Anal. Chem. 1985, 57, 1079-1083
not reflected in the yield as PIXE is relatively insensitive to changes in the sample major components. This is shown in Figure 5 which displays R from eq 3 for hair, carbon, orchard leaves, and bovine liver, normalized to the hair ratio. Although these four samples have different compositions, their yield ratios are quite similar. The ICRP reference man concentrations for hair gave a yield curve lying between the orchard leaves and bovine liver lines, showing a maximum 10% change in calculated concentrations. Of course, the charred sample composition had to be measured before this comparison, which yields an estimate on the final uncertainties, could be made.
ACKNOWLEDGMENT We thank J. Goulding who performed the neutron activation analysis and J. F. Chapman who supplied the atomic spectrometry results. We also thank the operating staff of the AAEC 3 MeV Van de Graaff accelerator for their assistance, in particular L. Russell whose work on the target chamber has made measurements so much easier. We thank L. Dale for his useful advice on powder sample preparation methods. Registry No. K, 7440-09-7;Ca, 7440-70-2;Fe, 7439-89-6;Ni, 7440-02-0; Cu, 7440-50-8; Zn, 7440-66-6; Pb, 7439-92-1; Brz, 7726-95-6; Mn, 7439-96-5; Co, 7440-48-4; Cd, 7440-43-9; Zr, 7440-67-7; Se, 7782-49-2;Bi, 7440-69-9; As, 7440-38-2; Cr, 744047-3; Ti, 7440-32-6; Sr, 7440-24-6; Rb, 7440-17-7. LITERATURE CITED (1) Cookson, J. A.; Pilling, F. D. Phys. Med. Bbl. 1975, 20, 1015-1020. (2) Houtman, J. P. W.; Bos, A.; Vis, R.; Cookson, J. A.; Tjioe, P. S. J . Radionanal. Chem. 1982, 7 0 , 191-208.
1079
Horowitz, P.; Aronson, M.; Grodzins, L.; Ryan, J.; Merriam, G.; Lechene, C. Science 1976, 194, 1162-1 165. Henley, E. C.; Kassouny, M. E.; Nelson, J. W. Science 1977, 197, 277-278. Chen, J. X.; Guo, Y. 2.; Li, H. K.; Ren, C. G.; Tang, G. H.; Wang, X. D.; Yang, F. C.; Yao, H. Y. Nucl. Instrum. Methods 1981. 181, 269-273. Baptista, G. B.; Montenegro, E. C.; Paschoa, A. S.;Barros Leite, C. V. Nucl. Instrum. Methods 1981, 181, 263-267. Pillay, A. E.; Pelsach, M. J . Radloandl. Chem. 1981, 63, 85-95. Whitehead, N. E. Nucl. Instrum. Methods 1979, 164, 381-380. Clayton, E.; Cohen, D. D.; Duerden, P. Nucl. Insfrum. Methods 1981, 180, 541-548. Clayton, E. Nucl. Instrum. Methods 1981, l g l , 567-572. Clayton, E. Nucl. Instrum. Methods 1983, 218, 221-224. Mayer, J. W., and Rimlni, E., Eds. “Ion Beam Handbook for Material Analysis”; Academic Press: New York, 1979; p 228. Chu, W. K.; Mayer, J. W.; Nicolet, M. A. “Backscattering Spectrometry”; Academic Press: New York, 1977. Hyvonen-Dabek, M.; Riihonen, M.; Dabek, J. T. Phys. Med. Biol. 1979, 2 4 , 988-998. Chittleborough, G. Sci. Total Environ. 1980, 14, 53-75. Montenegro, E. C.; Baptista, G. B.; De Castro Faria, L. U.; Paschoa, A. S. Nucl. Instrum. Methods 1980, 168. 479-483. Campbell, J.; Faiq, S.;Gibson, R. S.;Russell, S. B.; Schulte, C. W. Anal. Chem. l W l , 53, 1249-1253. Berti, M.; Buso, G.; Colautti, P.; Moschini, G.; Stievano, B. M.; Tregnaghi, C. Anal. Chem. 1977, 49, 1313-1315. Gibbons Natrelia, M. “Experimental Statistics”; National Bureau of Standards, Washington, DC. 1963; National Bureau of Standards Handbook 91. Giadney, E. S. Anal. Chim. Acta 1980, 118, 356-396. “Report on the Task Group on Reference Man (ICRP 23)”; Internatlonal Commission on Radiological Protection; Pergamon Press: Oxford, 1974. Doyle, 0. L.; Peercy, P. S . Appl. Phys. Left. 1979, 3 4 , 811-813. Sofieid, C. J.; Bridweli, L. B.; Wright, C. J. Nucl. Instrum. Methods 1981, 191, 379-382.
RECEIVEDfor review July 13,1983. Resubmitted and accepted December 26, 1984.
Saturation Effects in Gas-Phase Photothermal Deflection Spectrophotometry George R. Long and Stephen E. Bialkowski* Department of Chemistry and Biochemistry, UMC 03, Utah State University, Logan, Utah 84322
This paper descrlbes some effects of optlcal saturatlon on a photothermal deflectlon signal and presents a slmple theory to describe these effects. These effects Increase the sensltlvlty while decreaslng the relatlve error of the method as the lntenstty exceeds the saturatlon Intensity. Detectlon lknlts of 1.3 ppbv for chlorodlfluoromethane, 2 ppbv for dlchlorodlfluoromethane, and 3 ppmv for sulfur dioxide, In 13.3 kPa of argon, are found. These detectlon limits extrapolate to atmospheric detectlon llmlts of 170 pptv for chlorodlfluoromethane and 260 pptv for dlchlorodlfluoromethane. The correspondlng mass detectlon llmlts In the Infrared laser Irradlated volume are 55 fg for chlorodlfluoromethane and 70 fg for dlchlorodlfluoromethane.
Photothermal deflection spectrophotometry (PDS) is one of a class of several techniques that is used to measure small absorbances by probing the refractive index gradient created in the sample when absorption of radiation and subsequent thermal relaxation occurs ( 1 , 2 ) . PDS employs a pump laser operating on a frequency resonant with an absorption of the analyte to produce a temperature gradient in the sample. The 0003-2700/85/0357-1079$0 1.50/0
temperature gradient results in a refractive index gradient which subsequently deflects a probe laser beam. The angle of deflection is proportional to the absorbance of the sample. Theories that describe PDS have been discussed by Jackson et al. (3))and the technique has been successfully applied to a number of analytical problems ( 4 , 5 ) . One interesting fact presented in the theories that describe photothermal spectroscopy is that the observed signal is directly proportional to the energy of the excitation laser pulse, implying that high-energy excitation pulses should provide the optimal analytical sensitivity. Many commercially available lasers have energies exceeding 1 J/pulse. However, at high laser energies optical saturation of the analyte begins to occur and at this point these theories are no longer applicable. Recently we have described some effects of optical saturation in thermal lensing spectrophotometry (TLS) (6). One of these effects was the observation of a PDS signal greater than that of a TLS signal. This is a result of the fact that the PDS signal is proportional to the temperature gradient while the TLS signal is proportional to the curvature of the temperature profile (3,7). As the intensity of the pump laser exceeds the saturation intensity, the temperature profile in the sample begins to resemble a top-hat profile (8). The 0 1985 American Chemical Soclety
1080
ANALYTICAL CHEMISTRY, VOL. 57, NO. 0, MAY 1985
curvature of the temperature profile decreases while the maximum gradient increases, making the PDS signal greater than the TLS signal. In this study we discuss the effect of optical saturation on the PDS signal and consider the analytical utility of PDS experiments performed at these high laser energies. Toward this end detection limits for CF2HCl (FC-22), CFzC12(FC-12), and SO2 are presented.
EXPERIMENTAL SECTION The PDS apparatus is typical of those commonly used for photothermal spectroscopy (7).The excitation source is a pulsed TEA-C02laser capable of producing a maximum energy of about 0.1 J per pulse. The specifics of the TEA-C02laser have been discussed previously (6). In these experiments the C02laser was operated at a 3.75 Hz and was equipped with an intracavity iris to promote TEM,, operation. The excitation beam is focused into the sample cell with a 30 cm focal length BaF2lens. The l/e electricalfield radius of the focused beam was 0.053 cm. The beam radius was measured by scanning a razor blade across the beam while monitoring the transmitted energy. C02 laser wavelengths were determined with an Optical Engineering spectrum analyzer, Model 16-A. The R26 line of the 9.2 pm transition was used for SO2 and FC-22; the P32 line of the 10.6 wm transition was used for FC-12 (9). The C02laser energies were measured with a Laser Precision Model RJP735. The HeNe probe laser was a Uniphase Model 1105p. Fused silica lenses of varying focal lengths were used to adjust the propagation characteristics of the HeNe beam. The pump and probe laser beams were mixed with a germanium beam splitter that reflected the HeNe laser beam. The C02laser energy was monitored at this point using the reflected portion of this beam. Detectors used in this study were a lateral position sensing detector, Model LSC/50, from United Detector Technology and an EG&G SGD-040-APIN photodiode with a 0.006 cm pinhole. Amplification of the position sensing detector is done with a United Detector Technology sym/difference amplifier, Model 301B-AC,and an Analog Devices Model 436 operational divider with a gain of 10. In this setup the difference signal from the lateral sensing detector is divided by the sum signal. This accounted for any changes in the signal caused by probe laser intensity fluctuationsor deflection of the beam in other directions. The signal from the PIN photodiode was amplified using the ac-coupled LM741C operational amplifier described previously (6).
These detectors require different experimental arrangements to achieve maximum sensitivity. Jackson et al. (3) have shown that the maximum sensitivityof a lateral position sensing detector occurs when the spot size of the probe laser beam is about equal to the size of the detector surface. In these experiments this occurred 2.23 m from the sample cell. The equation that describes the response of the pinhole-PIN photodiode detector for an infinitely small pinhole is pv = COnSt(e-2P/w2- e-2(r-dd)2/w*)
(1)
where r is the position of the pinhole along the radial coordinate of the probe beam, C#J is the deflection angle, d is the distance from the cell to the detector, w is the radius of the probe beam spot at the detector, and A V is the observed voltage change. The pinhole was located one confocal distance past the focus of the HeNe laser beam, which was 0.86 m from the sample cell. The optimum position for the pinhole is at the inflection point of the probe beam intensity profile. At this point the signal from the photodiode is proportional to the deflection angle for small deflections. The fact that the pinhole-PIN photodiode detector's position along the radial coordinate of the probe beam is variable makes this detector more difficult to use, since both the probe beam offset and the pinhole offset must be adjusted to obtain the maximum signal. However, it did prove to be the more sensitive detector and was therefore used for the detection limit studies. Also, TLS signals are not observed with a position sensing detector, so the pinhole-PIN photodiode arrangement was used in experiments where TLS and PDS were compared. Data collection was done with a 20-MHz transient digitizer, Physical Data Corp., Model 552 A interfaced to a DEC LSI 11/2
microprocessor. Pseudo gated integration was used for data collection. This method of data collection has been described previously (6). The sample cell was constructed of stainless steel and was connected directly to the gas manifold to allow filling of the cell without changing its position. The cell used pressure fitted Harsaw laser grade NaCl windows and was wrapped with heating tape to allow bakeout under high vacuum. The dimensions of the cell were 7 cm in length with an inner diameter of 4 cm. The reagents used were Ar, >99.999% purity, SO2, >99.98%, and CF2HCl,>99.9%, all from Matheson, and CFC12,>98% from PCR.
RESULTS AND DISCUSSION The derivation of the PDS signal for a saturated, pulsed laser excited system is straightforward. A saturation intensity, or power density, I,, may be defined for a two level system as that intensity where the two-level population difference is half that of the total population. At this point (8)
hv 2ar where hv is the transition energy, LT is the absorption cross section, and r is the characteristic time for decay out of the excited state. For a fundamental mode laser beam, the intensity at any radius, r, from the center of the beam is
I, = -
(3) where Pois the total power in W and w is the beam waist radius to the l / e electric field points. The fraction, F, of species excited is (4)
where Ne is the number in the excited state and Nt is the total number of species. The calculation of the deflection angle from the fraction of species initially excited is performed in a manner similar to that described by Jackson et al. (3). Assuming that the number of species which relax during the excitation laser pulse is small compared to the total number excited, the heat generated at radius r is
CF(r)hv
(5)
where C is the number density concentration of absorbing species and the temperature distribution is thus
6T(r) =
CF(r)hv PCP
where 6T(r)is the temperature change, p is the molar density of the sample, and cp is the molar heat capacity. On combination of 2-4 and 6, the temperature change distribution is
where we have defined Io = 2P0/u2. The deflection angle, 4, can now be calculated for the zero time signal using the expression ( 3 )
where is the refractive index of the sample, (dn/dT), is the change in this index with temperature, V, is the gradient perpendicular to the propagation direction of the probe laser beam, and the integral is over the probe beam path, s. The perpendicular gradient is the differential with respect to r and
ANALYTICAL CHEMISTRY, VOL. 57, NO. 6, MAY 1985 0.1251
!
0
poooo
0.100
8
1.5
9 "
w
m
0 O . 0
mD*,
0 0
0.075-
o
-J
a
z 0
Lo
0.050
1081
*
-
0.025
0.0
'
- I 3 A - I 1
C
i
h
b
I
I
4
5
LOG CIo/Isl Flgure 1. Optimum probe beam offset vs. pump laser energy, calculated from eq 9.
0.000 .a00
- - I
.025
.050
.075
OFFSET (om)
Flgure 2. PDS signal vs. probe beam offset for pump laser energies of (0)26 mJ, (0)18 mJ, and (h)7 mJ. The pinhole-PIN photodiode
detector was used. for small deviations (deflection angles) the integral over this path is the interaction length, as in this case, the length of the sample cell, 1. Evaluation of eq 8 with the temperature change, eq 6, yields the final result
0.5
c\
2
2 z
This final expression does not give the time dependent behavior of the PDS angle. To determine this, the heat source expression in eq 4 may be used for the usual Green's function integral evaluation (3, 7). However, this integral equation is difficult to evaluate with this expression and we leave these evaluationsfor the future. Equation 9 does give the maximum deflection that can be obtained at zero time if the optimum displacement of the probe laser beam is determined. Since the thermal diffusion occurs as a result of a temperature gradient and decreases this gradient in time as the system approaches equilibrium, the maximum gradient must be that which occurs just after the excited species have relaxed. Equation 9 also shows that the deflection angle will in general be positive, i.e., will be such that the probe beam is defected away from the excitation beam. The refractive index change with respect to temperature is in general negative and thus 1 the deflection angle will be positive. Optimum probe laser beam offsets from the excitation laser beam position for a given intensity, Io, and saturation intensity, I,, can be calculated from eq 9. Figure 1illustrates the optimum offset vs. log Z,,/I,. This offset was calculated using a Newton interpolation algorithm (IO). At intensities below I , the optimum beam offset does not vary substantially with intensity. Since the level population difference at I , is only 0.5 that of the total population, one would expect the temperature distribution at zero time to reflect that of the pump laser beam profile and no change will occur with varying intensity. As the intensity of the pump laser exceeds I,, the initial temperature distribution must broaden and flatten out near the beam center. Thus, one would expect the optimum offset to increase in radius with increasing I above I,. this behavior is illustrated in Figure 1as well as in the experimental results shown in Figure 2. In the latter illustration the observed signal is plotted vs. the probe beam offset for several different laser intensities. The TLS signal occm at zero offset. Data were obtained with the pinhole-PIN photodiode detector so that both TLS and PDS data could be obtained with the same experimental setup. The probe beam optical geometry was optimized for TLS. Optimization of the probe beam optical geometry was not performed nor has it been discussed in the past. Thus the difference of 20% of the PDS signal
-0.
: Lo
0 0
-1.
-2.5
-4.5
I
I
-3.5
LOG
-2. 5
- .5
ENERGY (J)
Figure 3. Plot of log signal vs. log of the pump laser energy for (M) FC-12, (e)SO2, and (0)FC-22. The lateral sensing detector was used.
over that of TLS may n& be maximum observable with PDS optimization. Figure 2 also illustrates that the effect of intensity on both the TLS and PDS signals is to increase this signal even when the intensity is well beyond I,. We recently showed that based on the simple two level saturation model, the TLS signal should decrease with intensity above I, (6). There are several reasons why both signals continue to increase with intensity. Since vibrational level spacings are rather close to that predicted by a harmonic oscillator at lower energy levels (111, multiphoton transitions are likely (12). Other models that have been proposed for anomalous absorption cross-section for high-intensity infrared excitation include the heat bath feedback mechanism (13,14), and rapid relaxation into rotational states (1.516). However, no matter which nonlinear mechanism(s) is operative, there is a combination of saturation and nonlinear behavior occurring since the deflection signal is as large as or larger than that of the TLS one (6). Obviously one desires the large signal enhancement that is realized at high pump laser intensities. A study of the energy dependence of the PDS signal was performed for several different molecules, each having different saturative behavior. The results of these experiments are shown in Figure 3. The probe beam position was optimized at each energy used on the experimentalplots. The theoretical energy dependence of the PDS signal is shown in Figure 4 as calculated by eq 9 and using the offset optimization algorithm mentioned above. It is not possible to compare Figure 3 and 4 directly since the saturation intensity of the analytes cannot
1082
ANALYTICAL CHEMISTRY, VOL. 57, NO. 6, MAY 1985
0
I
I
I
1
I
I
I
1
X
2.51
x
x
0 X
2.04 X h
5
l
1.5'
X
X
e 0
X
0
e
0.0
k0
0
X
0
0. 7---7----5 10
7---
15
PRESSURE (kPa)
Flgure 5. Plot of pressure vs. PDS slgnai for (X) FC-22 and (signal X 10) (0)SO,-lateral sensing detector was used.
be exactly known, although the similarity of the observed and predicted behavior may be seen. Differences in the behavior of the three molecules studied appears to be due to their different saturation intensities and/or their multiphoton absorption cross sections. The pressure dependence of the PDS signal for FC-22 and SOz is shown in Figure 5. To understand this behavior it is necessary to examine the pressure-dependent terms in eq 9. The pressure dependence of dn/dT and p will cancel each other out at pressures above 1 kPa. The absorption cross section and the excited state relaxation time will change with pressure. The pressure-dependent cross section behavior depends upon the particular molecule and the wavelength used. In this case it was found that the absorbance of FC-22 did not vary more than 5% over the pressure range studied. The pressure dependence of the absorption coefficient for SO2 could not be measured due to its small value. The pressure-dependent term in eq 9 is I,, as defined in eq 2, n does not change significantly with pressure, therefore T is the major term affected by pressure. This should be the case even without the assumption of a two-level system. As the pressure is increased T will decrease and I, will, in turn, increase. This will cause a decrease in the signal with increasing pressure until I, becomes greater than the pump laser intensity. This decrease in the signal was not observed although it may occur a t higher pressures than those used in this study. One possible explanation for the fact that the PDS signal increases with pressures is that the assumption that thermal relaxation is slow compared to the pump laser pulse may not be correct. If this is the case, more energy than expected could
be absorbed into the system by a process in which the molecules absorb radiation, thermally relax, and absorb more radiation before the end of the excitation pulse (3, 13,14). The amount of energy absorbed by this process is related to the thermal relaxation rate which is in turn directly related to the pressure of the system. It is not clear at this point why the PDS signal increases linearly with pressure for SO2. The working curves in this study were linear over 4 orders of magnitude. The extrapolated detection limit for FC-22 is 1.3 ppbv in 13.3 kPa of argon or 55 fg in the beam volume. The resulting atmosphericpressure detection limit is 170 pptv. The detection limit for FC-22 using an electron capture detector (ECD) is 40-130 pptv; however this requires preconcentration and elaborate separation techniques (17). PDS has achieved nearly the same sensitivity with a much smaller amount of sample. The detection limit extrapolated from the FC-12 working curve was 2 ppbv in 13.3 kPa of argon. Increasing the cell pressure to an atmosphere did not change the PDS signal significantly. Therefore, an extrapolation to atmospheric pressure is valid. This extrapolation results in a detection limit of 260 pptv or 70 fg in the beam volume. This detection limit is 5 times lower than that previously obtained wing TLS (6). It was not possible to obtain the working curve for SO2 due to problems with surface adsorption. However, we estimate a detection limit of 2 ppmv. Ultrasensitive detection limits for SO2were not expected due to the small value of the absorption coefficient for SO2 at the wavelength used (9). Cross extrapolation of these detection limits in argon to those in other buffer gases is not straightforward because of the subtle changes in the quantities which reflect the saturation behavior of the particular analyte, e.g., n and T in eq 2. However, assuming that the changes in these values upon changing the buffer gas will have a neglectable influence on the signal, predictions of the sensitivities in other gases may be obtained by considering only the thermal characteristics of these gases (18). In this case, the detection limits in air should be only 2% better than those in argon. At this point there is still much work to be done in order to fully understand the effects of pressure and excitation laser intensity on the PDS signal. The optimum conditions for measurement have yet to be successfully obtained from theory and in the future, detection limits will probably decrease even further. Enhanced detection limits and subsequent measurement accuarcy may also be achieved by careful elimination of noise and interference sources in the experimental apparatus. The minimum detection limits found in these experiments were obtained by using the pinhole-PIN photodiode combination. The measurements obtained in this fashion were subject to HeNe laser pointing noise and intensity fluctuations. The use of a single mode intensity stabilized probe laser would reduce the source of these limitations. We estimate that the elimination of these noise sources would decrease the detection limit by a factor of about 3. Another source of error in these experiments is due to the alignment of the optical system. Misalignment of the overlap between the excitation and probe laser beam will not only result in changes in the maximum detector signal proportional to the deflection angle but will also result in a change in the temporal characteristics of this signal. Depending on the particular data collection procedure, these temporal changes could result in large errors. The relative error in the experimental measurements as a function of excitation laser energy is illustrated in Figure 6. These data were obtained using the lateral position detector for 100 ppmv FC-22 in argon. The data were averaged for 100 pulses and the variance and average value of these data were calculated. The relative error is calculated by dividing the square root of the signal variance by the signal. Since the
ANALYTICAL CHEMISTRY, VOL. 57, NO. 6, MAY 1985
The variance due to pulse to pulse excitation energy variations has a maximum at Io I,. At higher intensities the variance actually decreases. Thus the measurement precision actually increases with increasing intensity above I,. The relative error due to misalignment is much less than that due to intensity fluctuations. The total relative precision increase observed in these experiments is probably controlled by the decreasing error due to energy fluctuations of the excitation source with increasing energy.
I X
X ~
0.3j
X
x
W
I
-x 0.11
CONCLUSION
x
1
X
x
I
0.0 -5.0
I
I
I
I
I
-4.5
-4.0
-3.5
-3.0
-2.5
LOG [energy ( J ) I
Figure 8. Relative error of the PDS signal vs. pump laser energy for FC-22 at 100 ppmv at 13.1 kPa total pressure in Ar. The lateral sensing detector was used.
\\
‘““1
1083
/
\
These results show that optical saturation can be used as an advantage in PDS experiments. The sensitivity of the PDS signal is enhanced at pump laser energies above the saturation energy and relative error is actually reduced. The pressure studies show PDS to be well suited for analysis of gas samples up to atmospheric pressure. PDS should also show less effects from multiphoton processes than would TLS, since the PDS signal is produced at the inflection point of the temperature profile rather than at the peak as is the case with TLS. This means the intensity of the excitation source is less at the point where the PDS signal is being created and hence less multiphoton effects will occur. Since TLS and collinear PDS can use the same optical arrangement, PDS is a useful complementary technique for cases where intensities above I, are available. Registry NO.CF,HC1,75-45-6; CF2Clz,75-71-8;SOZ, 7446-09-5.
LITERATURE CITED
.OO
‘
1
V
3
I
-
2
I
4
I
0
i
b
b
k
b
LOG C Io/I SI
Flguro 7. Theoretical relative errors due to excbtion energy fluctuation (*5%) and alignment (*5%)
lateral position sensor was used, variance due to probe laser intensity noise is not manifested in these results. The major sources of variance are due to the excitation laser energy fluctuations from pulse to pulse and the excitation/probe laser alignment error. This alignment was reoptimized for each excitation laser intensity. The calculated relative errors are shown in Figure 7. These relative errors were calculated using eq 9 at the optimum excitation laser-probe laser alignment offset as discussed above. The relative error for excitation laser energy fluctuations was calculated by first determining the theoretical optimum alignment and then varying the laser energy by 5%. The square of the -5% to +5% difference is the variance. The position error was calculated in a similar fashion, only the variance was calculated by varying the optimum position by 5% of the displacement at low intensities
(Io .e 4).
(1) Hu, C.;Whlnnery, J. R. Appl. Opt. 1073, 72, 72-79. (2) Harris, T. D. Anal. Chem. 1982, 54,741A-750A. (3)Jackson, W. B.; Amer, N. M.; Boccara, A. C.; Fournler, D. Appl. Opt. 1081, 2 0 , 1333-1343. (4) Fournler, D.; Boccara, A. C.; Amer, N. M.; Gerlack, R. Appl. Phys. Lett. 1080, 37 (6),519-521. (5) Sell, J. A. Appl. Opt. 1964, 2 3 , 1586-1596. (6) Long, G. R.; Blalkowskl, S. E. Anal. Chem. 1084, 56, 2806-2811. (7) Fang, H. L.; Swofford, R. L. “Ultrasensitive Laser Spectroscopy”; Kliger, D. S., Ed.; Academic Press: New York, 1983:pp 176-230. (8) Svelto, 0. “Principles of Lasers”, 2nd ed.; Plenum Press: New York, 1982;pp 58-68. (9) Mayer, A.: Comera, J.; Charpentier, H.; Jarsaud, C. Appl. Opt. 1062, 9 , 1663-1669. (IO)Johnson, L. W.; Riess, R. D. “Numerical Analysis”; Addison-Wesley: Menlo Park, CA, 1982;pp 142-194. (11) Gulllory, W. A. “Introduction to Molecular Spectroscopy”; Allyn and Bacon: Boston, MA, 1977. (12) Twarowski, A. J.; Kliger, D. S. Chem. Phys. 1977, 2 0 , 253-258. (13) Stone, J.; Goodman, M. F. J . Chem. Phys. 1979, 7 1 , 406. (14) Seder, T. A. and Weltz, E. Chem. Phys. Lett. 1984, 104, 545-551. (15) Wood, 0.R.; Gordon, P. L.; Schwarz, S. E. I€€€ J . Quantum Electron. 1880. Q€-5, 502-513. (16) Burak, 1.; Stelnfeld, J. I.; Sutton, D. 0. J . Quant. Spectrosc. Radlat. Transfer 1080, 9 , 959-980. (17) Shlmohara, K.; Sueta, S.; Tabata, T.; Shigemori, N. Takl Osen Gakkalshl 1970, 74 (I),31-37. (18) Mori, K.; Imasaka, T.; Ishlbashl, N. Anal. Chem. 1083, 55
1075-1079.
RECEIVED for review October 8, 1984. Accepted January 22, 1985. This research was supported in part by BRSG SO7 RR07093-17 awarded by the Biomedical Research Support Grant Program, Division of Research Resources, National Institutes of Health.
