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Effects of Probe Beam Offset on Quantitative Measurement in Photothermal Beam Deflection Spectroscopy Masaaki Harada, Shigeo Obata, Takehiko Kitamori, and Tsuguo Sawada. Department of Industrial Chemistry, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan
INTRODUCTION Remarkable progress in science and technology has accelerated demands for development of highly sensitive measurement techniques capable of identification and quantification of a small quantity of chemical species. Photothermal spectroscopy has proved to be a highly sensitive spectrophotometric method,‘ and the detection limit absorption coefficient of a photoacoustic spectrophotometer, expressed in twice the signal-to-noise ratio, has reached down to 1O-e cm-1.2 Photothermal spectroscopy is a general term for calorimetric techniques that measure heat resulting from radiationless transitions in a sample and give optothermal information about the sample. Various detection schemes have been proposed and are widely used. Among them, photothermal beam deflection (PBD) spectroscopy is increasingly attracting much attention as an alternative to photoacoustic spectroscopy (PAS) for solid sample^.^ It is based on the “mirageeffect”,and the refractive index gradient formedby heat transfer to the surrounding medium is detected by deflection of the probe beam skimmingthe sample surface. The significant advantage of the PBD technique over PAS is that in-situ measurements are possible because there is no need for a cell. Since the first report,’ PBD has been applied to fields of analytical interest, such as measurements of Fourier transform infrared spectra of solids6 and thin-layer chromatography (TLC) densitometry.6 We have reported that the PBD method is more sensitive for smaller single microparticles a t higher modulation frequencies, which was explained as an enhancement of the temperature field gradient by the microparticle curvature.’ The sensitivity of the PBD method is about 2-3 orders of magnitude superior to that of a conventional absorption microspectrophotometric method. For example, the spectral difference between leukemia and normal white blood corpuscles is detectable.8 The vertical distance between the sample surface and the center of the probe beam is referred to as the normal offset in the text. As the PBD signal amplitude decreases exponentially with the increaseof the normal offset? it is necessary to keep the probe beam as close as possible to the sample surface to get high sensitivity. But, if too close to the surface, the probe beam is eclipsed, resulting in a drastic falloff in sensitivity.10 As the PBD signal amplitude is thus very sensitive to the normal offset, the normal offset must be kept a t exactly the same relative position during successive (1) Harris, T. D. Anal. Chem. 1982,54, 741-750A. (2) Kitamori, T.;Fujii, M.; Sawada, T.;Gohehi, Y. J. Spectrosc. SOC. Jpn. 1986,34, 359-365. (3) Low, M. J. D.; Lacroix, M.; Morterra, C. Appl. Spectrosc. 1982,36, 582-584. (4) Boccara, A. C.; Fourier, D.; Bodaz, J. Appl. Phys. Lett. 1980,36, 130-132. (5) Low, M. J. D.; Morterra, C. Appl. Spectrosc. 1984,38, 807-812. (6) Chen, T. I.; Morris, M. D. Anal. Chem. 1984,56, 19-21. (7) Wu, J.; Kitamori, T.; Sawada, T. J. Appl. Phys. 1991, 69, 70157020. (8) Wu, J.; Kitamori, T.; Sawada, T. Anal. Chem. 1991,63,217-219. (9) Jackeon, W. B.; h e r , N. M.; Boccara, A. C.; Foumier, D. Appl. Opt. 1981,20, 1333-1344. (10) Peck,K.; Fotiou, F. K.; Morris, M. D. Anal. Chen. 1986,57,13591362. 0003-2700/93/0385-2 18 1$04.00/0
1
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Figure 1. Schematic illustration of the theoretical model.
measurements, which is not easily practicable. Besides the probe beam offset, many experimental parameters, such as the probe laser beam profile and knife edge position, make quantitative analyses by PBD difficult. Though the PBD method is promising, these technical problems have hindered its quantitative treatment and its quantitative applications have been limited. In this report, we have proposed a calculation method which corrects the normal offset variations to overcome the cited problems. This correction method has been derived theoretically from the dependence of the PBD phase signal on the normal offset and validated experimentally. Improvements of reproducibility and quantitation have been examined by using the proposed correction method.
METHOD A schematic illustration of our theoretical model is shown in Figure 1. When an intensity-modulatedpump beam heats the sample whose surface is only absorbing, the probe beam passing parallel to the sample surface is deflected by the temperature field generated. Its normal deflection angle is calculated as11 W , t ) = AB exp[iwt - (1+ i)z/p,l
(1)
where z is the normal offset of the probe beam, t is the time, A is the constant proportional to excitation beam power, is the absorption coefficient of the sample, i is the imaginary unit, w is the angular modulation frequency, + = ( 2 D , / ~ ) l / ~ is the thermal diffusion length of air, and D, is the thermal diffusivity of air. This equation shows that the natural logarithm of the amplitude and the phase itself are linearly dependent on the normal offset with a slope of -l/pr And it is also easily shown that the amplitude is directly proportional to the absorption coefficient of the sample while the phase is independent of it. These findings are verified experimentally later. The signal amplitude and phase at any normal offset z are related to those a t a certain normal offset zo by (11) Murphy, J. C.; Aamodt, L. C. J. Appl. Phys. 1980,5I, 46804588. Q 1993 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993 Gold Particle
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the sample size. The probe beam was a He-Ne laser (Japan Laser Model JLH-PT11) beam, focused by a 100mm focal length convex lens just above the sample. The probe beam deflection was detected by using the knife edge and a photodiode (Hamamatau)detectionsystem. The signal from the photodiode was synchronously amplified by a two-phase lock-in amplifier (NF Model LI-575). In-phase and out-of-phase signal outputs were sent to an A/D converter (Adtek Model R488-AD/2) and processed by a personal computer (NEC PC-9801VM). The samples were scanned automaticallyby the steppingmotor-driven translation stage (Sigma Koki Model STM-80)in the %-direction (see Figure 2), and the scanning peak areas were calculated.
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Flgure 3. Block diagram of the experimental setup.
RESULTS AND DISCUSSION (3)
respectively. Therefore, all the experimental data taken at different normal offsets z can be converted to the signal amplitudes at the certain normal offset zo using the phase shifts as A(%,)= A ( z )exp[O(zo)- Wz)l
(4)
EXPERIMENTAL SECTION A rough sketch of the samples used is shown in Figure 2. The test samples were polystyrene microparticles (about 1 pm in diameter) collected on membrane filters. Antibody-coated, colloidal gold ultrafine particles (about 15 nm in size and red) were adsorbed on an antigen-coated polystyrene particle surface by an immunological reaction. The amount of the antibody was determined by quantitation of the adsorbedgold particles. Three kinds of immunological samples, immunoglobulin E (IgE), immunoglobulin G (IgG),and carcinoembryonicantigen (CEA), were used. Detailed descriptionsof the sample preparation will be reported elsewhere.12 A block diagram of the experimental setup is shown in Figure 3. The excitation beam was the 514.5-nm emission line of an Ar ion h r (Spectra Physics Model 164),and ita output power was 100 mW. The beam intensity was modulated by a mechanical chopper (NFModel 5584), and ita modulation frequency was set at 320 Hz to achieve the best signal-bnoise ratio. The modulated light was focused in a line shape by a cylindrical lens to match ~~
(12)Tu, C.-Y.; Kitamori, T.; Sawada, T. Anal. Chem., submitted.
Experimental Verifications. To demonstrate that eq 1 is applicable to densitometric quantitative measurements by the PBD method, the PBD signal dependencies on the normal offset and the sample absorbance were measured. The dependencies of the PBD signal amplitude and phase on the normal offset for the three samples containing different concentrations of the colloidal gold particles are shown in Figure 4. The immunological sample used in this experiment was IgE. The normal offset was scanned from 0 to 500 pm, and the measurements were made in 20-pm steps. The 25 data points are plotted in Figure 4 for each sample. Decreasing signal amplitude and scattered signal phase were observed with normal offsets less than 150 pm because of probe beam eclipsing. At normal offsets over 150 pm, however, both the phase and natural logarithm of the amplitude decreased linearly with increasing normal offset, as predicted from the theory. In addition, the experimentally obtained slopes were almost the same as those calculated from the thermal diffusion length of the air a t 320 Hz and independent of the sample concentration. These results show that the proposed method of correcting the normal offset can be applied to the surfaceabsorbing sample systems. It should be noted here that the phase signal from the samples used was independent of the sample absorbance, which made the correction procedure much easier. This situation would not be met for samples having a thick absorption layer, and the correction procedure would be much more complicated. Reproducibility. First the effects of the proposed signal correction method on reproducibility were examined. To avoid any influences caused by the uncertainty of an
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
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Table I. Improvement of Lower Limits of Determination by Signal Correction SD of peak lower limit area (AU) of determ (ng/mL) before correction after correction
0.098 0.090
5.6 2.5
32.6% to 5.86% , in the standard deviation. These results c (
4 mm
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4 mm Figure 5. Improvement of reproducibility by the proposed signal correction method. The uncorrected and corrected signals are respectively shown in (a) and (b).
immunological reaction, only one sample, containing the quantity of colloidal gold particles which corresponded to the 1.0 X 10-1 mg/mL concentration of human IgG, was measured repeatedly. The nitrocellulose film was stuck on a slide glass with a small amount of sprayed paste. After the PBD measurement it was removed, repasted on a new glass, and then measured again. This procedure was repeated 10 times. The results of 10 repetitive measurements are shown in Figure 5. The 10 data were digitally lined up along the abscissa in a row and did not come from the continuous scan procedure discussed in the quantitation section. The sample width was about 4 mm, and the total tangent scan distance was 40 mm. The raw data of the PBD signal amplitude are shown in Figure 5a. A large fluctuation of the signal amplitude was seen among the 10 measurements. This could be attributed to the differences of the sample heights resulting from different slide glass thicknesses and amounts of paste. The maximum fluctuation of the signal amplitudes reached 40% and was estimated to be 70 pm of the normal offset fluctuation from the results shown in Figure 4. This value is frequently encountered in ordinary quantitative measurements. The relative standard deviation of the peak areas was calculated as 32.6 % Under the present conditions, no high-precision measurements would be possible. Then these data were corrected for the normal offset variation using eq 5, and the results are shown in Figure 5b. A remarkable improvement of reproducibility by using the proposed signal correction method was obtained. The decrease of the average signal amplitude was due to the standard normal offset zo chosen in the calculation. Comparison between the standard deviation of the peak areas before signal correction and that after it shows that the reproducibility was improved by a factor of more than 5 , from
.
proved that the proposed method of correcting the probe beam offsets using the phase signal is an effective way to improve the reproducibility. Quantitation. Next the effects of the proposed method on quantitation were investigated. The immunologicalsample used in this experiment was CEA. Its solution was successively diluted by a factor of 10,from 8 ng/mL to 8 fg/mL; 10 samples containing different concentrations of colloidal gold particles were prepared, one of which contained no CEA. A 100-pL portion of each sample was blotted on the nitrocellulose film, in a row (see Figure 2). After scanning in the x-direction, the calibration curves before and after the signal correction were compared. Characteristically for an immunological reaction, a sigmoidal curve was obtained. The lower limits of determination for CEA were calculated from double the standard deviations of these data points. The results are listed in Table I. The lower limits of determination were 5.6 ng/mL for the noncorrected data and 2.5 ng/mL for the corrected data. Using the signal correction method, the lower limit of determination was improved by a factor of about 2. This effect of reducing the lower limit of determination resulted from reduction in the uncertainty of the signal amplitudes due to the normal offset difference. In this experiment the improvement by the proposed method was not so obvious as in the repeated measurements. However, in the experiment using the tilting sample support, the phase signal fluctuated somewhat and a remarkable improvement effect was seen. These results suggested that the proposed signal correction method would be successfully applied to making up for a lack of sample flatness. As the proposed method is based on data processing after the measurements, it needs no additional experimental operations, so that it is very simple and rapid. Moreover, this idea can be applied to any kind of sample system in principle, though the correction procedures become much more complicated. With this signal correction method the PBD technique can overcome its weakness in quantitative measurements.
ACKNOWLEDGMENT The authors thank Prof. S. Matsuzawa and Dr. H. Kimura of the Department of Forensic Medicine, School of Medicine, Juntendo University, Japan, for sample preparation and useful discussions.
RECEIVED for review March 1993.
23, 1993. Accepted May 20,
