Anal. Chem. 1988, 60, 2674-2679
2874
by using fiber optics is now under investigation in our laboratory and will be discussed in a later report.
LITERATURE CITED Rauhut, M. M.; Bollyky, L. J.; Roberts, E. G.; Loy, M.; Whltman, R. H.; Iannota, A. M.; Semsei, A. M.; Clarke, R. A. J . Am. Chem. SOC. 1967, 89, 6515. Lechtken, P.; Turro, N. J. Mol. fhotochem. 1974, 6 , 95. Wllliams, D. C.; Huff, G. F.; Seltz, W. R. Anal. Chem. 1978, 48, 1003. Zoonen, P.; Herder, I.; GoolJer,C.; Velthorst, N. H.; Frei, R . W. Anal. Left. 1988, 19, 1949. Rlgln, V. I.J . Anal. Chem. USSR (Engl. Transl.) 1981, 36, 111. Rigin, V. I. J. Anal. Chem. USSR (Engl. Transl.) 1983, 38, 1265. Rigin, V. 1. J. Anel. Chem. USSR (Engl. Transl.) 1983, 38, 1328. Scott, G.; Seitz, W. R.; Ambrose, J. Anal. Chim. Acta 1980, 115, 221. Williams, D. C.; Huff, G. F.; Seltz, W. R. Anal. Chem. 1078, 48, 1478. Rigin, V. I.J . Anal. Chem. USSR(Engl. Transl.) 1979, 3 4 , 619. Zoonen, P.; Kamminga, D. A.; Gwljer, G.; Veithorst, N. H.; Frei, R. W. Anal. Chlm. Acta 1085, 167, 249. Diaz-Garcia, M. E.; Sanz-Medel, A. Talante 1988, 33, 255-275. Spurlln. S.; Hlnze, W. L.; Armstrong, D. W. Anal. Left. 1977, 10, a a 7 - .-"-. inn~ Hinze, W. L. SoluilOn Chemlstry of Surfactants; Mittal, K. L., Ed.: Pienum: New York, 1979; Vol. 1, pp 79-127. Hinze, W. L.; Slngh, H. N.; Baba, Y; Harvey, N. G. TrAC, Trends Anal. Chem. (Pers. Ed.) 1984, 3 , 193-199.
"".
(16) Singh, H. N.; Hinze, W. L. Anawst (London) 1982, 107, 1073-1080. (17) Sanz-Medel, A.; Aionso, J. I.Anal. Chim. Acta 1984, 165, 159-169. (18) Cline Love, L. J.; Harbarta, J. G.; Dorsey, J. G. Anal. Chem. 1984, 5 6 , 1132A-1148A. Cline Love, L. J.; Grayeskl, M. L.; Noroski, J.; Weinberger, R. Anal. Chim. Acta 1985, 170. 3-12. Cline Love, L. J.; Skrilec, M.; Habarta, J. Anal. Chem. 1980, 52, 754-759. Armstrong, D. W.; Hinze, W. L.; Bui, K. H.; Slngh, H. N. Anal. Lett. 1081, 14; 1659-1667. Thompson, R. B.; McBee, S. E. S. Langmuir 1988, 4, 106-110. Malehorn, C. L.; Riehl, T. E.; Hinze, W. L. Analyst (London) 1988, 11 1 , 941-947. .. . .. . . Yamada, M.; Suzuki, S. Anal Left. 1984, 17, 251-263. Kato, M.; Yamada. M.; Suzuki, S. Anal. Chem. 1984, 56.2529-2534. Hinze. W. L.; Riehi, T. E.; Slngh, H. N.; Baba, Y. Anal. Chem. 1984, 56, 2180-2191. Klopf, L. L.; Nieman, T. A. Anal. Chem. 1084, 56, 1539-1542. Hoshino, H.; Hinze, W. L. Anal. Chem. 1987, 59, 496. Igarashl, S.; Hinze, W. L. Anal. Chem. 1988. 60, 446. Abdel-Latif, M. S.; Sulelman, A. A.; Gullbault, G. G. Anal. Left. 1988, 21, 943. Assolant-Vinet. C. H.; Couiet, P. R. Anal. Left. 1988, 19, 875.
RECEIVED for review July 19,1988. Accepted September 14, 1988* This work 'Onduckd with assistance from the Louisiana Education Quality Support Fund.
Ultrasensitive Photothermal Deflection Spectrometry Using an Analyzer Etalon Stephen E. Bialkowski* and Zhi Fang He
Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300
The theory and experlmentat scheme for uslng an analyzer etalon to detect photothermaldeflecth slgnals is developed. First, a theory for photothermal deflection spectrometry Is developed, whkh describes the observed signal decay In terms of the characteristic thermal decay tlme constant and whkh accounts for a flnlte probe laser beam walst radius. Second, a theory for the angular response for an analyzer etalon Is described. The analyzer etalon Is found to be extremely sensltlve to beam angle varlatlons and dramatlcally Increases the sensltlvlty of photothermal beam deflection measurements. A theoretkal enhancement over conventional deflectlon angle detectlon schemes of 100 Is calculated. Although the experlmental enhancement Is calculated to be only 0.4 of theoretlcal, a slngte laser pulse detectlon llmlt of 0.7 ppm (v/v) of CFC-12 In argon Is obtained by uslng a carbon dloxMe laser operatlng at 933 cm-' wlth a pulse energy of 1 mJ. This constitutes a slgnnkant Improvement over previously determlned detection Ilmlts. Ensemble averaglng can be used to decrease this llmlt In systems where analysls tlme Is not critical. The problems encountered In uslng this detectlon scheme are also due to the extreme angle sensltlvlty. The apparatus Is very susceptible to environmental factors such as air currents, laboratory temperature varlatlons, and vlbratlons.
Reported here is a new deflection angle detection scheme for photothermal spectroscopy. Photothermal deflection spectroscopy (PDS) is an ultrasensitive technique used for the measurement of small optical absorbance (1-4). Deflection of a probe laser beam path arises from a change in refractive
index (RI) that occurs when optical radiation from a second, pump laser light source is absorbed by the sample and not lost through subsequent emission of radiation. The energy is deposited in the sample in a finite volume and so results in a spatially anisotropic RI perturbation. To a first approximation, the linear gradient part of this RI perturbation is what is responsible for the deflection of the probe laser beam used to monitor the RI change in the sample. For the most part, experimental implementations of PDS have been based on position measurement of the probe laser beam spot at some distance past the sample cell. The two main methods for performing these position measurements have been to use a linear aperture that bisects the beam image, followed by a photodetector, or to use one of the bi-cell or lateral position sensors. Both of these methods rely on the fact that a deflection of the probe beam in the sample cell will result in a linear displacement proportional to the distance that the aperture or detector is positioned past the sample cell. But, since the probe laser beam, which is normally focused at the position where the RI perturbation occurs, is also diverging, the sensitivity of these position-sensitive schemes cannot be arbitrarily increased by moving the aperture or detector far from the sample cell. In the end analysis, there is no advantage to placing the detector at a distance beyond the Rayleigh range of the probe laser (1,5 ) . One exception to the beam-position-sensitive detection schemes is moire deflectometry (6). In this scheme, it is the beam angle itself that is measured by the change in probe laser intensity past a pair of matched ronchi rulings placed some distance apart. An advantage to this scheme is that the whole RI perturbation can be determined through the apparent spatially resolved deflection angles. This detection scheme is not dependent on the distance between the deflectometer
0003-2700/88/0360-2674$01.50/00 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
and the sample cell. However, in order to use this scheme the probe laser beam must be wide in order to approximate a nondiverging wave and to illuminate a number of lines on the ronchi rulings. Subsequently, an area that is typically much larger than that excited by a focused pump laser beam is monitored. The requirement for large probe beams results in a small overall intensity change and thus a low sensitivity. In this paper we describe the use of an analyzer etalon for the determination of deflection angle in pulsed laser excited PDS experiments (7,8).The flat mirror cavity analyzer etalon is a Fabry-Perot interferometer with a large free spectral range. It is normally used to determine the degree of monochromaticity or spectroscopic line width and is also extremely sensitive to the incidence angle of the probe beam (8). The main advantage to using the analyzer etalon is that the fringe width is very much narrower than other, single-pass interferometers and that the optical path of the interferometer does not contain the sample. For the flat etalon, the finesse, used to characterize the spectral resolving power of the analyzer, is also a figure of merit for the angular sensitivity. That is, the multiple internal reflections that give rise to the extremely narrow optical band-pass characteristics of the device also give rise to extreme angle sensitivity. As in the case of the moire deflectometer, this angle detection scheme is sensitive to angular beam deviations and not to beam displacement. In the optical configuration described below the probe laser beam does not have to be wide. In fact the probe laser can be focused in the same plane as that of the pulsed pump laser and at a radial offset resulting in a maximum deflection angle.
THEORY A. Photothermal Deflection Angle. The spatial temperature perturbation that occurs upon optical absorption of a pump laser beam with a pulse energy, Ep,and an electric field radius, w , is (9)
GT(r,t) = (21aEp/aw2pCp) exp[-2r2/w2(1
+ 2t/tC)](1 + 2t/tc) (1)
where a is the exponential optical absorption coefficient, 1 is the path length, t is time, t, = w2/4K is the characteristic thermal diffusion time where K is the thermal diffusion coefficient, and pCp is the heat capacity. Equation 1 was obtained by assuming that the pulsed excitation laser pulse width is much shorter than the characteristic thermal decay time, and thus the pulsed laser intensity is integrated by the absorbing sample. This is true in these experiments. The integrated intensity results in the pulsed laser energy dependence of the temperature change equation. In this limit, the time dependence is such that the temperature change is initially a maximum, thereafter decreasing due to thermal diffusion. Associated with this decrease in the maximum temperature change is a widening of the perturbation. In fact, the energy in the sample must be a constant although thermal diffusion causes the energy to disperse. The deflection angle of a paraxial ray passing through this perturbed medium is (IO)
2875
optical path is just that of a parallel ray propagating through the length of the cell. It can be seen that the deflection angle is a function of the radial offset of the paraxial ray from the origin of the pump laser beam. The maximum deflection angle occurs just after excited-state relaxation. This initial maximum deflection angle occurs for a ray at a radial offset of r,, = w/2, and thus the maximum deflection angle is @ma
= -(dn / d T),( 4 1‘YE, / rr nw 3pC,) e-1/2
(4)
The characteristic thermal decay constant can be obtained from the time required for the deflection angle signal to reach half of the maximum. Assuming that the pump and probe lasers are aligned for the maximum zero time signal, the ratio of eq 3 to that of (4) is the relative deflection angle $(r=w/2,t)/4,,=
= expt-1/(2
+ 4 t / t c ) l / ( l + 2t/tA2 (5)
When this ratio is 1/2, the relationship between this time and the characteristic time constant is t, = 14.87t1/2.In contrast, then the relationship found for photothermal lens spectroscopy obtained in a similar fashion is t, = 4.828t1/2. However, it is not possible to probe the RI perturbation only at this offset. In general, the finite beam waist of the probe laser will result in an overall deflection angle that is less than the maximum, since it will probe regions of the RI perturbation at radii that are less than optimum. The effect of a finite probe laser beam waist can be illustrated by considering the average or intensity-weighted deflection angle of a Gaussian probe laser beam offset from the origin by a factor of xo, with an intensity such that I = (210/rw,2) exp[-2((x x,J2 + y2)/wp2],where wp is the probe laser beam waist radius. Integration of the probe laser intensity over the space-dependent deflection will result in an average deflection angle for this beam. This average deflection is related to the probe beam centroid that would be measured by using a lateral position sensor. Substitution of the Cartesian coordinate equivalent to radius in eq 1, followed by differentiation with respect to the x axis coordinate yields dsT(x,t)/dx =
(-8xlaEp/anw2pCp) exp[-2(x2
+ y2)/w?] / w t 2 (6)
where w: = w2(1 + 2t/t,). The intensity-weighted angle along the x axis is ($(x)) = l/n(dn/dT)~S~S_~x[d6T(x,t)/dxl
exp[-2(x - xo)2 + y2/w,2] dxdy (7) Integration yields the analytical expression ( d x ) ) = (dn/dT)p(-8laEP/anpCp) (1 2t/t,)x0 exp[-2x02/(w? w,2)]/(w?
+
+
+ wp2)2 (8)
where ( 4 ( x ) ) is the probe laser intensity-weighted deflection angle or centroid shift along the x coordinate. Since the maximum temperature gradient occurs at zero time, the optimum beam offset, obtained by setting the derivative equal to zero, is xo2 = (w2 w,2)/4. Using this in the above expression and comparing this to the maximum deflection angle yields the ratio
+
where the important temperature gradient is that perpendicular to the path, ds, and (dn/dT)p is the isobaric temperature-dependent RI change. Using eq 1 in (2) results in d r , t ) = -(dn/dT)p(81aE,/rrnw4pCp)r exp[-2r2/w2(1 + 2t/tc)l/(l + 2t/tc)2 (3) where n is the RI of the unperturbed media, and it was assumed that the ray does not deviate significantly and so the
(d(x))ma/d-
= w3/(w2+ ~ p 2 ) ~ ’ ~
(9)
It is most important to note that the smaller the beam waist of the probe laser, the greater the apparent deflection signal. This is due to the fact that the smaller probe beam waist will monitor a volume with a greater RI gradient. Also, the finite probe beam waist radius will affect the apparent decay time constant.
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
B. Angle Sensitivity of the Etalon. In the theory describing the analyzer etalon, the transmitted intensity is given as (8)
Table I. Maximum Angular Sensitivities of the Solid Analyzer Etalon"
Zt/Io = (1- RI2/[(1 - R ) 2 + 4R sin2 ( 6 / 2 ) ] (10) where Io and I, are the incident and transmitted intensities, R is the reflectivity of the two mirror surfaces, and 6 is given by
6 = ( 4 r d / X ) ( n 2- sin2 ( ~ ) l / ~= (4rnd/X) cos p (11) where d is the distance between the two mirrors of the etalon, X is the wavelength of the incident ray, n is the internal RI, a is the external incidence angle relative to the surface normal, and @ is the internal angle. The internal and external angles are related by Snell's law and are equal for air spaced etalons. There are several angles that meet the maximum transmission criterion that sin2 ( 6 / 2 ) be zero. By combination of the above equations, it is easy to show that maximum transmission occurs when
mX = (2nd) cos2 p
(12)
where m is a positive integer and 1 / ( 2 n d )is the free spectral range in wavenumber. When the internal angle is near that required for maximum transmission, then sin2 ( 6 / 2 ) = (6/2 - r n ~and ) ~ equation 10 can be written as
I,/IO = 1 / [ 1
+ @(2n~!/X)~(COS p' - COS @)2]
(14)
and 0' is defined by p' = @ - e', e' being a small angular deviation. Using the cosine difference relationship
cos p' - cos
= -2 sin [(p'
+ @ ) / 2 ]sin [(p' - p ) / 2 ]
(15)
+
with p' @ = 2@and sin [(p' - @)/2]= -&/2 for small e' results in the transmission
IJI,, =
r2/(r2+ e'2)
(16)
where we have defined
r-l = F(2nd) sin @ / A
(17)
for simplicity. The latter equation is that of a Lorentzian with a half-width angle of r. Finally, the sensitivity of the solid etalon to a change in external angle is found by first noting that from Snell's law for small angles (Y 2: n@, and then taking the absolute value of the derivative of the transmitted intensity with respect to the small angular deviation. ld(It/Io)/del = 2 n 2 a 2 / [ r 2+ n2e2l2
2.0
5 10
0.595 1.19 3.57
30 60 100
7.14
11.9
10.0
1.80 3.59 10.8 21.5 35.9
2.98 5.95 17.8 35.7 59.5
2.45 4.91 14.7
29.4 49.1
4
"All sensitivity values are in mrad-'. Calculations assume a fused silica (n = 1.457) analyzer etalon with free spectral range of 0.25 cm-'' for a He:Ne laser (632.8 nm).
d
EM
4'
0 He-Ne
(13)
where @ is that required for maximum transmission, F is the reflectivity finesse defined by
F = r(R)'/'/(l - R)
1
finesse
fringe no. angle, mrad 2 3 6.0 8.2
(18)
where e represents the external incidence angle of a solid etalon. The condition for maximum angular sensitivity is found by setting the second derivative of the transmitted intensity equal to zero. This results in the relationship -e = 3-ll2(r/n). Hence ~d(It/Io)/de~max = 33lI2n/8r = 0.65n2F(2d/X)sin p (19) Clearly, maximum angular sensitivity increases with finesse and with the incidence angle of the probe laser beam. Solid analyzer etalons are usually made out of fused silica with an RI of 1.457 at 632.8 nm, having a free spectral range of 0.25 cm-l, a finesse from about 10 to 60 for a nominally flat mirror surface reflectivity of 0.95, and a thickness of 1.37 cm. For
Figure 1. Experimental diagram of the apparatus used in this study.
this device, the first fringe for 632.8-nm light occurs a t m = 63 087. The value of m decreases for angles greater than zero. Table I shows maximum angular sensitivities for typical analyzer etalons as specified above. It is assumed that there is no loss in finesse with incidence angle in making these calculations. This assumption is valid when the area of the incident beam is large relative to the displacement of the reflected beam (8).
EXPERIMENTAL SECTION The experimental apparatus is similar to that which we have used in previous pulsed laser PDS experiments (11). A diagram of the photothermal deflection spectrometer used in this study is shown in Figure 1. The excitation source was a TEACOPlaser that was housed in a shielded room in order to protect the signal processing electronics from the radio frequency interference that the laser emits. It produced a maximum energy of about 10 mJ per pulse. The pulse repetition rate was 3.75 Hz, and the laser was equipped with an intracavity iris to promote T E h operation. The laser had a hemispherical optical resonator with a plane diffraction grating and a concave Ge output coupler. The beam quality, inspected by using a graphite paddle, was found to be nearly Gaussian though not reproducible from pulse to pulse. The laser pulse was about 170 ns (full width at half-maximum(fwhm)) in duration with a t a i llasting a few microseconds. The COzlaser energy was measured with a Laser Precision Model RjP-735 interfaced to the DEC PDP 11/23 laboratory computer with a 12-bit analog to digital converter. The pulse to pulse energy fluctuations for this laser were large, typically &15%. The COz laser wavelength was determined with an Optical Engineering Model 16-A spectrum analyzer. The P(32) line of the 10.6-pm transition at 933 cm-' was used in these experiments. The infrared laser beam was collimated about 4 m from the output coupler. It passed through a conventional Venician blind style infrared spectrophotometer attenuator located 1focal length in front of the first lens. Prior to this lens, beam steering was performed by reflection off of a silicon mirror (MI). Lenses L1 and L2 are BaF, with focal lengths of 30.5 and 7.62 cm, respectively. The beam was first focused by a BaFz lens with a focal length of 30.5 cm (LJ. The focus passed through a -1-mm-
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
diameter copper substrate pinhole, and the diverging beam was focused again by a 7.62-em-focal-length BaFz lens (LJ. Light in high-order TEM modes of the laser beam, which includes those due to the periodic aperture of the infrared attenuator, are distributed off-axis at the focus, and thus do not pass through the pinhole. The only transmitted beam in a Gaussian, T E h profiie (12). A single-frequency Coherent Model 200 He:Ne laser (632.8 nm) is used to probe the resulting RI gradient. The probe beam is focused by a 17.5-cm-focal-lengthlens (L,) and is combined with the infrared laser at the Ge flat through which roughly half of the infrared energy is transmitted. Both the pump laser beam and the probe beam are focused at the same position in the sample cell through the NaCl window of the cell. The stainless steel sample cell was centered at the focus of both L3 and the combination set of L1 and Lz. This sample cell is 7 cm long and 4 cm diameter. The deflected He:Ne laser beam was focused into the etalon by a 25-cm-focal-length lens (L,) placed 34 cm past the sample cell. A Quanta-Ray Model FPA-1 solid analyzer etalon was removed from the housing and mounted in a Newport Research Corporation (NRC) Model MM2A mirror/beamsplitter mount. This 2.5-cm-diameter etalon was made of fused silica and had a finesse of about 10 and free spectral range of 0.25 cm-'. The angle of incidence between the probe laser beam and the etalon was adjusted by using the fine pitched mirror/beamsplitter mount tilt controls. All optical components with the exception of the C 0 2 laser were mounted on a 4 ft X 6 f t Modern Optics optical table. The requirements for optical mounting components are rigid in this experiment due to the extreme sensitivity of the etalon to beam angle. One-inch-diameter mounting rods (NRC Model 40) were used where possible to reduce acoustic frequency vibrations and low-frequency tilt of the reflective optical elements. Halfinch-diameter posts (NRC Models SP and VPH) were used to hold lenses, since their placement and motion is not as critical. Two special 3-point mounts were used to hold the He:Ne laser since thermal gradients can cause the laser frequency to drift. The optical system was easy to align by adjusting the tilt of the Si mirror used to direct the C02laser beam, the pinhole used for spatial filtering of this beam, and the Ge beamsplitter used to combine the paths of the two lasers. Deflection of the He:Ne laser beam was measured as an intensity change past the etalon with a United Detector Technology Model 10-DP photovoltaic detector. A laser line interference fiter was used to filter out stray optical radiation. The detector signal was buffered with a LF-547 operational inverter amplifier with a gain of 10 and was further amplified with a Tektronix Model AM-502 before passing into a Data Precision Model 523 10-bit transient waveform recorder. The waveform recorder was connected to the laboratory computer by a parallel interface for rapid data-transfer rates. A series of pulse delay generators were used to control the trigger timing to the C02 laser, the analog to digital converter used to sample the laser pulse energy signal, and the transient waveform recorder. Both ensemble averaging and a pulse by pulse signal method using empirically derived matched filter smoothing were utilized to collect the data (11-13). The reagent gases used were dichlorodifluoromethane (CFC-12), >99.98%, from PCR, and argon, >99.998%, from Matheson Gas. Both were used without further purification. Sensitivity measurements were performed with an analyzed standard of 9.9 ppm (v/v) CFC-12 in argon from Matheson Gas. Gas transfers to the sample cell were performed in a stainless steel submanifold attached to a high-vacuum gas manifold equipped with a Sargent-Welch Model 3134 turbomolecular pump. Pressures at the cell were measured with an MKS Model 220B capacitance manometer (0-15 P a ) and a Televac Model 1D solid state diaphragm pressure transducer (0-105 Wa). High-vacuum-manifold pressure measurements were performed with an ionization gauge. The sample cell was allowed to degas at -1 mPa for a 12-h period prior to the introduction of the analyzed gas mixture.
RESULTS AND DISCUSSION The probe laser beam optics were especially designed to take advantage of the angular sensitivity of the etalon. A small probe focus spot size, w = 28 pm, relative to that of the pump
2677
laser, w 0 200 pm, was used. As indicated by eq 9, this results in a deflection magnitude of about 60% of the maximum theoretically possible. The reason for being able to use this small probe laser beam waist was that the etalon is an angle-sensitive device, not a position sensor. The probe beam was refocused into the etalon by placing a lens past the sample cell. This lens did not result in a significant degradation of the signal since the deflection angle is maintained in the focusing process. Refocusing did, however, allow the use of a high-finesse etalon, i.e., one with a high number of internal reflections. Since the probe beam was focused into the etalon, the beam waist did not change significantly over the effective propagation length due to the multiple internal reflections inside the etalon. As a consequence, the probe beam was effectively a plan wave and the angular sensitivity was subsequently maximized. Without this focusing, the probe beam would be diverging throughout the course of the internal reflection process and the fringes would not be as sharp. Because of the high angular sensitivity of the analyzer etalon used in these experiments, it was not possible to measure the angular sensitivity of a fringe with any degree of accuracy. The fringes could be counted by observing either the reflection or transmission of the incident probe laser as the angle of the etalon was adjusted. For most experiments, the etalon was tilted to transmit the third fringe. Subsequent minor adjustments to the tilt angle were made by observing the PDS signal. Both the etalon tilt and the probe laser relative pump laser beam offset were adjusted to result in a maximum change in probe laser intensity past the etalon as detected with the photodiode. The theoretical advantage of the current etalon angle detection scheme over that of either a razor edge or a bi-cell detector can be calculated. Both of the latter detection schemes are probe laser beam position sensitive, and as such, the voltage responses are directly proportional to the probe laser beam waist a t the edge or detector ( I ) . The integrated probe laser beam intensity past the razor placed so as to block half of the beam profile is
and since for small deflection angles the beam position offset, dx,is linearly dependent on detector distance from the sample cell, dx = z d@,( I ) d(It/Io)/d@ = (2?r~u~)-'/~
(21)
Using the far field beam waist radius of w = z X / ( r w o ) , one obtains the angular sensitivity of this detection scheme independent of detector to sample cell distance.
When the parameters for the probe laser beam used in these experiments are employed, the angular sensitivity of the more conventional PDS detection schemes is 0.055 mrad-l. Comparing this to the angular sensitivity value from Table I corresponding to the etalon used in these experiments, i.e. a finesse of 10 at fringe 3, one can see that the current etalon detedion scheme is about 2 orders of magnitude more sensitive than previous experimental schemes. Experimental verification of this gain is discussed below. Electronic low-frequency roll-off was required in order to reduce the noise in most of the experiments we performed. This low-frequency noise was found to be due to vibrations in the optical elements and to sound and bulk air motion in the laboratory. The sensitivity to bulk air motion from the ventilation system was so severe that the signal could not be kept within the input limits of the transient waveform recorder when DC coupling was utilized. Experiments for the decay
2678
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
:
.0 .0
.2
. 4
.6
1.0
T I M E (MSEC)
Flgure 2. Ensembleaveraged transient deflection signal. This data is of a 9.9 ppm (vh) standard sample of CFC-12 in argon being excited with a -2-mJ focused laser pulse at 933 cm-'. A total of 5000 transients were averaged to obtain this data.
time constant had to be performed late at night when the laboratory temperature was stable enough that the air conditioner could be turned off, thus eliminating the major source of noise. Attempts to perform similar procedures during the day resulted in a steady increase in the room temperature, which in turn caused thermal expansion of the solid etalon. Without an oven for the etalon, the long-term stability under these conditions was only about 5 min. The environmental factors place severe requirements on the optical apparatus as well. In future experiments, we plan to use active feedback stabilization of the etalon angle. Figure 2 illustrates a typical ensemble-averaged signal transient observed in these experiments. This is an average of 4000 signal transients produced by exciting 9.9 ppm (v/v) CFC-12 in argon at about 100 kPa of total pressure and with an average pulsed infrared laser energy of -2 mJ. The C02 pump laser was tuned to operate on the P(32) line of the 10.6-pm transition at 933 cm-', which overlaps well with the R branch of the strong CC12asymmetric stretch band centered at 923 cm-' (14). The exponential absorption coefficient at this particular frequency measured at 1atm of total pressure and with use of a C02 laser has been found to be 0.035 Pa-' (15). The absorbance of this sample is 0.0028 AU for the 8-cm path length of the gas cell. However, the effective path length (16), i.e. the length over which the photothermal perturbation was monitored by the probe laser, is only about 2 Rayleigh parameters of the pump laser beam or about 1cm. This corresponds to an effective absorbance of 0.000 35 AU. The apparent rise time of this transient signal was limited by that of the photodiode and processing electronics while the gross signal decay time is due to both the thermal diffusion time constant and the 100-Hz low-frequency 3-dB roll-off of the Tektronix AM502 amplifier. Although the signal decay time is significantly shorter than that equivalent to the roll-off, we have found that this roll-off does affect the apparent decay time constant, making it appear somewhat shorter than without the low-frequency roll-off. The characteristic thermal time constant, t , = w 2 / 4 K ,where w is the pump laser electric field beam waist radius and K is the thermal diffusion coefficient, was determined from similar experiments. By measurement of the time required for the signal to reach one-half of the maximum value, and with use of the relationship discussed after eq 9 in the theory section, the characteristic decay time constant for these experiments was found to be 6.02 ms. When the thermal diffusion coefficient for argon is used, this time corresponds to an effective minimum pump laser beam waist radius of 664 pm. This calculated beam waist radius is in fair, i.e. a factor of -4, agreement with the measured
.OO
h-
?0
.I5
ll0
115
210
215
LASER PULSE ENERGY
3l0
315
410
(mJ)
Figure 3. Scatter plot illustrating the energy dependence of the transient signal average. Matched filtering was used to estimate the signal magnitude. The nonlinear energy dependence of the signal is due to both nonlinear excitation behavior of the 9.9 ppm (vh) CFC-12 in argon and the response of the etalon deflection angle detection scheme.
value. However, the characteristic thermal decay time constant is not strictly related to the minimum pump beam waist radius under these conditions, since the beam waist is not constant through the cell length (16). Since the probe laser passes along the axis of the converging/diverging COz laser beam, the apparent average pump laser beam waist will be larger than the minimum. The small, short time aberrations observed at periodic intervals after the signal onset are due to the photoacoustic pressure wave generated by the rapid expansion of the gas that occurs upon analyte excitation with the short pulse duration pump laser (17). The periodic repetition of this acoustic perturbation is due to the acoustic wave being reflected off the cylindrical cell walls. The wave is thus periodically refocused into the center of the cell where the probe laser detects the density variation due to the pressure increase. Later experiments performed with a modified gas cell in which two side arms effectively broke the cylindrical symmetry of the cell did not exhibit the well-defined acoustic wave perturbations to the signal (18). In Figure 3 we illustrate the pump laser energy dependence of the PDS signal. Each point in this scatter plot represents one pulse of the pump laser. This data was obtained over 1024 pulses where the average pump laser energy was varied with an attenuator that did not cause changes in beam profile or direction of propagation (12). An empirically derived matched filter was used to estimate the peak to peak magnitude of each signal transient (13, 19, 20). This filter has been shown to be the best possible filter, effectively admitting only those phase and frequency components known to be contained in the expected signal (20). The filter outputs the magnitude of the impulse response signal that is the optimum estimate of the peak signal potential in volts (19). The nonlinearity of the energy-dependent data is due to the combined effects of optical saturation and multiphoton transitions at the higher excitation pulse energies (11)and the nonlinearity of the etalon angular response. The data represented by the scatter plot obtained with the etalon apparatus compares favorably to that which we have previously obtained by using a more conventional PDS apparatus that utilizes a sharp edge to aperture the probe laser beam (11). Since this type of data can be analyzed in terms of the signal and noise components of the measurement series, it can be used to determine the analytical merit of a particular technique. To accomplish this, the data of Figure 3 was analyzed by using the fourth degree polynomial regression
ANALYTICAL CHEMISTRY, VOL. 60, NO. 24, DECEMBER 15, 1988
routine as described in ref 9. The average signal variance over this range was found to be 1.4 X lP V, and the signal to noise ratio (SNR), defined here as the ratio of the average signal at 1mJ of excitation energy to the average standard deviation, is 42.2 for this data. This corresponds to a single pulse limit of detection (SNR = 3) of 0.7 ppm (v/v) or about lo4 AU over the 8-cm-path-lengthcell for a 1-mJ laser pulse. In accordance with eq 4, lower detection limits obtained with greater pulse energies are possible. But nonlinear effects, in particular optical saturation of the absorption and dielectric breakdown, will ultimately limit the sensitivity (21). By comparison, in analyzing the data of Figure 3 of ref 9 by using the same techniques, we find a single-pulse LOD of 26.3 ppm (v/v) for 1-mJ excitation of CFC-12 using the more conventional PDS detection scheme. Thus the experimental advantage of -40 falls short of the 2 orders of magnitude predicted from the detection scheme theory discussed above. The reason for this is probably due to the increased environmental noise affecting the etalon detection apparatus. Of course, much lower detection limits can be obtained in both cases if ensemble averaging or multiple-pulse matched filter averaging is used, as Figure 2 illustrates. The real limit of detection will be controlled by the variance of the blank, not that of the sample. Nonetheless, this single-shot detection limit is an important figure of merit of the apparatus, as it characterizes the detection limits under conditions where sampling time is scarce.
CONCLUSION In summary, we find the etalon to be a useful device for photothermal deflection angle detections of very low absorbance samples. The etalon detector based spectrometer used in these experiments is among the most sensitive absorbance detectors to date. However, the current apparatus has a rather limited dynamic range of angles that can be linearly processed, limited to about one-fourth of an angular fringe width. Because of the limited dynamic range, this technique is currently most suited for gas-phase analysis where the matrix gas has no absorption, and where the analyte is present in trace quantities. This technique may not be useful for high-absorbance samples with the present implementation, since large deflection angles will cause the several fringes to come into constructive interference over the course of a signal transient. These high-absorbance sample signals appear to be a series of etalon transmission spikes instead of the characteristic
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impulse-response curve. Nonetheless, it is much easier to decrease sensitivity than to increase it. The linear range can be increased by decreasing the sensitivity. Perhaps the easiest way to do this is to attenuate tlie>excitationlaser pulse energy. Since the means by which to attenuate the high-intensity laser without causing beam wander is currently possible, this is a reasonable option. Finally, the etalon PDS detector, as with all sensitive angle detection schemes, is very sensitive to environmental factors. With the apparatus discussed above, these environmental factors ultimately limit the utility of this technique. These factors will either have to be controlled or the optical apparatus will have to incorporate active compensation for changes in temperature, air currents, and the like. We feel that active compensation will be the better method in the long run because precise temperature control of all of optical mounts and elements would be next to impossible and the elimination of the environmental artifacts will not lead to the development of an instrument of general utility.
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RECEIVED for review July 15,1988. Accepted September 12, 1988. This work was supported by CHE-8520050 awarded by the National Science Foundation.
