Anderson, Lininger, and Feinbergz was based on a Michelson interferometer utilizing self-pumped optical phase conjugate mirrors made in a single crystal of BaTiOs. After a time period required to record the optical elements responsible for the phase conjugate reflection, the interferometer exhibits a dark fringe across the output branch of the interferometer. The dark fringe output is independent of the relative path lengths and aberrations along the optical path of the two arms. The adaptive phase conjugate mirrors compensate for differences in optical path length in such a fashion as to give a A phase shift between the two returning beams at the output branch of the beam splitter. Thus the whole interferometer acts as a phase conjugate mirror; reflecting light back along the input branch of the beam splitter and not the output branch. After the dark fringe forms, a phase shift may be introduced in one of the interferometer arms. Phase shifts that occur on a time scale shorter than that required to reform the phase conjugate mirror result in fields that are no longer out of phase a t the beam splitter. Subsequently, light is radiated through the output branch of the interferometer. This is the basis for operation of the ONF. Light exiting the output branch is the “novel” component of the relative difference in phase shift, or similarly, refractive index, between the two arms. Thus this device is sensitive to changes in optical path length, not the path length itself. On the other hand, phase perturbations that occur on time scales slower than that (1) Anderson, D. Z.; Feinberg, J. IEEE J.Quantum Electron. 1989,25, 635-647. (2) Anderson, D. 2.; Lininger, D. M.; Feinberg, J. Opt. Lett. 1987,12, 123-125. 0003-2700/92/0364-1824$03.00/0
required to form the phase conjugate mirror are undetected. Finally, the response time of the ONF can be adjusted by changing the irradiance of the laser used to record the phase conjugate mirrors. The higher the irradiance, the faster the response time. Since the device can be made unresponsive to slow index changes, the zero fringe output “tracks” these slow changes. This results in the name “optical tracking novelty filtef.2 There have been several variations of the optical tracking novelty filters since the Michelson interferometer-based apparatus. Two-wave mixing3 and beam fanning4 have also been used. These designs are similar in that spatially distributed phase-altering signals that occur over time scales shorter than that required to write optical elements in the photorefractive materials are coupled out along normal ray paths. The beam-fanning-limiter apparatus is the simplest to set up and operate. The significant difference between the interferometer- and twewave-mixing-based novelty fiiters and that based on beam fanning is that the latter uses only one beam external to the photorefractive medium. However the beam-fanning limiter is not sensitive to the phase changes that are constant with the transverse coordinates. Relative phase shifts between either two interferometer arms or two pump beams cannot occur. It is a single-arm interferometer very similar in operation to the conventional schlieren apparatus.5 Asymmetric self-defocusingor beam fanning of a laser beam passing through a photorefractive medium has been known for some time.6 This effect is more pronounced in the highgain photorefractive materials like BaTiOB. BaTiOa is an optically nonlinear, photorefractive material that is very suited for experiments that rely on beam fanning. A beam incident on the crystal fans out in the plane determined by the optic axis of BaTiO3 and the incident beam axis. The fanning redistributes beam intensity over several degrees of angle. A BaTiO3 crystal acting this way can be called an “optical limiter” since it dumps excess energy away from the normal path.’,’ Although asymmetric self-defocusingcan occur due to photorefractive beam bending,’ the current explanation is based on diffraction.7 Essentially, the imperfections in the crystal structure scatter the coherent input light. The interference between input beam and scattered noise generates gratings within the crystal. The gratings cause the light to couple out through the noise paths. As the grating develops, most of the light is coupled out along the noise paths, thus depleting the light energy along the normal path. The mechanism for beam fanning is complex, and the details of the generating process may never be known. But effectively, the scattered light acts as one of the arms in the interferometer or one of the beams in the two-beam coupling apparatus. The mechanism is (3) Cronin-Golomb, M.; Yariv, A. J. Appl. Phys. 1985,57,4906-4910. (4) Ford, J. E.; Fainman, Y.; Lee, S. H. Opt. Lett. 1988,12,85€-858. (5)Sato, T.;Kojoma, H.; Ikeda, 0.;Odai, Y. Appl. Opt. 1987,26,2016-
2019. (6) Feinberg, J. J. Opt. SOC.Am. 1982, 72, 46-51. (7) Yariv, A.; Cronin-Goulomb, M. J. Appl. Phys. 1985,57,4906-4910. 0 1992 American Chemlcel Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
inconsequentialto the operation of the limiter. The fact that an optical element which fans out the coherent beam used to write the element indicates that the phenomenon results in a matched spatial rejection filter for this beam. An ONF is analogous to the electronic high-pass filter in that it only transmits optical images with a dynamic change of scene. Any phase or spatial modulation (thus novelty) of the input image causes an increase in the ONF output signal. This increase in turn enhancesthe signal contrast. The signal contrast is defined here as the instantaneous change in the intensity of the output signal divided by the background intensity. Pulsed-laserphotothermal spectrometry (PL-PTS) creates fast changes of scene by perturbing the refractive index of the sample. Sample excitation with the pulsed pump laser couples probe laser light out past the optical novelty filter. For fixed signal due to absorbance, improved spectroscopic precision follows from a decrease in the average transmitted light. This is a direct consequence of variance reduction in shot-noise-limited detection.8 As shown below, the opticalnovelty-filter-based PL-PTS spectrometer limits the timeaveraged irradiance of the probe laser and thereby accomplishes this precision improvement. Though least sensitive in response to absorbance, the beamfanning-limiter-basedspectrometer may be the most robust to environmental interferences and yields understandable results. Bialkowski has shown that it can be used to enhance signal contrast in pulsed-laser photothermal deflection spectrometry.9 The most useful feature of beam fanning is that the dc component of the probe laser is effectively blocked. Monotonous (versus novel) signal rejection of 95% or better was obtained. When used for IR PL-PTS detection, small IR optical absorptions are measured by observing copious amounts of visible photons with almost no dc background. One problem with the latter apparatus was that the relative pump-probe laser beam offset in the sample cell was difficult to adjust. Even though the ONF did enhance the signal contrast and thus precision, there would still be accuracy errora due to beam alignment errors. Moreover it was not as robust as the apparatus described below. Beam alignment errors can be overcome by using a probe laser waist that is wider than the pump. The wider probe beam also eliminates pump laser pointing noise errors. In this paper we describe an ONF PTS apparatus with a relatively wide probe laser that is based on the beam-fanning optical limiter. The optical limiter is treated as a matched spatial rejection filter for the monotonous probe laser. In the following Theory we present principles of operation of this ONF used in conjunction with PTS. BaTi03 placed in one of the transform planes of this apparatus acts as an ONF that transmits the dynamic portion of the input optical images. In PL-PTS the refractive index of a sample is perturbed periodically due to absorption of the optical energy from a pulsed laser. This causes a rapid phase shift in the probe propagating through the sample. This rapid phase modulation of the probe acta as a novelty in the input images to BaTiO3 acting as an ONF. The use of a BaTiO3 beam-fanning ONF to transmit the high Spatial and temporal frequency components of the dynamic photothermal signal enhances the output signal contrasts. The ONF signals are quantitatively compared to those obtained using pulsed-laser-excited photothermal lens spectrometry (PL-PLS) for gas-phase l,&butadiene. The PLPLS and ONF signals are compared in terms of their respectivecontrastratios and temporal responses. It is shown (8) Ingle, J. D.;Crouch,S. R. SpectrochemicalAnalysis;Prentice Hall: Englewood Cliffs, NJ, 1988. (9) Bialkowski, S.E. Opt. Lett. 1989, 14, 1020-1022.
X’
X
t
F U(X,,Y,)
CELL
t
F
F
-
?X,,Y,,
1825
F
-
BaTi03
IU(X,Y)12
DETECTOR
F@m 1. Schematic showing the photothermal slgnachneglng principle. The sample cell and BatiO3 are at the focal planes of the lens on the left. The detector Is placed at the focal plane of the lens on the right. (xq, yo),(x’, y3, and (x, v) define the planes of the sample cell,BaT103, andthedetector,respectively. (r(xo,yo)and W,y)representtheelectrlc fields of the probe beam at the cell and BaTlO3, respectlvely. The Irradiance at the photodetector Is &,y) = Ilr(x,v)12.
that the model used to describe the ONF signal is adequate to describe the differences between these two techniques.
THEORY Figure 1illustrates the ideal optical setup used in describing the optical novelty signals due to a rapid change in the phase of the probe beam. This arrangement is basically a 4F optical correlator with an adaptive element in the transform plane defined by (x’, y’).l0 The probe beam passes through the sample cell placed at the object plane (20,yo). A lens is placed one focal length beyond the object plane and focuses the collimated probe beam through BaTi03 at the transform plane (x’, y’). A second lens is placed one focal length beyond the transform plane. The image plane ( x , y ) is one focal length beyond the second lens. A square law detector is placed at the image plane. In conjunction,the lenses act as a telescope that images the object plane on the image plane. In the absence of periodic refractive index perturbations due to the photothermal effect, the probe beam continuously irradiates BaTiO3. Beam fanning is established within the crystal. Let the probe laser electric field be U(x0,yo) in the object plane. The electric field in the plane of BaTiO3 is the transform U(v,,v,) = S(U(xo,Y,)]
(1) where ’3(1 indicates a Fourier transform and v , ~= 2ux’IAF and = 2uy‘/xF are the spatial frequencies, F being the focal length of the lens. Loss due to beam fanning is initially proportional to the irradiance but reaches a maximum due to the saturation gain of the photorefractive material. This loss can be formulated as the relative transmissivity of the optical element recorded in BaTi034 vYt
T(x’,y’)= (1 + mo)/(l + m, exp[r,,(x’,y’;t)LI)
(2) mo is the fraction of beam intensity initially scattered, L is the interaction length, and I’,ff(x’,y’;t) is the effective gain coefficient at time t. The effective gain is the exponentially time-averaged gain rerf(d,Y’;t)= t[’JOmr(x’,y’;t’) exp[-(t - t’)/to)ldt’ (3) where tois the response time of the photorefractive medium, in the units of time per watts per square centimeter. The effective gain is spatially nonuniform. It is a minimum of (10) Lee, S. H.,Ed. Optical Information ?'recessing Fundamentals; Applied Topics in Physics Vol. 48; Springer Verlag: New York, 1981.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
zero where the input has just changed and a maximum of r, the gain coefficientof the media, where the input is stationary. The gain coefficient is in turn proportional to the timedependent irradiance
r (x’,y’;t )
by a Fourier transform of the field in eq 10. Thus U(V,4,d = 3{U+(X,,Y,) 1 Substituting for U+(xo,yo)from eq 10 gives
(lla)
l ~ ( x ’ , y t’ );I 2
(4) A continuous extended coherent plane wave yields an irradiance at BaTi03that results in a 6-function-like gain. The transmissivity 0:
T(x’,y’)= Tmin for
x’ = 0 and y’ = 0
(5a)
?“,in, the minimum transmissivity corresponds to reff being maximum, i.e. r.ff = r. The transmissivitty at all other locations
T(x’,y’)= T,,
for
x’ # 0 and y’ # 0
(5b)
the unperturbed transmissivity. The minimum limiting transmissivity allowedby the optical element recorded in the crystal is
x’ = 0 and y’ = 0
= T(X’,Y’)u-(VX,,Uy,)
[S(X’,y’)6(X’J’)
+
~ ( ~ ’ , y ’ ) i ~ ( A @ ( ~U-(xo,yO) , , ~ o ) } I (12) The irradiance at the image plane is Substitution of eq 12 into eq 13 and simplification give
(5c)
Thus in effect the optical element recorded in BaTiOa will limit the optical transmissivity to Tminat the central region. In PL-PTS the refractive index gradient dependent phase ahift induced in the path of a probe is given by AWo,y0)= (2a/A)~pathAn(xo,~o) ds
U+(Vx,,Vyt)
E ( x , y )= IU(X,Y)(2= 13{U+bJx4Jy4~12 (13)
T(x’,y’)= Tmi,= (1+ mo)/{l+ rn, exp[rLlj for
If we assume that the duty cycle of the experiment is low (Le. the relative time during which the refractive index perturbation present in the cell is far less than one), then the spatially-dependent transmissivity is the same as that of the plane wave.
(6)
The integral is over the path that the probe takes through the medium. The refractive index change, An, is in turn related to the temperature AT by11
E(x,y) = E0[72min + T ~ ~ , ~ A @ ( X ~ , Y ~ ) ~(14a) ~I where Eo is the irradiance of the incident probe beam. Note that the transmission coefficients 72,in and 72- represent minimum and maximum transmissions respectivelysince they are proportional to the transmissivities Tminand Tmu.
E(x,Y) Eo[Tmin + ~m~IA@(xo,~o)I~l(14b) Thus the irradiance at the detector is related to the “image” of the photothermal phase shift. For the time-dependent photothermal-induced phase shift produced by a Gaussian pump laser with a pulse energy Q and a beam waist w, the change in irradiance at the image plane is hE(x,y) = EoT,,[(dn/d~8alQ/*W2pC,(1+ 2t/t,)I2 x
exp{-4(x2+ y2)/w2(1+ 2t/t,)} (15)
where Q is the pump beam energy, CY is absorption coefficient, w is the pump beam radius, p is the density of the gas, Cp is the molar heat capacity of the matrix gas, t, = wV4K is the characteristic diffusion time, and K is the thermal diffusion coefficient. The transmission coefficient a t the object plane is
@a) which, in the case of small phase shifts, can be approximated by T ( X ~ , Y= ~ )exp[iA@(x,,~,)l= 1
+ iA@(xo,y0) (9b)
In the following equations U- represents the incident electric field of the probe laser and V+the exiting field. The electric field exiting the sample cell is U + ( X ~ , Y ~~ ()X O , Y O ) V - ( X ~ ,=Y11 ~+ ) ~AWXO,YO)I U-(XO,YO) (10) The electric field at the BaTiOs adaptive filter is obtained (11) Sell, J. A. Photothermal Inuestigatiom of Solid and Liquids; Academic Press: New York, 1989.
where 1 is the interaction path length. This equation was obtained by assuming that the beam path s does not deviate significantly from the unperturbed path. The change in the radiant power obtained with a large area photodiode is A+ = 1 6 ~ ~ o T , , [ ( d n / d l ? ~ l ~ / ~ C ~ ] 2+[ w 2t/tc)]-’ z(l (16)
It should be recognized that the radiant power is proportional to the square of the product ale. This is in contrast to the theoretical PL-PLS signal which exhibits a linear dependence on a1Q. EXPERIMENTAL SECTION The experimental apparatus used in these experiments is shown in Figure 2. It is similar to one used previously for PLPTS signal enhancement.9 The pump laser is a line-tunableTEA COz pulse laser constructed in this laboratory. This laser operates at 5 Hz. The pulse duration is 170ns, full width at half-maximum, with a tail of a few microseconds. The pump laser is installed in a Faraday cage to reduce the radio-frequency interference that can affect the signal-processingelectronic devices. An intracavity iris is used to assist TEboperation. The beam radiant intensity profile on the surface of a graphite paddle appeared by eye to be nearly Gaussian. The pump laser delivers a maximum of 10 mJ of energy at the sample cell. The pump beam energy is monitored by using a pyroelectric detector, IRD (Laser Precision Model RjP-735),interfaced to a laboratory computer with 20-MHz 80286/80287 processors,through a 12-bitanalog to digital converter Data Translation Model DT 2801. The COz laser is tuned to the 9P28 line at 1039.36 cm-l. The laser line is measured with an Optical Engineering Model 16-A
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
ll
ATTNY c
PD
L3
CELL - 1 ;
1827
L2
L1
1
M1
IRD Flgure 2. Experimental apparatus setup used in these experiments. The TEA Conlaser, line tuned to 1039 cm-I, Operating at 5 Hr, excites the sample 1,3-butadlenemixed with argon matrix gas in the cell. The water-cooled Ar+ probe laser detects the photothermal perturbations of the sample. A Gaussian spatial fllter (SF) In combination with the lens L4 expandsthe probe beam. Mlrrors M1 and M2 and the germanium (Ge-Bs) beam splitter are used In comblnatlon to direct the pump and probe beams In the cell so that they are collinear along the axls of the cell. A pyroelectric detector (IRD) monitored the pulse energy. An attenuator (ATTN) Is used to vary the pulse energy. Lens L1 focused the pump beam onto a pinhole to fliter laser modes other than EMm. Lens L2 focused this laser mode into the cell. L3, a glass achromatic lens, focused the probe beam onto BaTIOe. A sillcon photodiode (PD)
detected unfanned 514-nm radiation from BaTi03.
-
spectrum analyzer. The analyte, 1,3-butadiene, has an exponential absorption coefficient of 1.88 x m-l Pa-' at this wavelength. The absorption is linear even at the high irradiances with the focused TEA COz laser.12 The energy of the pump laser was varied using a conventional venetian blind infrared reference beam attenuator. The attenuator does not change the beam position or angle and the pump beam. A 30.5-cm focal length BaFzlens (Ll) focuses the optical energy of the pulse laser through a pinhole of diameter 0.397 mm which acts as a spatial filter. This spatial filter ensures that TEMm is the only mode at the sample cell.13 The second BaFz lens L2, focal length 7.6 cm,focusesthe laser into a spot approximately400pm in diameter at the sample cell. The probe is a water-cooled Ar+ laser (Coherent Model 70) operating at 514 nm and between 10 and 50 mW of power. The probe beam is diverted into the sample cell using a germanium beam splitter (Ge-BS). The probe beam is expanded by using a combination of a Gaussian spatial filter, SF, and an achromatic lens, L4, as shown in Figure 2. The diameter of the probe beam at the entrance window of the sample cell is 1cm. The relatively large diameter used in this apparatus is deliberate so as to reduce the pointing noise of the pump laser. The pump and the probe beams are aligned so that they were collinear along the major axis of the sample cell. Lens L3, focal length 17.5 cm, a glass achromatic lens, focused the probe beam onto the BaTiO3 crystal. The BaTi03 crystal is oriented with respect to the incoming probe beam at an angle such as to avoid internal reflection or self-pumped phase conjugation and to obtain a maximum beamfanning effect. We found that angle of about 80' between the incident probe beam and c-axis (optic axis) of the crystal gave satisfactoryresults, in terms of signal enhancement. Silicon photodetector PD (United Detector Technology Model PIN 10-DP) monitors the 514-nm radiation not fanned by the BaTiO3 crystal. The photodetector signal passes through a transimpedance amplifier to a Tektronix Model 502 amplifier. The signals are recorded using an 8-bit transient waveform recorder (Markenrich Model WAAG)interfaced with the laboratory computer. An oscilloscope(PhilipsModel PM 3320) is used to display the signal profiles. Note that the CO2 pump beam does not pass beyond lens L3 and therefore does not interact with the BaTiOs crystal. In case of PLS experiments, the above arrangement remains unchanged except that BaTiOa and lens L3 are removed. A pinhole is placed in front of the photodetector to monitor the probe beam irradiance at its center.
-
(12) Bialkowski, S. E.; Long, G. R. Anal. Chern. 1987,59,873-879. (13) Bialkowski, S. E. Rev. Sci. Imtrurn. 1987,58, 2338-2339.
0
3
6
9
12
15
18
21
24
27
T I M E (MSEC)
Contrastratb versus time using the PLS conflguratbn.These data represent an average of 500 transients. The analyte pressure is 33.2 Pa in a total pressure of 1.01 X lo5 Pa. Flgure 3.
1,3-Butadiene was obtained from Matheson Gas, 99.86% purity. Argon was used as the matrix gas (Liquid Air Corp., UHP). Both gases were used without further purification. Gas mixtures were made in a stainless steel gas-handling manifold attached to the sample cell. This manifold was attached to a vacuum manifold with 2-in. diffusionand rough pumps. Initially, 133Pa of analyte was allowed in the cell. Argon was added rapidly to the cell to ensure thorough mixing, until the total pressure was 1-01X lo5 Pa. The desired analyte pressure, for example 33.2 Pa was achieved by successive dilutions using the matrix gas. The analyte pressures in both the BaTiOa ONF and PLS experiments ranged from 33.2 to 2.0 Pa. In every case argon was added to the total pressure of 1.01 X 105 Pa. Optimum signal was obtained by making necessary alignments of various optical components.
RESULTS AND DISCUSSION The purpose of this study is to compare photothermal signals obtained using the ONF to those obtained using a PLS setup. The 4F optical setup shown used in the theory section is not required for these measurements since an image of the photothermal perturbation is not measured. Only the first transform lens is needed. This lens serves to Fourier transform the spatial phase shift induced in the sample cell by pulsed-laser excitation. Heating of this lens does not result in a signal for two reasons. First, the lens is not in the Fourier plane. Thus phase shifts induced by heating this lens will not result in a perturbed image at the BaTiOs limiter. Second, the COZbeam radius is large at this lens. This decreases the irradiance, and also heating will cause a spatially uniform phase shift due to thermal expansion. A constant phase shift does not result in a signal past the limiter. Past the ONF the spatially-dependent signal is integrated with a detector with a large active area (1-cm diameter). This ONF setup is most appropriate for quantitative measurements. Equation 16 is most appropriate for these experiments. In order to compare the PLS and ONF experiments, the data are processed to eliminate dependence on probe laser power. Typical processed data obtained by averaging 500 transients are shown in Figures 3 and 4. Figure 3 displays the time-dependent PL-PLS signal in terms of the contrast ratio. Figure 4 shows the contrast ratio recorded with the BaTiOs ONF configuration. The analyte concentration is 33.2 Pa in both cases. The contrast is defined as the ratio of background-corrected PTS signals to the backgroundcorrected measure of the Ar+ laser power. Background correction consisted of subtracting the measure of the ambient light, photodiode dark current, amplifier offset, etc., from the signals. As seen in Figure 4 the PL-PLS signal is a decrease
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
4
"I
0. 30
_I
a
I
184
I
I
t-
c
z
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0. 20
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_J
a
k
in
J
a
a Lz c
z
D
u
I.--r,_I
LL
z 0
1
0. 00 0
TIME (MSEC) Figure 4. Contrast ratio versus time using the ONF configuration. These data represent an average of 500 transients. The analyte pressure is 33.2 Pa in a total pressure of 1.01 X lo5 Pa.
lensing
(Pa)
_ _ _ _ _ _ _ ~
33.2 16.6 8.30 4.15 2.08
(a) ~
4.43 X 3.00 X 2.00 x 1.36 X
10-1 10-1 10-1 10-1
8.89 x lo-*
limiter (b) 2.50 X lo1 1.53 X 10' 4.75 1.40 6.44 x 10-1
improvement (bla) 56.4 51.0 23.8 10.3 7.24
in probe laser beam power due to the divergent thermal lens that is formed within the sample. The irradiance increases due to gain in the photorefractive medium for the ONF experiments. Visually, the PL-PLS signal would appear as pulsating optical signals, of the same frequency as that of the pulse laser, whose intensities drop at the center of the beam spot, whereas the ONF signals appear as the pulsating bright spot against the low-intensity background. We noticed that the location of the optical signals obtained in the ONF experiments can be moved by changing the pump beam orientation with respect to the cell axis. This can be done by slightly tilting the surface of the mirror M1 shown in Figure 2. This observation implies that the modes being transmitted through the ONF are indeed those arising from the photothermal perturbations of the samples. This observation indicates that the irradiance is due to the image of the photothermal phase shift. Table I lists the contrast ratios obtained in each experiment and for a given concentration. The contrast ratios in the case of ONF experiments are significantly higher than those obtained in PLS experiments. The last column in Table I shows the ratio by which the PLS signal is improved by an ONF. The standard deviations of the PLS and ONF signals are 0.126 and 9.39, respectively, and the standard deviation of the improvement ratios is 20.4. Note that the contrast ratios displayed in the last column decline with lower analyte concentration. This implies that a t the lower analyte concentrations PLS is a better technique. Comparisonof results presented in Table I revealsthe useful feature of the ONF-based apparatus, namely its efficiency in blocking the dc component of the probe laser. The stationary or monotonous portion of the signal is significantly rejected. In effect it is a matched rejection filter for the probe laser. This allows infrared absorption measurements of the analyte with virtually no background noise. The data presented in Table I support the results of the PLS experiments in which a circular stop was used as a spatial
3
EXCITATION PULSE ENERGY ( m J ) Figure 5. PLS signal, in volts, as a function of excitationpulse energy in millijoules. The analyte pressure is 33.2 Pa. 0. 35
Table I. Contrast Ratios in Photothermal Lensing (a) and Optical Novelty Filter (b) Experiments optical anal* pressure
2
I
0. 30 0. 25
"1
0
0. 10
0.05] 0.00
EXCITATION PULSE ENERGY ( m J ) Figure 6. ONF signal, in volts, as a function of excitation pulse energy in miilijouies. The anaiyte pressure is 33.2 Pa.
filter to block the central portion of the probe beam.14 Increasing the diameter of the circular stop to the probe beam waist improved the signal to background ratio. Reduction of the constant background illumination of the detector showed a remarkable signal-to-noise ratio (SNR) improvement. A 3-fold improvement in the SNR ratio was reported using that configuration. The circular stop spatial filter used in that experiment is a static, nonadaptive filter. The ONF on the other hand, is a dynamic and adaptive filter. Spatial filtering of the thermal lensing signal was also achieved by masking the central portion of the probe beam with radially symmetric masks.l5 The PL-PLS and BaTiOs ONF signals as a function of pump laser beam energy are also recorded at a given analyte concentration. The data display a scatter plot that represents optical signal as a function of the excitation beam energy. Each point in this scatter plot presents one pulse of the pump laser. A total of 1024sample points are obtained by variation of the pump laser at a given analyte concentration. The data collected in this manner give some insight into the signal and noise components in a given configuration. Figure 5 shows the PLS signal, as a function of excitation pulse energy. Similarly, Figure 6 shows ONF signal as a function of the excitation pulse energy. Figure 7 shows the relative signals from PLS and ONF configuration experiments. For the convenience of comparison of time-dependent behavior of PLS and ONF signals, both are plotted on the same scale. The PLS signal in this ~
~
~
~~~~~~
~
(14)Slaby, J . O p t . Cornrnun. 1987,64, 89-93. (15)Jansen, K.L.; Harris, J. M.Anal. Chern. 1985,57, 1698-1703.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
0.0
I
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I
I
I
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2
3
4
I
5
T I M E (mSEC)
Flgurr 7. PLS and ONF relathre signals versus time. The top trace is the unprocessed signal obtained with the ONF apparatus, while the bottom trace is the PLS signal processed in the usual manner.
figure is processed so as to yield the PLS signal defined in standard form.16 Notice that the ONF signal decay is slower compared to the PLS signal. The PLS signal is proportional to 1/[1 + 2 t / t J 2 whereas the ONF signal decays as 1/[1 + 2t/t,], as seen from eq 16. The data displayed in Figures 5 and 6 prove the analytical merit of the ONF configuration over PLS configuration. Superposition of these figures would indicate that the ONFbased configuration produces improved signalsat higher pulse energy. At the lower pulse energies however, PLS seems to be better, and the same is true a t lower analyte concentrations. The ONF-based technique outperforms PLS a t relatively higher pulse energies. Dependence of the PLS and ONF signals on the excitation pulse energies can be seen from eqs 8 and 16. The PLS signal is proportional to the pulse energy, Q, whereas the ONF signal varies directly as Q2. Therefore a t pulse energies of 1mJ or less PLS signal is larger and at the higher pulse energy the ONF signal is larger, as observed in our experiments. The response time of the photorefractive medium, which is the time required to establish the gratings in BaTi03,is on the order of 1s9J7 for 100-mW power probe beam with the spot size of 0.5 mm2. Photothermal perturbations following absorption of the pulse optical energy last for a time duration of about 25 ms. As a result changes in the spatial modes caused by photothermal perturbations are transmitted along the normal path, far before the crystal responds to the novelty in the input and sets up the grating. The spatial filter thus allows the transmission of the novel spatial modes arising from the photothermal-induced phase shift in the sample. Whereas the stationary monotonous background resulting from continuous irradiation of the crystal is eliminated. This results in the optical signals with significantly improved contrasts. The single-beam interferometer using ONF showed similar reaulta.4 This interferometer, like our apparatus, was sensitive to the phase modulations in the input. The output video images of the moving objects displayed highly enhanced edges of these objects with very low visibility of the extended surfaces. The ONF thus acts as a motion-detecting device. The high contrast ratios obtained in our experiment conform with this earlier observation. Although several applications of ONF-based apparatus have been suggested for image processing,4J7our experiments demonstrate significant implications to absorption spectro~~
(16)Twarowski, A. J.; Kliger, D. S. Chern. Phys. 1977, 20, 259-264. (17)Cronin-Golomb,M.;Biernacki, A. M.;Lin,C.;Kong, H. Opt. Lett. 1987, 12, 1029-1031.
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photometry. The signal contrasts are greater than expected from optical absorption of the sample. Earlier experiments using ONF for photothermal deflection spectrometry showed signal contrasts of 14 for a sample absorbance of =lO-3 AU/ cm.9 This, in the shot-noise-limitedmeasurements, represents an improvement of 4 orders of magnitude over conventional optical absorption. The results obtained, under the same conditions, in these experiments showed the contrast of 56.4 for a sample absorbance of =lo-3 AU/cm. The interaction path length of the Ar+ beam in the sample was taken as 1cm as before. Thus, although the contrast has increased 4-fold, the order of magnitude of the enhancement remained the same. As shown in Table I, the irradiance at the detector and thus the signal contrasts decrease with analyte concentration. This observation, like their dependence on the pulse energy, can be explained on the basis of eqs 8 and 16. The PLS signal is derived from the temperature gradient which in turn depends on the absorption coefficient a. Lower analyte concentration means the number of molecules absorbing the radiation and undergoing thermal relaxation is smaller. This would result in a smaller temperature gradient and PLS signal of lower magnitude. The ONF signal is likewise affected by lower analyte concentrations. Because, as the number of the analyte molecules decreases, the phase modulating capacity of the sample, an essence of the ONF operation, decreases. The ONF signal, however varies as a2. This renders the ONF to be a better technique in general, when one tries to discriminate small absorbance changes on a relative large absorbance background. The nonlinear response predicted by (16) is advantageous for analysis in the presence of interferant absorption. For fanning efficiencies approaching 1 and small absorbances, (16) can be rewritten as
A 4 / 4 ~=~c(Qab2 (17) where c is a proportionality constant. The change in radiant power for a small change in absorption is
64 = 40c(Q1)22a6a
(18)
where 64 is the change in power for a constant absorption, a,and a small change in absorption, 6a. Thus the sensitivity of this detection scheme is enhanced by constant background absorption. The sensitivity enhancement factor is 2a. Sensitivity to small changes in absorbance increases with increasing constant background absorbance. For shot-noise-limited detection, the SNR and thus the precision for conventional absorption spectrophotometry is proportional to 6T/dT. Thus the maximum precision in conventional spectroscopy decreases with increasing background absorption. The detection of small analyte absorptions with large background absorption is thought to limit ultrasensitive absorption spectroscopy.18 But the ONF apparatus results in a precision that is independent of background absorbance. The 6T/dT limiting precision for the ONF is d c 2 Q l 6 a . Thus the ONF-based PL-PTS spectrometer not only increases the overall measurement precision by increasing the contrast but also circumvents the background absorption limitation of conventional spectroscopy. It can be said that for relatively higher absorbances and pulse energies above 1.5 mJ the ONF becomes a better technique yielding relatively higher contrasts. But combination of relatively low concentrations and low pulse energies makes the ONF technique less effective compared to PLS. This fact is reflected in the dependence of the radiant power on the square of the product a1Q in the case of the ONF (18)Harris, T. D.; Williams, A. M. Appl. Spectrosc. 1985, 39,28-32.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 17, SEPTEMBER 1, 1992
experiments. Although the PLS technique also depends upon the excitation pulse energies and sample absorbance, it remains sensitive to the temperature changes within the sample since ita output depends on temperature gradient which in turn varies directly as the product of pulse energy, 8. .,and absorDtion coefficient a. Our model and observations suggest that the radiant signal power is independent of the relative position of the thermal perturbation as long as there is overlap between the pump and probe laser beams. This is in contrast to conventional PL-PLS. In the latter signal magnitude is a function of the relative position of the pump and probe lasers. This results in pointing noise error and difficulty in experimental reproducibility.19 Pointing noise errors are apparently reduced using the ONF setup. Pointing noise giving rise to relative beam offset of the pump laser will not result in a change in signal magnitude. However pointing noise in the probe laser c&ld resilt in an increase in the background light power, thereby decreasing the contrast ratio. Since BaTi03requires about 1s to record the beam-fanning hologram, only the probe laser pointing noise below 1 Hz would be eliminated. Nonetheless, the signal magnitude should be the same. Finally, experimental reproducibility is easier to obtain since the pump and probe laser beams do not have to be exactly aligned. (19)Long, G. R.;Bialkowski, S.E.Anal. Chem. 1986,58,80-86.
In conclusion we have demonstrated a significant application of the BaTiO3 beam-fanning ONF to infrared absorption spectrophotometry. Two separate tests were run, and the results are both in agreement with the adaptive matched spatial rejection filter theory developed for quantitative description of this apparatus. Though in its develoDmental form, the apparatus- yields encoura&ng results. I& performance in enhancing signal-to-noise ratios in the shot-noise limit was remarkable. It was found that photothermal perturbations induced by the infrared laser were imaged, as indicated by the corresponding movements of the image and the infrared source. This suggests that this apparatus can be used to obtain two-dimensional profiles of the infraredabsorbing substances. Experiments are currently being performed to capture these images and process them to yield the temporal and spatially-dependent phase shifts in the sample.
ACKNOWLEDGMENT This work was partially funded by NSF Grant CHE 9005769 and NIH Grant SSS-4 1P41 RR 06030-01 Al. We also wish to thank Prof. Joel M. Harris a t the University of Utah for the generous loan of the BaTiOs crystal. RECEIVED for review February 12, 1992. Accepted May 29, 1992. Registry No. Barium titanate, 12047-27-7.
