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Anal. Chem. 1986, 58,1706-1710
Pulsed Laser Thermal Lens Spectrophotometry of Liquid Samples Using an Optical Fiber Beam Guide with Interference Orthogonal Signal Processing Stephen E. Bialkowski Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300 An apparatus for thermal lens spectrophotometry of liquid samplesIsconshucted udngapuleednhgen laserexdtstkn source a m l a w laser probe. Both laser beams are passed through a fused a k a optlcal fiber prlor to bdng Hghtly focused Into the sample cell. The optical flber k used to reduce mode and pointtng varlatlons in the laser outputs. A dlgltal correlation filter is developed and used for estlmatlon of the thermal lens signal. Thk dlgltal estbnatlon procedure exhlblts a consMerably enhanced slgnal-to-nolse ratio over that of other estknatlon methods. Moreover, It is relatively Immune to background Interference and rapM In estlmatlon time. Finally, the effectlve sample path kngth for focused beams In pulsed laser exclted thermal en lsis examlned from a theoretical b a a . It is found that the slgnal will be very near maximum for cell path lengths on the order of 4 times the Raylelgh range.
Pulsed laser excited photothermal spectrophotometry is an ultrasensitive technique for concentration estimation of analytes that do not fluoresce subsequent to absorption of light at the excitation wavelength ( I ) . There are several potential advantages to pulsed laser excitation, over that of continuous wave (CW) excited photothermal lens spectrophotometry (TLS), that have been discussed in a number of recent publications (2-8). The pulsed laser excitation techniques have large theoretical enhancement factors a t a small excitation beam radius (2-4), the signal magnitudes are not dependent on solution flow a t moderate rates (7,8), in contrast to the related CW laser excited techniques which are very sensitive to flow (!+I1 1, and there is a potentially higher signal-to-noise ratio (SNR) due to the high-frequency components that make up the rapid rise time of the TLS signal (6). However, pulsed laser are in general noisy sources. The pulse energy can vary substantially, and mode or pointing noise can result in a large errors. Mode noise is due to transverse mode fluctuations that will result in different focused beam spatial profiles in the sample, and pointing noise will result in minor shifts in the focus position. The errors associated with the latter two noise sources are due to the sensitivity of the photothermal spectrophotometric signal to the spatial overlap of the pulsed excitation laser beam and that of the CW probe. Pulse energy variations can be corrected for in a simple fashion by monitoring this energy, but the mode and pointing variations are very difficult to detect and the corrections would not be simple. Pointing noise in the pump and probe beams has been found to be a major limiting factor in the accuracy of the pulsed laser excited photothermal deflection technique (6) and appears to be one of the limiting factors in the CW TLS technique as well (12). Since pointing noise is generally greater in the high-gain pulsed discharge lasers, it is probable that this is the main source of error in pulsed laser TLS. The purpose of this study is to optimize the SNR of the pulsed laser TLS signal by the reduction of laser source noise and the utilization of optimal impulse response digital filtering techniques. Identification of determinant noise sources in 0003-2700/66/035&1706$01.50/0
pulsed laser excited photothermal signals has been previously performed (4-6). There are two main types of noise or errors in the signal measurement. The first type of noise, termed instrumental noise, is independent of the signal magnitude. Thus, this noise is present in the data even when the pump laser is not operating. Shot noise and to a lesser extent thermal noise in the photodiode signal detector are sources of instrumental noise in TLS, since the analytical signal is a small perturbation in the intensity of the probe laser. Other sources of instrumental noise include that associated with the analog electronic circuitry and digitizing errors. Reduction of instrumental noise is primarily accomplished by measurement bandwidth reduction and signal-averging software procedures. This study examines the use of adaptive correlation filtering techniques to obtain better signal magnitude estimates on a pulse-by-pulse basis. The second type of noise is that which is proportional to the signal magnitude resulting in constant SNR data. Proportional noise occurs when the alignment between the two laser beams is perturbed. The main sources of this proportional noise in photothermal signals are pointing and mode noise of the pump and probe lasers, vibration of the optical components, and acoustic refractive index variations over the optical path. Mode and pointing noise will limit both the precision and the accuracy of the measurements. Although higher sensitivities are possible with signal averaging, the standard deviation of this measurement will ultimately control the limit of detection (13). One way to improve the limit of detection is to decrease the noise by analysis and subsequent elimination of the sources of proportional noise or errors. To this end, spatial filtering has been found to reduce the proportional noise (6). However, spatial filtering only corrects transverse mode noise; it does not correct for pointing noise. It has been speculated that utilization of fiber optic components for beam transmission in the experimental design would reduce or eliminate the pointing noise errors (6). In this paper, this prediction is examined. A fused silica fiber optic is used to transmit both the pulsed pump laser and the CW probe. In addition to flexibility in experimental design offered by the utilization of optical fibers, the limited number of propagation modes should decrease the pointing variance beyond the fiber (14). EXPERIMENTAL SECTION The experimental apparatus is similar to that described previously (8). A Laser Energy, Ind., Model N2-50 nitrogen laser was used as the pump laser. This laser is a sealed tube, coaxial-excited laser operating at 337.1 nm. The maximum pulse energy was typically 50 pJ with a pulse width of 10 ns. The maximum pulse repetition rate used in these experiments was 10 Hz. The output from the pump laser was combined with that of a 5-mW Coherent Radiation HeNe laser at a dichroic beam splitter that transmitted the 632.8-nm probe laser radiation and reflected that of the pump. These spatially combined beams were then coupled into a Newport Corporation Model F-LFI laser-fiber illuminator. This illuminator consists of a 3-m plastic clad, stepped index, 200-pm core fused silica optical fiber and all optics required to couple the laser beams into and out of this fiber. Laser light exiting this fiber was focused into either a 5-mm-path-lengthfused 0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
silica spectrophotometer cell or a 1-mm-path-length square glass tubing, with a lox microscope objective. The latter objective has a focal length of about 15 mm. The sample cell was placed such that the focus of the probe laser was at the inside surface of the front face of the cell. The maximum pump laser energy at the cell was about 2 wJ. Two optical filters were used to absorb the pump laser radiation past the sample cell. First, a 1-cm-pathlength fused silica spectrophotometer cell containing a concentrated solution of 2-mercaptopyridinewas utilized to absorb most of the 337.1-nm light. Second, a Schott OG-590 colored glass filter attenuated the pump laser and some optical element fluorescence light not absorbed by the solution filter. The solution filter was necessary in order to reduce fluorescence from the colored glass filter. All optical components were mounted on a vibrationdamped optical table. The center of the probe laser beam was detected past the optical filters and a 0.5-mm radius pinhole with an EG&G Model SGD040-A PIN photodiode, biased for linear operation. A Tektronix Model AM-502 differential amplifier was used to increase the magnitude of the signal. High- and low-pass filtering was performed with this amplifier. The amplified signal was recorded with a Physical Data Model 522.4 &bit, 20-MHz transient signal recorder. Digitized transients were transferred to a DEC LSI 11/23 computer for processing. The pump laser energy was monitored by detection of fluorescence at the microscope objective optics with a United Detector Technology Model PIN-1ODP PIN photodiode. A Corning 7-54 colored glass filter was utilized to block the scattered probe laser light from this detector. The pump laser energy signal was sampled and digitized with a programmable gain, 12-bit A/D converter. Photodiode response linearity was checked against a Laser Precision Model RjP-735 energy monitor. Trigger timing for the pump laser and signal recording devices were controlled with a series of programmable time-delay generators. Reagents used in this study were iodine, resublimed, Fisher ACS grade; ethanol, US. Industrial Chemicals, U.S.P., 200 proof; and 2-mercaptopyridine. The latter was synthesized by Dan Comins at Utah State University. Sample absorbance measurements at 337 nm were performed with a Beckman DB spectrophotometer.
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-.2-
-.3-
BACKGROUND
-.4 -.5
I
I
I
I
I
CORRELATIW NHCTION
-.3
!
.E
I
I
1
I
I
.I
.2
.3
.4
I
TIME CMSECI
Figure 1. (A) Signal and background data obtained by averaging 1000 transients. The signal is of aqueous -20 I.LM2-mercaptopyridlne. (8) Orthonormalirationresults in the correlation function.
RESULTS AND DISCUSSION Noise power spectra are instrumental in determining the types of measurements errors that can be expected from an apparatus (6). Several single transient recordings of the dc coupled, amplified detector photodiode signal were obtained without operating the pump laser. The noise power spectra were calculated from the Fourier transformed time-dependent data. These noise power spectra did not exhibit the substantial flicker noise component that has been observed in previous measurements (6). The noise was essentially “white” m character. However, there were several reproduced spectral features that could be attributed to 60-Hz power line and other low-frequency interferences. The TLS signals had rapid rise times, as discussed below; and high-pass filtering, 3-dB point at 1kHz, did not significantly affect the magnitude of these signals. High-pass filtering was not utilized in most experiments since the SNR was the desired parameter. The advantage to using high-pass fiitering in small signal experiments was that the base line was steady from pulse to pulse, and thus the transient recorder could be operated with an input range such as to result in minimum digitization error. The signal estimate was obtained by determining the zero retardation correlation of each individual transient with a modified signal-averaged transient (15). Figure 1illustrates a typical background-corrected averaged signal, the associated background, and the resulting correlation vector or function. The data captured by the transient recorder upon each pulse of the pump laser is made up of four components, assumed t o be independent (16)
X ( t ) = S ( t ) + B(t) + E ( t ) + C
(1) where X ( t ) is the time-dependent measurement, S ( t ) is the
TLS signal, B(t)is the background, E ( t ) is the random error or noise, and C is a constant base line. The correlation vector is constructed as follows. E(t)is reduced by signal averaging the transients, both with a sample, X ( t ) = S ( t ) B ( t ) + C, and without, X ( t ) = B(t) C. S ( t )is then determined as the difference between these two averages. These latter two signals are shown in Figure 1. A vector, S ’ ( t ) , which is orthogonal to both X ( t ) = B ( t ) + C and a constant base line, is constructed from S ( t )with a modified Gram-Schmidt orthonormalization algorithm (16,17). The factorization matrix contains the information to reconstruct the original vectors from the orthogonalized set (17). This factorization matrix is upper triangular, and so the coefficient determined from the dot product of the last orthonormal vector with the signal vector is proportional to the least-squares coefficient
+
+
t
s
= rCS’(t)X(t)
where r is a constant equal to the inverse of the last element of the factorization matrix and s is the estimate of the signal magnitude. Upon each pulse of the pump laser, a signal transient is recorded, and the signal estimate is obtained as the vector dot product of the single pulse transient with the correlation vector. In theory, this procedure will result in a better signal estimate than the gated sampling routine used previously (4-8). In the limit of “white” noise, this correlation is equivalent to matched filtering, known for yielding the best signal estimate (16). Further, by effectively “fitting” each transient to an N point function, an SNR improvement of the signal estimate, proportional to the square root of N , is obtained (15).
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986
Table I. Comparison of Data Processing Methods type of processing“
std signal
dev
SNR
SNRb improvement‘
corrected SNRd
i
a z
gated
c3
samplinge sample blank correlation/ sample
07
blank orthogonal correlationg sample blank
3
0.880 0.380 0.000 0.354
2.32
7
0.331
6.45 1.62
2.80
16
0.175
07
+
_1
U
2.30 2.40
2la
_1
W
K
462 -5.51
9.76 9.17
47.3
22
2.14
“All measurements are three replicates of 1000 points each. *Reported SNR are the average mean to standard deviation ratios. SNR improvement calculated from the square root of the number of points used in the measurement; 50 points were used in gated sampling, 256 in correlation, and 512 in orthogonal correlation. dCorrected SNR is the SNR divided by the SNR improvement. eReferences 4-6. fReference 14. #This work.
Results of signal estimates obtained from the orthogonal correlation method described above, the direct correlation method (15), and the base-line-corrected gated sampling technique (4-8) are compared in Table I. The direct correlation is similar to the orthogonal method but does not account for reproducible background. The gated sampling technique uses two “gates”. One gate samples the base line before the TLS signal, and the second gate samples the TLS signal near the maximum, but after the radio frequency interference burst of the nitrogen laser. Table data is of three replicate measurements of 1000 pulse averages obtained for both 0.063 absorbance iodine/ethanol solutions and blanks, in the 5-mm sample cell. Standard deviations calculated for the lo00 pulse data files did not very significantly at 5%F distribution levels between replicate measurements. The predicted SNR improvement ratios are based on the number of points sampled per transient, which for the gated sampling technique is the sum of transient recorder channels for both the base line and signal gates. This calculation yields the maximum “white” noise limiting SNR improvement for the correlation techniques since the aperture or sampling function varies in time. Even when corrected for this overestimated SNR improvement, the orthogonal correlation technique has a SNR that is better than the gated sampling technique. The relatively poor SNR of the direct correlation technique is due to the large background contribution to the measured signal. The relative signal and background signal of the samples were almost identical with those illustrated in Figure 1. The orthogonal correlation technique may be more limited in application than gated sampling. When a transient digitizer is used for signal recording, the input range is adjusted such that all bits of the dynamic range are utilized. This in turn minimizes instrumental errors. In the small signal limit, the signal magnitude is much less than that of the reproducible interference. For the orthogonal correlation technique to operate, the input range must be adjusted so that this interference is recorded without truncation. As a consequence, the precision of the sampled signal will decrease at the expense of not truncating the interference. On the other hand, the gated detection scheme will be less accurate in the same limit, since the contribution of the interference to the measured signal is not determined and subsequently corrected for. One way to avoid the dynamic range limitation of the orthogonal correlation technique may be to use a truncated interference vector when calculating the correlation vector. To test the effectiveness of the laser-fiber illuminator in eliminating proportional noise, a series of experiments were
PULSE ENERGY (mJ)
Flgure 2. Relative thermal lens signal vs. 337-nm pulsed excitation energy for -0.01 absorbance iodlndethanol solution In a 5-mm-
path-length cell. There are 3000 individual signal transients plotted. Signal estimation was performed wkh orthogonal correlation filter. performed to examine the type of noise predominant in these measurements. This was done by examining the signal estimate as a function of the pump laser energy. Data obtained by using the estimation procedure described above are illustrated in Figure 2. The correlation vector was calculated from an average of 1000 transients, each being 512 points in length. The pump laser energy was varied by changing the discharge potential over the course of the 8-min experiment. This did not affect the trigger-to-laser pulse delay time. It is clear from this figure that the signal variance does not change significantly with pump laser energy. This is taken to indicate, but does not prove, that the mode and pointing noise of the nitrogen laser have been effectively reduced by using the laser-fiber illuminator. It has been shown that the use of short-focal-length optics will also result in decreased pointing noise contribution to the signal error (12). S‘ince a short-focal-length microscope objective was utilized in this apparatus, the decreased measurement error is probably a consequence of both the focusing geometry and the optical fiber. The curvature of the TLS signal vs. energy plot is due to a static thermal lens being formed at the higher repetition rates (1, 7, 8). After being coupled into the optical fiber, pointing and mode noise in both pump and probe lasers will result in respective intensity variations at the output of the fiber. However, the particular laser beam to fiber coupling optics utilized in this illuminator were not very sensitive to alignment error. This i s fortuitous in reducing pointing and mode errors, but detrimental by the fact that it indicates poor coupling efficiency. In fact, only 4% of the energy at 331 nm was transmitted through the fiber. Nonetheless, the pulse laser energy at the sample cell was about the same as that of the more conventional TLS apparatus used previously (8). Finally, since the variance is not a function of signal strength, it is likely that the two main sources of noise are the high-frequency intensity fluctuations of the probe laser, which would give rise to nonzero correlations, and shot noise in the photodiode detector. Low-frequency intensity variance of the probe laser, i.e., on the order of the sample time, will result in erors proportional to the signal magnitude (6). The “white” noise character of the noise power spectrum, coupled with the fact that there is little proportional error contribution, indicates that the predominant source of measurement error is due to shot noise. The small pump laser beam radius used in these experiments should result in a maximum TLS signal as well as reduced errors due to pointing noise (12). The smaller beam waist will result in a reduced interaction length through the
ANALYTICAL CHEMISTRY, VOL. 58, NO. 8, JULY 1986 1
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