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(19) Stuper, A. J.; Jurs. P. C. J . Chem. Inf. Comput. Sc/. 1976, 16, 99- 105. (20) Rohrbaugh, R. H.; Jurs, P. C. "UDRAW", Quantum Chemistry Exchange, Program 300, 1988. (21) Stuper, A. J.; Brugger, W. E.;Jws, P. C. Computer-AssrStedStudi8s of Chemkal Struct~~e and BioEogical Functhm ; Wiley-Interscience: New York. 1979: DD 83-90.
to Ch8mlCal S ~ C f U f r 9and gnWY ~ l C u ~ ~ WlbY: t 7 s ~New Y W k 1985. (24) maper, N. R.; Smith, H. Applied Regression AM&&, 2nd ed.;wiieyIntersclence: New York. 1981. Identi(25) Belsby, D. A.; Kuh. E.; WelsCh, R. E. R m & Dhmti~ ~: end sources of mMMw; Wiiey-Interscience: ,,ng New York, 1980.
(26) Alien, D. M. Technical Report 23, Department of Statlstlcs, Untverslty of Kentucky: Lexington, KY, 1971. (27) Snm, R. D. TechnomeMcS 1977, 19, 415-427. (28) Anet, F. A. L.; Yavari, I . J . Am. Chem. Soc. 1977, 99, 2794-2796. (29) Hawthorne, D. G.; Johns, S. R.; WUHng, R. I. A&. J . Chem. 1976, 29, 315-326.
under Grant CHE&15786. The PRIME 750 computer and the Sun 4/110 workstation were purchased with partial financial support of the National Science Foundation. Portions of this paper were presented a t the 197th National American Chemical Society Meeting, Dallas, TX, April 1989.
Background Illumination Filtering in Thermal Lens Spectroscopy Jerzy Slaby Institute of Experimental Physics, Warsaw University, Hoia 69, 00-681 Warsaw, Poland
A thermal lens spectrometer wtth spatial flltering d a probe beam has been analyzed. A circular opaque mask placed in the probe beam dgrtificantty reduces the constant, signadindependent detector response, whereas useful thermal lens signal Is much less affected. I n thk modlfled conflguratbn, In compar"n to the debslcal arrangement, 54dd enhance ment of m a l to constant background ratlo has been experbnentaily verified. Theory Is presented where diffraction at the bbcking fltter Is calculated and improvement of thermal lens signal to constant background Is dlscus~ed.Asswntng the typical configuration, WHh a detector In the center of the problng beam, we have obtained expressions applicable for both single and dual-beam arrangement. Experimental data are weH reproduced by theoretlcal curves.
1. INTRODUCTION
The first observation of a thermal lens (TL) inside a laser cavity (1) led to the new technique of thermal lens spectroscopy. The extracavity single-beam thermal lens spectrometer was developed by Chenming Hu and Whinnery (21, and thermal lens spectroscopy (TLS) was vastly improved when a dual-beam version of the method was developed by Swofford and Morell(3). Now the TLS technique can be used in many various fields including molecular and solid-state spectroscopy, material testing, combustion studies, plasma diagnostics,research on heat diffusion, transport phenomena, and phase transitions studies. Sensitive, laser-based absorbance measurements have proved to be an invaluable analytical tool particularly for molecular systems, where strongly absorbing molecules are much more common than strongly fluorescent ones. The general scheme of the TLS ( 4 ) is usually modified in various ways to enhance specific features of the instrument's performance. A very interesting, although perhaps the simplest, arrangement of the TL spectrometer ever constructed was presented by Imasaka et al. (5),where optical fibers are applied for both introducing light into the sample and monitoring the outgoing light beam. In such a system no additional optical elements are nece&saryand a more simple experimental setup is hardly imaginable. Another confiiation, one of the most important arrangements of the TL spectrometer, is a 0003-2700/89/0361-2496$01 S O / O
crassed-beam instrument (6,7) designed and particularly well suited for studying extremely small volume samples. A very elegant approach for improving classical thermal lens spectrometry was suggested by Janssen and Harris (8), where optical proceasing is used to directly determine the probe beam spot size. A radially symmetric mask, with a parabolic transmission profile, ensures greater immunity to spatial noise and also results in more precise measurements, compared to the usual beam-center detection. The present paper considers a similar category of TL spectrometer, with optical proceasing applied to obtain better performance characteristic of the instrument. In order to detect a thermal lens, a laser-heated sample is placed some distance,typically about confocal parameters, either after or before the waist of a probe beam. In a thermal lens method, however, there is constant nonzero detector response, even when no absorption occurs and no thermal lens is generated. This may be a serious problem since the preaence of a background masks the signal of interest. Moreover, strong background requires a large dynamic range of the detector to precisely recover the weak useful signal. Reducing signal-independent detector illumination is thus of practical interest. We have presented this sort of thermal lens detecting arrangement in ref 9, where we report preliminary experimental data on partial separation of useful signal beam from the unperturbed probe beam, and we discuss its implications to signal/noise ratio. This approach is particularly advantageous if probe beam fluctuations are the limiting noise source. In the case when beam wander is more important, reduction of the pointing noise and improvement of detection limit by means of spatial filtering were reported by Long and Bialkowski (10) for a pulsed-laser operated TL spectrometer. The present paper gives new experimental evidence of filtering out the undesired background signal, with a 5-fold gain in signal to background over the usual scheme of a thermal lens instrument. Rigorous diffraction calculations have been performed to supplement the propagation model (9) with some considerations that are necessary to give a proper quantitative descriptionof fdtered detection of thermal lens. This new model gives a simple and satisfactory explanation of filtered system operation. Moreover, as we show in application to experimental data, the model can be used to predict exactly the signal to backgroud improvement expected in a filtered measurement configuration. 0 1989 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 22, NOVEMBER 15, 1989
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Flgurr 1. Optical configuration for filtered probe beam system of thermal lensing detection: S, sample; SF, spatial filter; D, photoda tector; 0, posRion of the waist of probing laser beam.
2.
THEORY
2.1. Probe Beam Propagation in a Filtered System. The basic concepts fundamental to the thermal lens effect are very straightforward, but a complete quantitative description of this technique is quite elusive. This is so because rough simplifications are made on both stages of the theory necessary to describe the effect: first, in solving the heat diffusion equation, therefore in what the refractive distribution in a sample illuminated by a heating beam is, and second, in the calculation of probing beam propagation in a medium with gradient index of refraction. Carter and Harris (11)made an interesting comparison of various models describing the thermal lens effect. The authors have demonstrated that quite different parameters describing physical properties of a sample can be deduced from experimental data. It is a rather confusing situation, but even such an important feature as the time constant of thermal lens evolution turns out to be dependent on the model used in the calculations. In recent yeam significant effort has been made to reach a better understanding of thermal lens detection. In ref 12 and 13, contrary to previous studies, a more rigorous diffraction approach is used and true phase shift, different from the ideal parabolic model, is assumed. The excellent results of these two papers, however, cannot be so easily applied for the description of a TLS system containing a spatial filter. These papers discuss the light amplitude only in the very center of a probe beam. Precise knowledge of light field amplitude in the whole filter plane is necessary to determine the signal value expected in the system considered in the present paper. One possible way to solve this problem is to use the model of a thermal lens presented in ref 14. If there is only small absorption and consequently a low rate of heat release in a sample, then for times shortly following the illumination onset one can assume that the temperature rise in the sample is proportional to the amount of energy deposited and is a Gaussian function of coordinates. For that reason a Gaussian probe behind a thermal lens can be decomposed into the sum of two Gaussian beams, with different confocal parameters and waist locations. One of the beams has its amplitude proportional to thermal lens strength, whereas the other is just the original unperturbed probe. This model quite naturally suggests a detection scheme with a high-pass spatial filter in the path of a probing beam. The scheme of the detection system considered in the present paper is shown in Figure 1. A thermal lens is generated in a sample S placed in input plane 1 of the system, in the converging part of the probing Gaussian beam. A probing beam, after passing through the sample, travels to the second reference plane 2, containing a circular mask SF. This is the filter plane of the system. The filter plane can be located at any distance x from the waist plane of the probe beam. It is noted that at x = 0, filtering is performed in the spatial Fourier spectrum of the probe beam. For generality, however, arbitrary nonzero x is allowed in the present analysis. The sample is a distant no from the waist of the probe. Finally, far from the filter plane 2 is the detection plane of the system,
with a detector D and a pinhole in front of it, centered on the optical axis. Propagation of the probing beam from the first reference plane to the detector plane can be described as a two-etage process. The first stage is Gaussian beam propagation in free space, and for any position along the system axis, one can easily determine the beam size, its radius of curvature, and its amplitude (15). The second stage is the propagation of a wave diffracted at the mask, which is placed in the filter plane. The amplitude of this wave can be found by means of the diffraction integral. Light field amplitude ai of the probe beam incident onto the sample can be written as
ai(r, X = -xo) = w o / w exp[i@- 1.2(1/w2- i k / 2 R ) ]
(1)
It is simply the amplitude of a Gaussian beam with a radius of curvature R and beam diameter 2w. Beam size at the waist plane is wo and denotes the initial phase shift and can be set to zero at the waist plane X = 0. If the sample is thin, then the light field amplitude ab behind the thermal lens, as stated before, can be decomposed into the sum a&, X = -xo) = ai(r) as(r)
+
The second component,a&), is another Gaussian beam (141, the magnitude of its amplitude being proportional to the power absorbed in the sample. This wave is thus the useful signal wave and, according to the assumption of small perturbation, las(r)l
