Anal. Chem. 1986, 58,80-86
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elucidate the competitive nature of these reactions.
CONCLUSIONS NIMS has been shown to be a simple, rapid, and sensitive technique for detection of certain individual inorganic stack gases. While peak shape and resolution are suitable for use of NIMS in monitoring emission gases as complex mixtures, sensitivity will be limited by equilibrium chemistry, which is the basis for formation of product ions from analyte. With a known gaseous matrix, NIMS response may be calibrated and understood on the basis of electron attachment mechanisms. However the present radioactive-based source will be sensitive to matrix composition and will preclude use of NIMS as a general sensor. LITERATURE CITED (1) (2) (3) (4) (5) (6) (7)
(8) (9)
(10) (11) (12)
Ramasamy, S. M.; Monola, H. A. Anal. Chem. 1982, 5 4 , 283. Hayakawa, S.; Sekido, S. Anal. Chem. Symp. Ser. 1983, 77,3. Wang, C.; Zhou, E. Anal. Chem. Symp. Ser. 1983, 77,7. Kley, D.; McFarland, M. Afmos. Techno/. 1980, 72, 63. Reid, J.; El-Sherlblnu, M.; Garslde, B. K.; Balllk, E. A. Appl. Opt. 1980, 19, 3349. Kato. M.; Yamada, M.; Suzuki, S. Anal. Chem. 1984, 56,2529. Carr, J. W. Anal. Chem. 1979, 5 1 , 705. Spangler, G. E.; Collins, C. I. Anal. Chem. 1975, 4 7 , 393. Dam, R. J. I n "Plasma Chromatography"; Carr, T. W., Ed.; Plenum Press: New York, 1984 pp 177-213. Karasek, F. W. Inf. J. Environ. Anal. Chem. 1972, 2 , 157. Spangler, G. E.; Lawless, P. A. Anal. Chem. 1978, 5 0 , 290. Eiceman, G. A.; Leasure, C. S.; Vandiver, V. J.; Rlco, G. Anal. Chlm. Acta, In press.
(13) Rlco, G.; Vandiver, V. J.; Leasure, C. S.; Elceman, G. A. Anal. Insfrum. 1985. 13. 289. (14) Karasek, F. W. Anal. Chem. 1971, 4 3 , 1982. (15) Karasek, F. W.; Tatone, 0. S. Anal. Chem. 1972, 4 4 , 1758. (16) Karasek, F. W.; Tatone, 0. S.; Kane, D. M. Anal. Chem. 1973, 4 5 , 1210. (17) Benoit, F. M. Anal. Chem. 1983, 55,2097. (18) Azria, R.; Tronc, M.; Goursaud, S. J. Chem. Phys. 1972, 56, 4234. (19) Karasek, F. W.; Kane, D. M. J . Chromafogr. 1974, 9 3 , 129. (20) Spangler, G. E.; Lawless, P. A. Anal. Chem. 1978, 50,884. (21) Wernlund, R. F.;Cohen, M. J.; Kindel, R. C., Proceedings of New Concepts Symposium and Workshop on Detection and Identification of Explosives, US. Departments of Treasury, Energy, Justice, and Transportation, Reston, VA, October 31, 1978, p 185. (22) Leasure, C. S.; Eiceman, G. A. Anal. Chem. 1985, 57, 1890. (23) Spangler, G. E.; Cohen, M. J. I n "Plasma Chromatography"; Carr, T. W., Ed.; Plenum Press: New York, 1984; pp 23-24. (24) Vandiver, V. J.; Leasure, C. S.; Elceman, G. A. Int. J. Mass Specfrom. Ion Processes 1985, 66, 223. (25) Karasek, F. W.; Spangler, G. E. I n "Electron Capture"; Ztatkis, A,, Poole C. F., Eds.; 1981; p 384. (26) Janbusec, B. K., Brauman, J. I.I n "Gas Phase Ion Chemistry"; Bower, M. T., Ed.; Academlc Press: New York, 1979; Vol. 2, pp 53-86. (27) Streitwelsh, A.; Heathcock, C. H. "Introduction to Organlc Chemistry"; McMillan: New York, 1976, pp 1184-1187. (28) Table of Selected Values of Chemical Thermodynamic Properties "Handbook of Chemistry and Physics"; CRC Press: Boca Ratan, FL, 1984. (29) Bartmess, J. E.; McIver, R. T., Jr. I n "Gas Phase Ion Chemistry"; Bowers, M. T., Ed.; Academlc Press: New York, 1979; Vol. 2, pp 87-1 21.
RECEIVED for review June 21, 1985. Accepted September 4, 1985.
Error Reduction in Pulsed Laser Photothermal Deflection Spectrometry George R. Long and Stephen E. Bialkowski* Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322
Pulsed lasers are characterlzed by poor pulse-to-pulse energy and mode stabiilty thereby llmltlng their use In experlments sensitive to spatial variations. I n this paper we present both experimental and computational methods of reduclng the errors assoclated with mode and pointing instablllty In photothermal defiectlon experlments where a pulsed laser Is employed. By use of these methods, a substantlal reduction In the slgnal varlance can be realized. These methods give the pulsed laser experlments a precision approaching, and In some cases exceedlng, that of contlnuous wave laser techniques.
Photothermal spectrophotometry has been shown to be a very sensitive method for the analysis of species that undergo radiationless relaxation from an optically excited state. There are actually several techniques used in photothermal spectrophotometry that are related by the fact that they all probe the refractive index profile created by the radiationless relaxation of the analyte (1-3). These techniques are all based on the effect that the refractive index profile, created by the radiationless relaxation mechanism, has on the propagation of a laser beam used to monitor this profile. The exact method of probing the refractive index profile differentiates among the techniques. For example, the gradient of the refractive index is monitored in photothermal deflection spectrophotometry (PDS) ( I , 4-7) and in moire deflectometry (8), and
the effect of the curvature is monitored in thermal lens spectrophotometry (2,9-13). These techniques all have about the same absorbance sensitivity when the effects due to the particular solvent system and excitation laser intensity are taken into account (I, 3 ) . However, it has been noted that although these collective techniques are classified as ultrasensitive, the precision of the measurements is generally poor owing to a wide variety of noise sources associated with the use of lasers (2, 4, 11-13), In this paper we examine the errors associated with the use of pulsed laser excitation sources in PDS. In PDS, a probe laser beam is deflected by the refractive index gradient induced in the sample by the excitation source. The magnitude of deflection is related to, among other things, the absorbance of the sample, the excitation laser energy, and the spatial region probed by the monitor laser (I). The latter relationship requires that the refractive index gradient in the sample be the same for excitation pulses of the same energy and that the spatial overlap between the excitation and monitor laser beams be known or at least reproducible. Maximum sensitivity is obtained when the excitation and monitor laser beams are focused into the sample cell making the photothermal techniques not only ideal for microprobe analysis but also highly susceptible to errors associated with spatial noise. Most pulsed lasers have poor longitudinal and transverse (TEM) mode stability, and their pointing noise characteristics are generally poorer than continuous wave (CW) lasers ( 2 ) . Both TEM instability and pointing noise result in a spatial
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intensity distribution at the sample cell that is not able to be reproduced on a pulse-by-pulse basis. Since the refractive index profile in the sample is related to the intensity profile of the excitation laser, these instabilities can introduce significant errors into the PDS signal. The result is a reduced precision due to increased correlation between the measured laser pulse energy and the resulting photothermal signal. Pulsed lasers also have poor pulse-to-pulse energy variances, with output energies typically f10% of the mean energy for any given pulse. When pulsed laser sources are utilized it is perhaps better to examine the correlation between the laser energy and the signal by the use of regression techniques. Even though there are difficulties associated with the use of pulsed lasers in photothermal spectrophotometry, there are reasons that compel us to overcome these difficulties. Pulsed infrared laser photothermal spectrometry is ideal for the analysis of many classes of analytes under a variety of conditions. Some advantages are the following (4, 11-13): (1) Most polyatomic species have vibrational absorption spectra that have finite absorbance within the tuning range of the pulsed infrared gas lasers currently available. Very few of these same species can be excited by using visible and ultraviolet laser sources since the absorption of the latter radiation is limited to those species that have one or more chromophoric groups. Further, energy relaxation quenching of infrared excited species is more probable than fluorescence at moderate gas pressures owing to the long fluorescence lifetimes and efficient quenching mechanisms. (2) The tunability of pulsed gas infrared lasers allows for spectral discrimination of samples that have several species present. The wavelenth range over which molecular infrared lasers may be tuned is less than that of visible dye lasers and the spectral coverage of the molecular lasers is restricted to discrete lines. However, absorption line widths in the infrared region are typically much narrower than those in the visible region for gas-phase samples. (3) Rise times of the analytical signal are very much faster than that of the related CW laser excitation technique. For gas-phase analyks at standard conditions, this time is typically on the order of nanoseconds, while rise times for CW laser excited signals are on the order of milliseconds, with the maximum analytical signal not being obtained for several tens or even hundreds of milliseconds. The rapid rise times of the analytical signal has important implications. Pulsed photothermal signals will not be degraded by flowing samples as long as the rise time of the signal is less than any gas dynamic times (14-16). In this work, a pulsed infrared COz laser is used to excite PDS signals in gas-phase analytes. Characteristics of the lasers, the optical apparatus, and the data processing procedures are analyzed in terms of sensitivities and ultimate precision. The experimental optimization procedures and data processing methods presented in this paper are shown to effectively reduce the noise due to pulsed laser energy and mode variations. Further, the measurement precision is increased by rejection of data obtained from different parent distributions while modeling the energy response with nonlinear functions. The procedures and methods described here are generally applicable to experiments that are sensitive to spatial variances.
EXPERIMENTAL SECTION The optical arrangement for these experiments is similar to that described previously ( 4 ) . The apparatus is illustrated in Figure 1. Briefly, a pulsed transverse discharge excited atmospheric pressure (TEA) carbon dioxide laser was used as the excitation source, and a helium-neon (HeNe) laser was used to probe the resulting refractive index gradient. The C02laser was grating tunable. In most experiments an intracavity iris is used to promote TEM, operation in the COz laser (12). The energy of this laser was monitored at a germanium beam splitter using
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Flgure 1. Experimental apparatus. The TEA-CO, laser is constructed from a TEA gain section, an intracavity aperture (A), a grating tuning element (G), and an output coupler (OC). The output is spatially filtered with lenses L1 and L2 and a plnhole (PH). The spatially filtered beam is focused with lens L3, through a beamspliier (BS), into the cell. The reflected portion is monitored wRh an energy monitor (EM). The HeNe monitor laser is imaged with lens L4 in the cell and the beam deflection is monitored with the detector PSD.
a Laser Precision Model RjP735 gain progammable energy monitor. Approximately 50% of the excitation laser energy was reflected into the energy monitor by the beam splitter. The germanium beam splitter was also used to mix the excitation and probe lasers in a collinear fashion. Excitation laser wavelengths were determined with an Optical Engineering Model 16A spectrum analyzer. The COz laser pulse was about 170 ns fwhm. The major difference between these experiments and those previously described is that spatial filtering of the excitation laser was used. Spatial filtering was performed by focusing the COz beam through a 1 mm diameter pinhole using a 50.8-cm focallength BaFzlens. Two additional BaFz lenses with focal lengths of 30.5 cm and 12.7 cm were placed after the pinhole to give the entire optical arrangement an effective focal length of 17.8 cm. The probe laser was a Uniphase Model 1105p laser operating at 632.8 nm. The probe laser was imaged at the focal plane of the COzlaser beam in the sample cell using a 50-cm focal-length fused silica lens placed at a distance of 1 m from both the probe laser and the sample cell. Thus, the probe laser was at the back focal plane of the lens, and the sample cell was at the front focal plane. The minimum beam waist of the probe laser was located about 20 cm in front of the beam focus of the COzlaser. The excitation laser was focused at the center of the 7-cm gas sample cell fitted with sodium chloride windows. All optical components with the exception of the C02 laser were mounted on a 4 X 6 ft Modern Optics optical table with pneumatic vibration isolation legs. Deflection of the HeNe laser beam was measured with either a United Detector Technology Model LSC-5D lateral detector or a Model SPOT-2D bicell detector, both of which are position-sensing detectors (PSD). The lateral detector was placed as far from the gas sample cell as possible. This distance was limited by the spot size of the probe laser at the detector since the spot size must be less than or equal to the minimum dimension of this detector. The bicell detector was operated by placing a 50-cm focal-length lens 50 cm from the sample cell. This lens focused the probe laser at a distance of approximately 65 cm past the lens, and the bicell detector was placed at this position. Thus, the lateral displacement of the deflected probe laser beam at 50 cm was retained while focusing the probe laser beam waist. This increases the detector sensitivity since the response of the bicell is inversely proportional to the radius of the probe laser spot. Output from these PSD’s was amplified by using a United Detector Technology Model 301B-ACsum/difference amplifier and subsequently processed with an Analog Devices Model 436 operational divider. The difference output of the 301B-AC amplifier was divided by the sum output with the 436 operational divider resulting in an electronic signal proportionalto the position of the probe laser spot on the detector. A Datel-Intersil, Inc., Model FLT-U2 active filter was utilized as a tunable high-pass filter in some of the experiments. This filter was usually tuned
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to reject signal frequency components below 1 kHz. PDS signals produced by the detector-amplifier arrangement were collected with a Physical Data Corporation Model 522-A, 20-MHz transient digitizer, interfaced to a DEC LSI 11/23 microproceasor. A psuedo-gated sampling routine was used to process the transient digitizer data. The excitation laser energy signal was sampled with an ADAC Corporation Model 1012,16-channel, 12-bitprogrammablegain analog-to-digital(A/D) converter. This converter has a 50-11s sampling aperture time, while the output from the RjP735 energy monitor was a pulse of several milliseconds duration. The repetition rate of the experimentalapparatus was 3.75 Hz. This repetition rate was derived from, and was synchronousto, the 60-Hz ac line. Trigger timing for the transient digitizer, excitation laser, and A/D converter was controlled by a series of digital time-delay modules with delay precisions of 5 ns. The data collection method allowed the simultaneous collection of signal and excitation laser energy data for each pulse of the C02laser. Analysis of this data was then performed in a fashion similar to that described by Jones et al. (17). Reagent gases used in this study were dichlorodifluoromethane (FC-12)>99.9% and chlorotrifluoroethane>99%, both from PCR, sulfur dioxide >99.98%, and argon >99.998% from Matheson. Gas transfers to the sample cell were performed in a stainless-steel UHV gas manifold. Pressures in the cell were probed with an MKS capacitance manometer. An oil diffusion pump was used to evacuate the sample cell and transfer manifold between gas sample fillings.
RESULTS AND DISCUSSION It was stated in the introduction that the use of pulsed infrared lasers has several advantages when utilized in photothermal spectrophotometric analysis. However, some of these advantages can only be realized if the measurement is sufficiently precise. In earlier studies we examined some of the determinant errors in pulsed infrared laser photothermal spectrometries (4,11). Saturation conditions yield improved precision and increased sensitivity. However, the saturation intensity is variable and unpredictable for any one analyte. Therefore, the wavelength-dependent saturation intensity can be a useful diagnostic, but only if precision measurements can be made under both linear and saturation conditions. As a starting point for the reduction of the signal measurement errors, we first examine the sources and magnitudes of the instrumental errors associated with the apparatus. When reduction of the determinant errors results in signal variance on the order of the instrumental error, the error reduction task will be complete. The sources of variance can be grouped into two main categories. The first category is that of the instrumental noise and is characterized by variance that is not dependent on the signal strength. This category includes shot noise from the PSD, noise associated with the analog electronic circuitry, digitization errors, vibrations in the optical components resulting in probe laser spot position variance at the PSD, and pointing noise of the probe laser. All of these sources result in signal variance even when the excitation laser is not operating and thus are considered here to be instrumental. Other than choice of components, there is little that can be done to decrease the instrumental noise level. The signal-to-noise figure of merit of the PDS data will, of course, be maximized when the optical arrangement is such as to maximize the PDS signal. At the same time, the sensitivity of the background signal to vibrations and probe laser pointing noise is also dependent on the particular optical arrangement. For example, by assuming that the pointing noise origin is in the laser itself, minimum background signal variance due to probe laser pointing noise may be realized when the probe laser itself is imaged at the PSD plane with long focal length optics. But in doing so, the PDS signal magnitude can decrease, and the proportional errors resulting from the same pointing noise may increase. Experiments were conducted to determine the total root mean square instrumental noise and the frequency distribution
of this noise. Frequency distributions were obtained from the power spectrum of Fourier transforms taken of several single transient digitizer recordings (18,19). The composite noise spectrum was found to be flat from 100 Hz up to about 100 kHz. The high frequency roll off of this noise spectrum, starting at about 100 kHz and rolling off a t about 3 dB/ decade, was due to the operational amplifiers used to process the PSD signal. Below 100 Hz, there was a large increase in noise power, most probably due to line interference and flicker noise sources. The low-frequency components of the noise power spectrum are shown in Figure 2A. Flicker noise was most predominant below 50 Hz, and line interference peaks at 60 Hz and harmonics were often observed. Sources of this low-frequency flicker noise are most likely due to vibrations and pointing noise of the probe laser. Identification of these noise sources was confirmed by rapping the optical table to induce vibrations and by “cold start” cycling of the HeNe laser to induce pointing noise. The utility of the active filter can be seen at this point in parts C and D of Figure 2. The active filter rejected frequencies below 1 kHz, and thus the flicker noise did not significantly contribute to the total noise when this filter was used. Subsequently, instrumental noise contributions due to the pointing noise of the probe laser did not have to be minimized through optical element placement as discussed above, but rather they were rejected as flicker noise with the active filter. Use of the active filter also changed the signal response time as illustrated in parts B and D of Figure 2. Although the decay time was reduced by over an order of magnitude, the signal maximum was only slightly reduced when using the active filter. Finally, the total root mean square noise between 1 and 100 kHz was found to be about 5 mV when using the LSC-5D and 20 mV when using the SPOT detector.
It is difficult to specify the frequencies sampled by the psuedo-gated integration routine used to collect and process the data since this was a time-domain function (12). This data processing routine utilizes two gates of about 10-ps duration each. One gate samples the base line and the other the signal. The difference between the two gate values is the analytical signal. The time interval between the two gates was typically 100 ks, giving a Nyquist limiting frequency of 5 kHz. The power spectrum of this gated sampling function had a major band-pass component at this frequency (18). This component rolled off to 0 at 0 Hz. The integral of the sampling function power spectrum relative to that of a delta function indicated that the sampling function reduced the white noise contribution to the signal by approximately 90%. Since the experiment was synchronized to the 60-Hz line frequency, the line interference frequencies did not result in a variable signal error because the dc component of the sampling function power spectrum was zero. The second category of error-producing sources is that of source noise. These errors are characterized by a constant signal-to-noise figure of merit, giving rise to proportional errors. To understand the sources of proportional errors in these experiments, it was recognized that the signal is proportional to the deflection angle of the probe laser originating at the point where the focused excitation laser creates the refractive index profile. Any variation in the refractive index profile, as probed by the probe laser beam, will result in proportional errors. There are two ways in which these errors can be produced. The first is by variations in the spatial overlap between the probe and the focused excitation laser beams, and the second is by variations in the profile of this focused excitation beam. Pointing noise in both lasers will result in proportional errors associated with spatial beam overlap in the sample.
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Figure 2. Low-frequency instrumental noise power spectra and time-resolved signals obtained with the SPOT detector. The noise power without active filter is shown in A, and the tlme-resolved signal in 6 . Noise power and time-resolved signals with active filtering are shown in C and D, respectively. The noise power spectra were obtained without sample excitation, and the time-resolved signals are those obtained for 1000 sample averages of 320 ppbv CF,CI, In argon at 100 kPa. The excitation laser wavelength was 10.71.9 pm.
Proportional errors due to pointing noise in the probe laser may be minimized by optical design. Assuming that the source of the pointing noise vector is within the laser itself, proportional errors due to this pointing noise can be eliminated by imaging this laser in the plane of the excitation laser beam focus, that is, in the sample cell. The focus of the laser beam does not coincide with the image of the laser and in minimizing the proportional pointing errors, the PDS sensitivity is decreased. Nonetheless, these proportional errors are minimized, and the signal sensitivity is not significantly degraded by using long focal length optics to image the probe laser at the sample. Since the pointing noise contribution to the instrumental noise was mostly low frequency, a large improvement in the precision of the data was realized with this configuration. By far the greatest source of proportional errors in these experiments is due to the high level of variance in the beam quality of the TEA C 0 2 laser. Because of the inhomogeneous nature of the transverse discharge and the large cavity volume, transverse discharge molecular lasers are particularly notorious for their poor beam quality. There are four main optical varianres that are characteristic of these lasers, which will result in proportional errors if not treated properly. The first is the pulse-to-pulse energy variance. This variance can be accounted for by monitoring the pulse energy and subsequently modeling the energy-dependent deflection signal with a regression routine. In fact, this variance is useful since the saturation behavior of the particular analyte can only be elucidated if the laser energy is varied. A related variance is that due to longitudinal mode locking. The wide gain band width of TEA COz lasers results in several competing longi-
tudinal modes originating from the same excited state (20). As a consequence, the laser delivers a nonreproducible selfmode-locked pulse. Self-mode locking results in intensities that are not able to be related to integrated pulse energy without knowledge of the temporal behavior of the pulse. Thus PDS signals due to nonlinear absorption phenomena, such as multiphoton absorption, are not necessarily proportional to the integrated laser pulse energy. Saturation is in fact a nonlinear phenomenon that occurs in these experiments. However, the sensitivity of a PDS signal to energy, and therefore intensity variations, is decreased when saturation is occurring (4). Subsequently, self-mode locking should not result in significant proportional errors in these experiments. We have not attempted to control the mode-locking characteristics of the excitation laser used in these experiments. The two remaining types of optical variance are TEM fluctuations and pointing noise. These two sources result in a spatial variance of the energy profile in the sample cell. The PDS signal is very sensitive to these spatial variances. Some control over this sensitivity can be realized by optimization of the optics. Again, imaging of the laser at the plane of the sample cell will reduce some of these errors. However, the reduction of errors in this case does not outweigh the reduction in signal, and other methods of reducing these sources of error were sought. One method used to increase pulse-to-pulse TEM stability and reduce the pointing noise of the carbon dioxide laser was to employ an intracavity aperture. This reduces the “Q” of the laser cavity for higher order modes, effectively spoiling the non-TEMoomodes (20). In these experiments an intra-
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EXCITATION ENERGY (mJ) Figure 3. PDS signal vs. excitation energy data for several different iris diameters. Intracavity iris diameters were (A) 1.5 cm, (B) 1.1 cm, (C) 0.8 cm, and (D) 0.5 cm. The sample was 0.17 kPa sulfur dioxide in 13.2 kPa Ar. The R26 line of the 9.6-pm transition was used.
cavity iris was placed directly in front of the grating in the laser cavity. An adjustable iris was used so that the aperature diameter could be varied for optimum operation. There was a trade-off between the pulse energy and the TEM quality when the iris diameter was varied. The effect of the iris diameter on the PDS signal is shown in Figure 3. With the smaller iris diameters the correlation between the PDS signal and the excitation laser energy is significantly increased over that obtained with either no intracavity iris or a wide iris setting. This high correlation in turn allows precision modeling of the excitation laser pulse energy dependence of the PDS signal. It is interesting to note that the signals obtained with large iris diameters are less than would be expected from observing the energy dependence of the signal when small iris diameters are used. This is probably due to the fact that energy distributed in high-order transverse modes does not contribute proportionallyto the PDS signal. According to the theories of Fourier optics, a fraction of the total energy in the higher order modes at the input plane of the focusing element will result in an off-axis, non-Gaussian energy distribution at the focal plane (21). The energy in the non-Gaussian portion of the focused beam profile will result in an off-axis temperature increase that may not be sampled by the probe laser. Further, the off-axis temperature increase may decrease the signal by decreasing the gradient of the temperature profile. In either event, deviation from the Gaussian TEMooprofile a t the input plane of the focusing element will result in a smaller signal for a given energy, skewing the error distribution to the low signal side. Skewing of the excitation laser energy dependent PDS signal to low values can also be observed in Figure 4. In this figure, the COzlaser was operated with a small aperture, and the pulse energy at the sample cell was varied over a wide range by slowly bleeding an absorber gas out of an auxiliary infrared gas cell. Data that are of lower signal magnitude than the majority are probably not within a normal error distribution for TEh-produced signals. These abnormal data are all skewed to low values indicating that n o n - T E h pulses are still occurring, although not as often as without the aperature. Further reduction in errors due to the occurrence of higher order TEM pulses may have been possible by decreasing the intracavity iris diameter even more. However, further reduction in the iris diameter resulted in a large reduction in the COz laser pulse energy. Figure 4 also illustrates the effect that transition saturation can have on the excitation laser energy dependent PDS signal. The deviation from linearity a t the higher laser energies is due to saturation. To reduce data obtained with the intracavity iris, a non-
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EXCITATION ENERGY (mJ) Figure 4. PDS signal vs. excitation energy data for 20 Pa C2F,Ci in 13.2 kPa Ar using a 0.5 cm diameter iris. The P22 line of the 9.6-hm transition was used. The smooth curve is that of a quadratic model robust regression analysis.
linear model was used with a data reduction routine that was not sensitive to the type of error distribution exhibited by the data. In these experiments, the data were modeled by using a linear power series in laser energy with the robust regression algorithm (22,23). The power series was chosen because it effectively represents any energy dependence of the signal that may occur. A second-order power series was generally sufficient for accurate modeling when transition saturation was occurring, but higher order models were required on occasion. Robust regression analysis uses a weighting factor to account for nonsymmetric error distributions of the data (22). It also provides a good method for rejection of data that fall outside the range of a normal energy distribution. Data of which the residuals fall outside of a range related to the median residual of the entire data are given a zero weight and thus are rejected. This allows data of the type shown in Figure 4, that is those with a skewed error distribution, to be accurately modeled. When robust regression analysis was applied, it was found that the points that have a Tukey’s biweight (22,23) of zero were generally far below the calculated regression line. The rejected data exhibited low correlation and were most likely due to the effects of transverse mode noise in the excitation laser. Utilizing the intracavity iris and the robust regression data reduction routine provided increased precision by reducing the pointing noise and TEM variation contributions to the signal error and by rejecting data that fell outside of a normal error distribution. However, robust regression analysis generally requires a fair amount of computation time to find the “best fit” to the model because of its reiterative nature (22, 23). Modeling of data similar to that of Figure 4 required approximately 3 min using a FORTRAN coded routine running the laboratory microprocessor. Using a typical leastsquares data reduction routine with the same model required only a few seconds (24). There are two application of PDS currently being developed in this laboratory that require rapid data reduction. They are the application of PDS to selective >GCeffluent detection (11, 13) and spectral discrimination. Since the skewed data could not be modeled with a leastsquares routine, it was desirable to eliminate the non-TEMW modes so that this more rapid data reduction could be performed. To eliminate high-order TEM sample excitation, spatial filtering of the excitation laser beam was performed outside of the laser cavity. This was accomplished by focusing the excitation laser beam through a pinhole. The intensity profile
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of the laser spot at the focus is related to the Fourier transform of the intensity profile of the unfocused beam (21). Light intensity from the higher order modes of the laser beam will be distributed off-axis and will not pass through the pinhole. The transmitted beam can have a Gaussian, TEMm intensity profile. Spatial filtering also reduces the pointing noise by transmitting only a limited range of pointing vectors from a single noise source. In our apparatus, it was found that spatial filtering was only effective when the intracavity iris was also used. This was because the spatial filter was only partially effective in eliminating pointing noise, and without the intracavity iris, the pointing noise source location may have varied within the volume of the laser cavity. Typical data obtained by the use of spatial filtering are illustrated in Figure 5. With spatial filtering, the signal data error distributions were more symmetric. Since spatial filtering effectively eliminated the errors presumably due to the high-order transverse modes, error-skewed PDS signal data rejection was not required, and conventionalregression methods could have been used. The intracavity iris combined with spatial filtering resulted in data that exhibited high correlation between the excitation laser pulse energy and the PDS signal. Linear and quadratic correlation coefficients for the quadratic model were typically as high as 0.9994 for 100 data seta. The error levels calculated from the variance in the model parameters were between 2 and 15 mV, which is on the order of the instrumental noise. Thus, even with further reduction of the proportional errors, it would not have been possible to realize a substantial increase in the precision of the data at these signal levels. Rather, at this point the apparatus is limited by the precision in data collection. The precision in the data collection is limited foremost by the transient digitizer, which has a maximum relative precision of one part in 256. This relative precision severely limits the utility of the present apparatus. Low precision will not allow spectral discrimination of multicomponent samples when the relative absorbances of the different analytes are less than the relative precision of the digitizer. Also, the dynamic range of the input signal is limited to 2 orders of magnitude, severely limiting the utility of this apparatus as a GC detector. Transient digitizers with 12-bit word lengths are currently available. Use of such digitizers will increase the overall precision of the apparatus, which will, in turn, allow for spectral discriminatory measurements to be made. Further, the increased dynamic range will make this apparatus more useful for GC effluent detection. Optimization of this apparatus has resulted in better limits of detection for CFzClz over those of our previous studies (4,
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12). By use of the SPOT detector and the active filter, a signal-to-noise ratio of 50 was obtained for a 13.4 kPa sample of 3.27 ppmv CFzC12in argon, and with an excitation energy of 3.44 mJ. The limit of detection reported for this species in ref 4 was 260 pptv at 100 kPa total pressure, for a signal-to-noise ratio of 1 after 1000 averages, and with an excitation energy of about 10 mJ. An equivalent limit of detection can be calculated from the data obtained in the present study. With corrections for the signal-to-noise improvement with 1000 averages and the difference in excitation energies, the present detection limit is 90 pptv of CF2Clzin argon at 100 kPa. This improved limit of detection reflects the improvement in the signal-to-noise ratio to only a minor extent. The limit of detection is a sensitivity measurement and is not necessarily improved when determinant errors are reduced. Rather, the improved limit of detection found in this study is more likely a result of the greater sensitivity of the SPOT detector, over that of the pinhole-photodiode detector used in ref 4. The limit of detection for one average is a more meaningful measure of the sensitivity for GC effluent analysis. In this case, a detection limit of about 3 ppbv should be able to be observed in dynamic samples at 100 kPa with a 10 mJ excitation laser pulse energy. It is interesting to consider other optical methods for the further reduction of errors. One method for reducing the pointing noise in the excitation laser even further would be to use a second intracavity aperture a t the output coupler. We plan to incorporate this method in the near future. But, with advances in materials technology in infrared optics, it may someday be feasible to manufacture single-mode infrared transmitting optical fibers and infrared holographic optical elements. Propogation through optical fibers can improve the beam quality and holographic optics can be designed to minimize pointing noise problems (20,21). The technology already exists for the elimination of pointing and TEM noise in visible optical beams with the use of single-mode optical fibers. Improving the quality of the visible beam is nearly as easy as spatial filtering, and the flexibility of the optical setup is very high when optical fibers are utilized. We are currently in the process of evalutation the use of optical fibers for elimination of the monitor laser pointing noise contributions to the signal errors.
CONCLUSION If the above techniques are employed, the greatest sources of noise in pulsed infrared PDS experiments are digitization error from the data collection devices, pointing noise from the HeNe probe laser, and vibrations of the optical elements. These sources of noise also limit the precision of CW photothermal techniques. With the increased precision, pulsed infrared PDS may be a very attractive technique for trace analysis as well as for application to chromatographic and on-line detection. Registry NO.CF2C12,75-71-8;C2F&l, 79-38-9;sulfur dioxide, 7446-09-5. LITERATURE CITED Jackson, W. B.; Amer, N. M.; Bocarra, A. C.; Fournler, D. Appl. Opt. 1981, 20, 1333-1343. Fang, H. L.; Swofford, R. L. “Ultrasensitive Laser Spectroscopy”; Kliger, D. S..Ed.; Academic Press: New York, 1983; pp 175-182. Harrk, T. D. Anal. Chem. 1982, 5 4 , 741A-750A. Long, G. R.; Blalkowskl, S. E. Anal. Chem. 1985, 5 7 , 1079-1083. Sell, J. A. Appl. Opt. 1984. 23, 1586-1597. Dovichi, N. J.; Nolan, T. 0.; Welmer, W. A. Anal. Chem. 1984, 56, 1700- 1704. Nolan, T. 0.; Weimer, W. A.; Dovlchl, N. J. Anal. Chem. 1984, 56, 1704-1707. Glatt, I.; Karny, 2.; Kafri, 0. Appl. Opt. 1984, 23, 274-277. Twarowski, A. J.; Kllger, D. S. Chem. Phys. 1977, 20, 253-258. Dovichi, N. J.; Harris, J. M. Anal. Chem. 1981, 53, 669-692. Nickolaisen, S. L.; Blalkowskl, S. E. Anal Chem. 1985, 57, 758-762. Long, G. R.; Bialkowski, S. E. Anal. Chem. 1984, 56, 2806-2811. Nlckolalsen, S.L.; Bialkowski, S. E. Anal. Chem., In press.
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(14) Sepaniak, M. J.; Vargo, J. D.; Ketter, C. N.; Maskarinec, M. P. Anal. Chem. 1984, 58, 1252-1257. (15) Pang, T. J.; Morris, M. D. Appl. Spectrosc. 1985, 3 9 . 90-93. (16) Leach, R. A.; Harris, J. M. J . Chromatogr. 1981, 278, 15-19. (17) Jones, L. M.; Leroi, G. E.; Myerhoitz, C. A.; Enke, C. G. Rev. Scl. Instrum. 1984, 55, 204-209. (18) Maimstadt, M. V.; Enke, C. G.; Crouch, S. R. “Electronicsand Instrumentation for Scientists”; Benjamin Cummings: Reading, MA, 1981; Chapter 14. (19) Brigham, E. 0. “The Fast Fourier Transform”; Prentice-Hail: Engiewood Cliffs, NJ, 1974. (20) Yariv, A. “Optical Electronics”, 3rd ed.; Hoit, Rinehart and Winston: New York, 1985.
(21) Lee, S. H. “Optical Information Processing”; Lee, S. H., Ed.; SpringerVeriag: New York, 1984. (22) Phillips, G. R.; Eyring, E. M. Anal. Chem. 1983, 55, 1134-1138. (23) Campbell, N. A. Appl. Stat. 1980, 2 9 , 231-237. (24) Bevington, P. R. “Data Reduction and Error Analysis for the Physical Sciences”; McGraw-Hili: New York, 1969.
RECEIVED for review May 22,1985. Accepted August 19, 1985. This research was supported by BRSG SO7 RR07093-17 awarded by the Biomedical Research Grant Propam, Division of Research Resources, National Institutes of Health.
Sizing Synthetic Mixtures of Latex and Various Colloidal Suspensions by Photon Correlation Spectrometry Muriel Cintr6, Sylvain Cambon, Dominique Leclerc, and John Dodds*
Laboratoire des Sciences du G h i e Chimique-CNRS-ENSIC, 1, rue Grandville, 54042 Nancy Cedex, France
A Maivern 4600 photon correlation spectrometer has been used to measure the size of submicrometer particles uslng data treatment by the method of cumuiants and by the exponentlai sampling method. Blnary mixtures of standard latex particles, 1091399 nm and 220/945 nm, together with two simulated wide distributions, both 91 mm to 945 nm, have been investigated together with various real coiloldai suspensions, such as paint, mlik, lymph, cement, and formazlne. The cumuiants method is found to be unsuitable for binary mixtures, whereas the exponential sampling method applied to wide distributions and real systems can glve more Informatlon in the case of double population systems.
Colloidal suspensions, defined by IUPAC as those containing molecules or polymolecular particles having at least one dimension between 1 nm and 1 bm, are of growing importance in fine chemical processing and in biochemical and biomedical applications. This comprises a wide diversity of systems including mineral microparticles, emulsions, biomolecules, and microorganisms, but a common requirement for correct use in industrial and research applications is a means of characterizing their properties and, of particular importance, is a means of measuring their particle size. The determination of the average size of submicrometer particles is now possible by several new techniques such as hydrodynamic chromatography and field flow fractionation; photon correlation spectrometry (PCS) offers many advantages over these methods. The technique is finding wide application in the study of colloids, for example, viruses, Pusey ( l ) and , the conformation of DNA molecules, Jolly et al. (2). Photon correlation spectrometry is only one of the many names used for the technique. Others are, dynamic light scattering, intensity fluctuation spectroscopy,or quasi-elastic light scattering. The method is based on the measurement of fluctuations in the intensity of light scattered from a suspension of particles undergoing Brownian movement. Analysis by autocorrelation leads to a value of the coefficient of Brownian diffusion that can be related to particle size by the Stokes-Einstein equation. Detection of such fluctuations in light requires a photomultiplier with a sufficiently rapid response detecting emission from a sufficiently small volume for the effects not to be 0003-2700/86/0358-0086$01.50/0
smoothed out. The theory of the method is given in standard works, such as Berne and Pecora (3),or is discussed extensively in recent symposia, Dahneke ( 4 ) ,which should be consulted for full details. The application of the method is now well established for measuring monosize or narrow distributions of particles. At the present time the central problem is the application to multimodal or wide distributions and in the practical application of what involves very sophisticated numerical analysis. In the case of a suspension of monosize particles the time base autocorrelation function of the fluctuations in intensity of light scattered from a suspension is a single exponential. The determination of the time constant of the autocorrelation function then leads to a value of the diffusion coefficient and hence the particle size. In the case of a suspension containing a range of particle sizes, the autocorrelation function is the superposition of several exponentials and the normalized correlation function becomes
Here r is a function of the Brownian diffusion coefficient and the magnitude of the scattering vector F(T) is a normalized distribution function containing details of the size distribution. The problem is therefore to invert eq 1to obtain F ( r ) from measurements of G(T). Unfortunately the problem is illconditioned, no solution is guaranteed, if a solution exists it may not be unique, and the convergence to a unique solution may not be uniform. Several methods have been proposed for obtaining a solution and have been reviewed in Chu et al. ( 5 ) and Dahneke (4). Here we use two methods: the Pusey cummulants method and the exponential sampling technique. The Pusey cummulants method is now well established and fully detailed elsewhere (I). Briefly it yields the first two moments of the required distribution function, the first moment giving the average diffusion coefficient and the second moment a measure of the polydispersityof the sample (called here the Pusey polydispersity factor). The method is well adapted to narrow distributions but fails for wide and multimodal distributions. This is the basic resident numerical treatment in the Malvern 4600 apparatus used in this work. The exponential sampling method is an alternative treatment adapted for wider distributions. 0 1985 American Chemical Society
