1188 (9) (10) (11) (12) (13) (14) (15) (18) (17) (18) (19) (20) (21) (22)
Anal. Chem. 1988, 60, 1188-1193 Pierce, F. D.; Brown, H. R. Anal. Chem. 1978, 48, 893-695. Pierce, F. D.; Brown, H. R. Anal. Chem. 1977, 49, 1417-1422. Kirkbrlght, G. F.; Taddla. M. Anal. Chlm. Acta 1978, 100. 145-150. Hershey. J. W.; Kellher, P. N. Spectrochlm. Acta far?6 1986, 418, 713-723. Welz, B.; Melcher, M. Analyst (London) 1984, 109, 573-575. Welz, 6.; Melcher, M. Analyst (London) 1984, 109, 577-579. Welz, B.; SchubertJacobs, M. J . Anal. At. Spectrom. 1986, 1 , 23-27. Aggett, J.; Hayashl, Y. Analyst(London) 1987, 12, 277-282. Belcher, R.; Bogdanekl, S. L.; Henden, E.; Townshend, A. ~ n a k s t (London) 1975, 100, 522-523. Aggett, J.: Aspell, A. C. Analyst (London) 1976, 101, 341-347. Gulmont. J.; Plchette, M.; Rhlume, N. At. Absorpt. News/. 1977, 16, 53-57. Dornemann, A.; Kleist, H. Fresenlus’ 2. Anal. Chem. 1981, 305, 379-381. Peacock, C. J.; Singh, S. J. Analyst (London) 1981, 106, 931-938. Bye, R. Analyst (London) 1986, 1 1 1 , 111-113.
(23) Brindle, I. D.; Ceccarelli Ponzonl, C. M. Analyst(London) 1987, 112, 1547-1 550. (24) Boampong, C., unpubllshed results. (25) Miller, J. C.; Mlller, J. N. Statlstlcs for Analytical Chemlstry; Wiley: New York, 1984; pp 82-107.
RECEIVED for review October 6, 1987. Accepted February 1, 1988. The Fondacion Gran Mariscal de Ayacucho of Venezuela is thanked for providing a graduate scholarship to C. M.C.P. The Canada Department of Employment and Immigration is thanked for providing a summer studentship (Challenge ’87) for L.P. Funds for the purchase of the Spectraspan were providedby the (hvernment of Ontario BILD program.
Dual-Beam Absorbance Measurements by Position-Sensitive Detection Curtiss N. Renn and Robert E. Synovec*
Department of Chemistry, BG-10,Center for Process Analytical Chemistry, University of Washington, Seattle, Washington 98195
A sknple, reliable, and rugged absorbancedetector has been dedgmd and Wed that empbys a -e detector with a dual-beam optical arrangement. The mathematical formulaHon lor OpHCal and electronic null condltlone Is presented and experimentally observed as opthum. The devlce requlres a single detector and no movlng parts, ideal for process analysis condltlons or general appllcatlon. An absorbance level of 6 X lod AU (8 X root mean square) was achieved wlth the mlcrobore hlgh-performance llquld chromatographic separation of the two isomers of FD 81 C Blue Dye 2 uslng a HeNe laser source and the absorbance detector w#h a capillary flow cell. PosdbWes for elmultaneous refractive index ( R I ) monltorlng or, conversely, R I effect reductlon are discussed.
Molecular absorbance spectroscopy is a popular tool of the analytical chemist. Much has been reported in terms of static solution measurements ( 1 , 2 ) ,and flowing solution measurements (3, 4 ) , i.e., with high-performance liquid chromatography (HPLC) and flow injection analysis (FIA). In the context of HPLC, one is generally interested in determining the identity and quantity of certain sample components, in relation to some analytical problem or condition. Molecular absorbance in the ultraviolet to visible portion of the spectrum (UV-vis) is a highly sensitive technique for many chemical species of interest and when coupled with HPLC affords a fair level of selectivity via wavelength selection (5, 6). The common modes of absorbance detection employ fixed-wavelength, variable-wavelength (scanning), or multichannel (photodiode array) detectors (7). If improved solute detectability is a concern, many laser-based approaches to HPLC and FIA absorbance detection have been developed based upon thermal lens spectroscopy (8-181, Fabry-Perot interferometry (19),indirect polarimetry (20),and high-frequency amplitude modulation (21,22). In each of these laser-based methods, quantitative analysis is ultimately limited by some 0003-2700/88/0380-1188$01 SO/O
form of noise. Often the laser is the culprit, by limiting either detectability or precision in the measurements due to laser “flicker” noise. Signal processing and the translation to solute properties are often highly variable and “system” dependent for many of these laser-based approaches. Absorbance detection is quite popular for process control applications, where the analytical instrumentation should be not only sensitive and selective but also rugged, reliable, and relatively inexpensive to purchase and maintain (23, 24). Though excellent in terms of absolute solute detectability, many of the laser-based absorbance detectors require more development, in terms of the requirements for process control applications. This paper deals with a novel development, in which a dual-beam arrangement,that is conventionally utilized for optimized absorbance detection to ensure precision and accuracy in quantitation, is employed with a position-sensitive detector (PSD), which is conventionally applied in optical alignment. The development is a dual-beam absorbance detector, with excellent signal and noise characteristics, ideal for process control. The approach to dual-beam absorbance detection employs a PSD which has two distinct advantages relative to other approaches. First, a single detector is employed which is inherently uniform in performance characteristics, in contrast to dual-photodiode systems which suffer from temperature and electronic fluctuations and light response differences (6). Dual-photodiode systems are more difficult to prepare and maintain as compared to the PSD system described here. Second, both electronic and optical nulls are employed with the dual-beam PSD absorbance measurement which improves detector reliability and function. It is accomplished without any moving parts, i.e., mechanically, which must be avoided for process instrumentation if at all possible. Light source modulation has conventionally been accomplished mechanically. Recently, optoacoustic modulation was incorporated in a dual-beam absorbance detector, coupled with a single photodiode and signal processing via demodulation (21). This system is presently too costly and cumbersome for minia0 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
Dual-Beam Position Sensitive Detection
PSD BS
I I
_*-'
..-
;em4'
--------E
Figure 1. Dual-beam arrangement with the position-sensitivedetector. He&, HeNe laser; BS, beam splkter;L1, 5cm focal length lens; CC, splltter; cell (Interfaced to microbore HPLC system): L2, 2.5 cm focal length lens: M, mirror; ODF, optical denslty fitter; PSD, positlon-sensltlve detector (A, output A; CE, common electrode; B, output B, as in Figure 2).
turization for process instrumentation. A new approach to dual-beam absorbance detection via a PSD is described in terms of the analytical signal(s) provided and the noise characteristics of the device in the dual-beam context. It is shown that the PSD-based detector provides an absorbance detectability comparable to commercially available instrumentation, Le., 1 X AU (3 X to 1 X root mean square noise). The detector effectivelyreduces laser intensity noise to better than a 2 X lo4 level (3 X root mean square noise) relative to the absolute laser intensity which is comparable to amplitude modulation techniques (21,22). The device is studied at a fixed wavelength for selective detection.
EXPERIMENTAL SECTION The experimental schematic of the dual-beam PSD-based absorbance detector, employed for microbore HPLC detection is shown in Figure 1. The light source was a 5-mW, plane-polarized HeNe laser (Uniphase, 1105P, Sunnyvale,CA) with 0.1% amplitude fluctuations (root mean square) and 0.02 mrad pointing stability after a 15-min warm-up. Note that the device is not limited to a laser as the light source. A laser is convenient both for microbore HPLC detection, which is demonstrated, and for examination of the noise reduction properties of the dual-beam PSD approach. The laser provides a continuous wave (CW) output, yet a dashed line is used in Figure 1 only for clarity in defining the dual-beam optical path. The CW laser output was split by a beam splitter (MellesGriot, 03FNQ057,Irvine, CA) into sample and reference beams. The sample beam is focused by a 5.0 cm focal length lens (Melles Griot, DCX Sillica, Irvine, CA) through a capillary cell (200 pm i.d. X 600 pm 0.d.) which is at the end of a microbore HPLC system. Note, that the system is, in general, not limited to a capillary cell. Other flow cell configurations typically used in absorbance detection, such as the z configuration, may be readily applied. The sample beam polarization plane was perpendicular to the capillary cell in order to reduce reflection losses (25). Upon exiting the capillary cell, the sample beam is imaged by a second 2.5 cm focal length lens (Melles Griot, DCX Silica, Irvine, CA) to a ca. 1mm round spot on the 2.5 mm X 33 mm PSD (Hamamatsu, S1352, Hamamatsu City, Japan) which was experimentallyfound to eliminate all but the largest refractive index changes occurring in the capillary cell (25). The reference beam is directed from the beam-splitter to a mirror which directs the reference beam to the PSD. In order to maintain an optical null at the PSD for the sample and reference beams (prior to any absorbance in the sample beam) an optical density filter (Melles Griot, 03FNQ045, Irvine, CA) is placed in the reference beam. The PSD is highlighted in Figure 2, as discussed further in this paper. The microbore HPLC system consisted of a syringe pump (ISCO,LC-2600, Lincoln, NE) coupled to a 0.5-pL injection valve (Rheodyne,7520, Cotati, CA) and on to a 1.0 mm X 250 mm C18 column (Alltech, Adsorbosphere HS, Deerfield, IL) which was connected to the capillary cell of 3 cm length with a total volume of 1 pL, as discussed previously in the dual-beam arrangement (Figure 1). A reversed-phase HPLC separation and detection of the two isomers of a blue dye (H. Kohnstamm and Co., FD & C Blue Dye 2,131256, New York) were demonstrated (26) by using 50% H20 and 50% CH,OH, by volume, with 4.75 g/L p toluenesulfonic acid at pH 7.4 as eluent.
1189
Output
I
::
/amp'e
[Output
B
Resistive P Layer
I
High Purity Silicon Substrate
I N Layer
Common Electrode
Flgure 2. PosHion-sensMve detector configurationvia duabeam optical and I,,, are the incident reference and sample arrangement. IRsf beams, respectively, separated by a distance X , in relation to the PSD length L . Outputs A and B are currents in relation to the common electrode (27).
The analytical signals from the PSD, as discussed in the theory section, were simultaneously collected via a laboratory interface (MetraByte,DASH-16, Taunton, MA) that facilitated the analog to digital (AID) conversion for subsequent storage and analysis with a personal computer (IBM-XT, Armonk, NY). Since the PSD has no built-in time constant capacity, other than the inherent frequency range due to RC effects within the supporting circuit, direct memory access (DMA) was employed via the laboratory interface board (Metra Byte, DASH-16, Taunton, MA) with a data acquisition rate of lo00 pointsls, averaged and stored on the fly, to a rate of 1 pointls. This was adequate for the chromatographic information, Le., solute peaks, and also proved important for optimizing, Le., reducing, the PSD output noise. All software used in this work was written in-house. Each sample for the HPLC results was injected at least 3 times to ensure reproducibility. For study of the capillary cell and PSD positioning dependence, both components (Figure 1) were mounted with high precision X-Y-Z translational stages (Newport,46O-XYZ, Fountain Valley, CA). The stages are not necessary in general for application of the device.
THEORY An equation must be derived that relates absorbance, in the conventional dual-beam sense, to the PSD output characteristics. In conventional dual-beam absorbance measurements, there is a reference beam, ZReh and a sample beam, Z h p l e . In conjunction with Figure 1,the locations of Zm and Z h p l e are shown in Figure 2 in the context of the PSD output A and B, the distance separating the incident locations of ZRef and ZSample, labeled as X, and the length of the PSD, L. For the derivation of the PSD outputs, Ibf and Isample will be labeled as IR and Is, respectively. The construction and function theory of the PSD may be found elsewhere (27),but the pertinent features of the function theory will be applied here in the context of dual-beam detection. Output currents are measured at electrodes A and B, at the opposite ends of the PSD, connected to a common electrode. When an incident beam strikes the PSD surface, a photocurrent is produced that travels through the resistive P-layer to each electrode A and B. Thus, both electrodes receive information for a given incident beam. This information is in the form of an output current that is directly proportional to the incident beam intensity and inversely proportional to
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
the resistance from the point of incidence to a given electrode (27). For the reference beam, one may write
IA,R= IO,R(RL- R,)/RL
(1)
IB,R= Io,R%/RL
(2)
and
For the sample beam, one may write IA,S
from eq 5-11. After simplification with eq 14, eq 15 becomes
= IO,S(RL - RX - R m ) / R L
(3)
= IO,S(RX + Rm)/RL
(4)
and IB,S
where IA,R, IB,R, IA,s, and IB,s correspond to output electrode currents, IO,R and Zo,s correspond to total currents produced by the incident beams prior to any absorbance for the reference and sample beams, respectively, and Rj corresponds to the resistance for a given distance labeled by the subscript j. For the purpose of the derivation and eq 1-4, m is a distance between IRefand output A in Figure 2. Since the resistivity is uniform across the PSD (27),the resistances may be replaced in eq 1-4 by distances
IA,R= Io,R(L- m ) / L
(5)
IB,R= I o , R ~ / L
(6)
IA,S= IO,& - X - m ) / L
(7)
IB,S= IO,S(X + m ) / L
(8)
Experimentally in the dual beam arrangement, the PSD obtains information at both electrodes, A and B, from both incident beams
IA= IA,R+ IA,S
(9)
IB = IB,R+ IB,S
(10)
and
where ZA and I B are the total currents measured at electrodes A and B, respectively. The PSD was configured to provide two final outputs, referred to as the ratio and sum signals. These outputs are defined as
+ IB
(13)
Beyond working at an electronic null, one wishes to work at an optical null in order to improve the signal-to-noise ratio (S/N). An optical null occurs when the incident reference and sample beams are of equal intensity prior to any absorbance, i.e., io,^ = Io,s. From eq 13 the optical null condition states that
L=X+2m
ratio = -X ( 2.303 T ) A
L which states that the ratio signal is linear with absorbance, A , at small absorbances, with a dependence on the fraction of the detector surface utilized to separate the sample and reference beams, i.e., X / L . Further the ratio signal is linear with sample concentration a t small A , since Beer's law is followed
A = tbC
(19)
where t is the molar absorptivity of the sample, b the path length, and c the molar concentrationof the absorbing sample. The ratio signal is independent of the light intensity since eq 11 provides intensity normalization. The sum signal also provides absorbance information, without any PSD length dependence but with light intensity dependence. From eq 5-10, and 12, one obtains sum = IO,R(l
+
(20)
which for small absorbance becomes sum = IO,R(2 - 2,3034)
(21)
RESULTS AND DISCUSSION
using eq 9 and 10. One is primarily concerned with the ratio signal in the dual-beam arrangement. If IA = IB,the PSD ratio signal is operating at an electronic null. Substituting into eq 9 and 10 from eq 5-8 and simplifying
IO,R(L- 2m) = Io,s(2X + 2m - L )
For small absorbances, eq 17 is simplified to
The validity of eq 17,18,20, and 21 will be studied through experimental results. The analytical utility of the dual-beam arrangement with the PSD will be studied in the context of reducing noise via an electronic and optical null.
and sum = IA
Since I,, = at the optical null condition, and absorbance, A , which should not be confused with electrode A, is equal to -log (Is/Io,s),eq 16 reduces to
(14)
which further suggests that IO,^ and I0,sare equidistant from the center of the PSD, from the symmetry of eq 14 and Figure 2. If an absorbance occurs in Io,s,the resultant current at the PSD is Is, and the ratio signal becomes
When measuring the ratio signal of the PSD, one must realize that the limiting noise is dependent upon the electronic noise characteristics of the PSD and the position stability of the incident light beam or beams. Specific discussion of the PSD noise characteristics are discussed elsewhere (27). The contribution and deconvolution of these two noise sources were considered. Since the analytical signal of interest, i.e. absorbance, is transformed, in a sense, from an intensity measurement to a beam position displacement, one must measure and subsequently improve the position detectability of the PSD. The position detectability, at the limit of detection (LOD) is defined as the condition when the ratio signal is equal to 3 times the standard deviation of the PSD noise for a specified time width. For a single beam incident upon the PSD, instead of the dual-beam arrangement, the PSD was moved via a translational stage so the ratio signal could be accurately and precisely related to the position movement, AX. The slope of ratio signal versus AX was found to be 5.8 X pm-' while the standard deviation of the noise (root
ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
mean square) was equal to 2.0 x 10” in ratio units for either the single- or dual-beam arrangement. Thus, the position resolution AX obtained for the PSD was 0.34 pm (root mean square). If one considers 3 X root mean square as the position resolution LOD, a 1.0-pm beam shift is detectable. This quantity, AX, must be minimized to optimize the PSD in the deal-beam approach for absorbance detection. In principle, one may also detect refractive index (RI) changes when using a capillary flow cell. A combined RI and absorbance detector based upon a capillary flow cell was reported recently by Bornhop and Dovichi (18). From previous work concerning RI sensitivity with capillary flow cells (25), one might expect a sensitivity of about 2 rad/RI unit for a well chosen capillary. If the PSD is located 100 cm from the capillary flow cell (see Figure l),the LOD of 1.0 pm (3 X root mean square) position resolution translates into a RI detection limit of 5.0 X lo-’ RI. The imaging lens, L2 (Figure l), eliminates RI sensitivity, as applied in this work. This is particularly important for solvent gradients vis-a-vis capillary flow cell detection. Further, with focus at the center of the capillary cell the RI signal was negligible, while operating away from the center of the cell (18,25) both RI and absorbance signals are detectable by the ratio signal, while the s u m signal would yield only absorbance information. This is accomplished with a single, unmodulated light source, in contrast to the previous work of Bornhop and Dovichi (18). Since we are more interested in the absorbance detection capabilities of the dual-beam PSD-based device, the RI signal is not emphasized in this paper, yet readily available for use. Indeed, both RI and absorbance signals were observed when the system was properly adjusted. The contribution to the limiting noise due to the pointing stability of the light source was investigated. This was accomplished by measuring position resolution, AX, when the PSD and laser are separated by two distinct distances: 8 and 120 cm. A t 8 cm, pointing stability should not be as much a fador as at 120 cm. This experiment WBS done with the laser and PSD only with a single beam. It was found that at 120 cm the noise was statistically equivalent to the noise measured at a distance of 8 cm. This suggests that the dominating, i.e., limiting, noise is from the electronic characteristics of the PSD and subsequent circuitry, as suggested (27). Yet, the position resolution at 3 X root mean square of AX = 1.0 pm, is 7 times better than the manufacturers specifications. Accordingly, one may find a PSD with better noise characteristics, and thus a smaller AX capability, which would lead to a better dualbeam detector. This will be discussed further, in terms of the absorbance LOD. Given that the position resolution is 6.0 X for the ratio signal for 3 x root mean square, one may predict an absorbance LOD in the dual-beam arrangement by rearranging eq 18
A = ratio - (2.iO3)f; Assuming the sample and reference beams are out to opposite ends of the PSD, Le., X I L = 1, an absorbance LOD is calculated as 5.2 x AU. Clearly, if AX can be reduced, then AU (3 the absorbance LOD can be improved, yet 5.2 X X root mean square) is quite satisfactory considering a single detector is employed and light modulation is not required, i.e., moving parts or costly instrumentation. The dual-beam PSD ratio absorbance measurement effectively “stabilizes” the incident laser intensity fluctuations to a 1.2 X (3 X root mean square) level, comparable with dual-beam optoacoustic modulation techniques for conventional absorbance detection (21). This is about a factor of 20 improvement (reduction) in the HeNe laser amplitude noise when no effort is made to minimize amplitude fluctuations.
1191
Table I. Absorbance Ratio Signal as a Function of Sample and Reference Beam Separation Distance, X,for a Constant Injected Solute Quantity ratio (exptl)*
X,”mm 3.40 8.00
61
13.12 19.06 22.22
216 301 361
ratio (eq 23)‘ 54 128
115
210 306
357
“Calculated as in text. bPeak height, in ratio units, of a chromatographically retained absorbing solute of constant injected quantity at low absorbance, i.e. experimental data. Predicted ratio signals, from eq 23, after fitting the experimental data via linear regression. After assuming eq 18 is valid, in order to calculate the inferred absorbance LOD, via eq 22, one must test eq 18 experimentally. This was facilitated by injecting known quantities of an absorbing sample into a microbore HPLC system with subsequent detection with the dual-beam PSD as in Figure 1. First the dependency of X I L , i.e., the relative spacing between, I0,s and IO,^, was studied by injecting a constant quantity of the absorbing sample at low concentration and experimentally changing X (Figure 2) by first moving the mirror (Figure 1) on the reference beam and then adjusting the PSD position via a X-Y-Z translational stage to achieve an electronic null. For this particular PSD, the conversion from voltage to distance was 1.47 mm/V. X was calculated for five different distances by alternately blocking the sample and reference beams, I0,s and IO,R,and measuring the voltage for each beam. The results for this study are given in Table I, which fit the expression,based upon linear regression (LR)
,
ratio = 16.12X - 1.34
(23)
where X is in millimeters and ratio is the absorbance signal measured according to eq 18. Collectively, the data in Table I yield a relative standard deviation (RSD) of 8.470,calculated by
RSD(LR) =
ratio(expt1) - ratio(eq 23) ratio(eq 23)
n-1
L
which is reasonable since at small X , experimentaluncertainty began to limit the precision of the data. The y intercept of eq 23 suggests that at ratio = 0 the plot is in error by only about 0.1 mm. This strongly supports the validity of eq 18. Thus, even though an absorbance is actually occurring, at X = 0, the PSD does not sense the absorbance since the apparent “center-of-intensity”,vis-a-vis both beams, has not shifted. Obviously, for the remainder of the work, the largest possible X was chosen, which was limited due to the finite size of the incident beams such that X I L was about 0.85 instead of the “ideal” 1.00. According to eq 18 and Beer’s law (eq 19), the ratio signal should be linear for small absorbances. It is interesting to use eq 17 in order to calculate the ratio signal as a function of absorbance, A . This is shown in Figure 3. The function according to eq 17 is labeled as B (Figure 3), while for small absorbances a linear function is observed labeled as A, shown extrapolated from B. Various analyte concentrations, at low absorbance, were detected with the system and the resultant calibration curve, ratio signal vs concentration,was linear with a correlation coefficient of 0.99, consistent with Figure 3. This is important since it implies that the new detector provides an accurate measure of absorbance. The point at which the
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ANALYTICAL CHEMISTRY, VOL. 60, NO. 11, JUNE 1, 1988
-
0 t-
a
a
150
ABSORBANCE Figure 3. Ratio signal as a function of absorbance for the dual-beam PSD-based arrangement: (A) linear approximation (eq 18): (B) exact relatlonship between the ratlo signal and absorbance (eq 17).
ratio absorbance signal becomes nonlinear in Figure 3 may be put in quantitative terms by calculating the relative error in absorbance that occurs from assuming a linear relationship, eq 18, instead of the exact relationship, eq 17. The relative absorbance error was calculated as A(eq 17) - A(eq 18) relative absorbance error =
A(eq 17)
(25)
A 3% relative error in absorbance,A, occurs for an absorbance of 0.26 AU, which corresponds to a ratio signal of 0.30. This is clear from Figure 3 also. Linearity is comparableto existing commercial absorbance detectors. Similarly the sum signal provided a linear signal as suggested by eq 21. With optical density filters of A = 0.60 and A = 0.30 placed in the sample beam, lo,s, the ratio absorbance signal was measured to test eq 17 for high absorbance. In both cases eq 17 accurately predicted the observed PSD ratio signal to within a few percent. An interesting case is to place an optical density fiiter, in this case A = 0.60, in front of the beam splitter in Figure 1,i.e., between the laser and the beam splitter. This reduces the total currents, prior to any absorbance, by the incident beams, lo,s and 10,R, by a factor of 4,assuming the optical density filter is accurately calibrated. From eq 17 and 18, the ratio absorbance signal should not be affected by this filter, while eq 20 and 21 indicate that the sum absorbance signal should reduce in absolute magnitude by the same factor of 4. Experimentally, these two expectations were confirmed by injecting the same quantity of the absorbing sample, at constant X,before and after adding the optical density filter between the laser and the beam splitter, and measuring the detected peak height from the ratio and sum outputs. This result further emphasizes the idea that the dual-beam PSD absorbance measurement is much more accurate and resilient toward intensity fluctuations in the light source, than if unstabilized or not normalized. Further one would expect the new system to be fairly resilient toward stray light, due to the intensity normalization inferred by eq 11, coupled with the close proximity of the sample and reference beams, i.e., one detector. The detector reduces many sources of error common in absorbance measurements (%),such as signal to noise, drift, RI effects from the flow cell, and accuracy. The dual-beam PSD arrangement was demonstrated in the absorbance detection following the separation of the two isomers in FD & C dye 2 (26). A 6.4-ng portion of the dye was injected. This is shown in Figure 4 where, experimentally, A (3 x the absorbance LOD was determined to be 6.0 X root mean square). These values are in close agreement with the theoretical absorbance LOD calculated by eq 21. The dual-beam absorbance measurement via a PSD shows ex-
200
250
3 3
TIME, SEC Figure 4. Reversed-phase mlcrobore HPLC separatlon of the two isomers of FD & C Blue Dye 2 (6.4 ng Injected) and detectlon by the dual-beam PSD-based absorbance detector (Figure 1). Injection dlsturbance occurs at 190 s.
ceptional promise either for process control instrumentation (23,24)or in reducing laser noise in capillary and microbore HPLC detection schemes. Optimum device performance requires discussion. When the noise on the dark current on the sum is measured (since the ratio is not defined when no light is incident upon the detector), an inferred absorbance LOD of 1.0 X lo4 (3 x root mean square) is calculated. This calculation assumes the noise on the ratio signal would be roughly twice that on the sum signal, which was observed when low-frequency noise was eliminated via the optical null. Thus, there is potential for the device to function with a factor of 60 improvement in absorbance LOD. Since the pointing stability of the light source did not contribute significantly to the noise, as discussed earlier, the discrepancy between the observed and theoretical absorbance LOD is difficult to determine. Electronic noise in the PSD circuit appears to be the primary source of noise. We are investigating approaches to reduce this factor. Fiber-optic approaches are also currently under investigation to determine if improving mechanical stability translates into better detector performance. Our approach to compensate for light source intensity fluctuations should be an improvementover feedback systems employing two photodiodes (29). The PSD-based detector employs a single light-sensitive surface, while two photodiodes may not have identical spectral response curves. From a practical point of view, it is difficult to achieve matched performance for two photodiodes, thus requiring more frequent calibration. The PSD-based device provides an absorbance signal that is quickly calibrated by the PSD electronics with a present time constant of about 1 ms. Stabilization of the light source is accomplished with fewer components, over a shorter “path”, via the PSD approach compared to optical feedback approaches employing two photodiodes. Stabilization of the source intensity by optical feedback approaches, via two photodiodes, has a recovery, i.e., time constant, on the order of 1 s (29). Essentially, the PSD approach is not dependent upon feedback technology and, thus, independent of the light source, yet provides equal or improved light source intensity stabilization with a more rapid response. Certainly, absorbance detectors based on optoacoustic modulation have similar detection limits, with the capacity for faster response (21,221,but cost, simplicity, and ease of miniaturization should also be considered. Further, the new device may be applied for simultaneous RI and absorbance detection with a single, unmodulated light source. This might be accomplished as explained in the text, i.e., using both the ratio and sum outputs, or possibly by combining
Anal. Chem. 1988, 60, 1193-1202
absorbance detection along the axis perpendicular to the capillary, as demonstrated here, coupled with RI gradient detection along the axis parallel to the capillary as described by Pawliszyn (30). Making both of these measurements simultaneously, yet separately, would require a two-dimensional PSD. Two-dimensional PSDs are commercially available, and some interest in their use in laser beam deflection sensing has been reported (31). Future work is in this direction.
ACKNOWLEDGMENT We thank R. Olund for his electronics expertise in preparing the circuitry associated with the PSD. LITERATURE CITED Upor. E.; Mohoi, M.; Novak, G. I n Comprehensive Analytical Chemlstry; Svehla, G.,Ed.; Elsevier: New York, 1985; Vol. 20. Willlams, D. H.; Fleming, I. Spectroscopic Methods in Organic Chemistry; Urmo: Bllbao, Spain, 1984; 224 pp. Stevenson, R. L. Chromatogr. Scl. 1983, 23, 23-86. Dolan, J. W.; Berry, V. V. LC Mag. 1984, 2 , 290. DlCesare, J. L.; Ettre, L. S. J. Chromatogr. 1982. 251, 1-18. Abbott, S. R.: Tusa, J. J. Llq. Chromatogr. 1983, 6 , 77-104. Green, R. B. I n Chemical Analysis: Detectors for Liquid Chromatography; Yeung, E. S., Ed.; Wiley: New York, 1986; Vol. 89. Leach, R. A.; Harris, J. M. J. Chromatogr. 1981, 218, 15-19. Buffet, C. E.;Morris, M. D. Anal. Chem. 1982. 54, 1824-1825. Buffet, C. E.; Morrls, M. D. Anal. Chem. 1983, 55, 376-378.
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RECEIVEDfor review November 30,1987. Accepted February 8. 1988.
Partial Least-Squares Methods for Spectral Analyses. 1. Relation to Other Quantitative Calibration Methods and the Extraction of Qualitative Information David M. Haaland* and Edward V. Thomas
Sandia National Laboratories, Albuquerque, New Mexico 87185
Partial leastgquares (PLS) methods for spectral analyses are related to other multlvarlate callbratlon methods such as classical least-squares (CLS), Inverse least-squares (ILS), and prlnclpal component regression (PCR) methods which have been used often In quantitative spectral analyses. The PLS method which analyzes one chemlcal component at a tbne Is presented, and the basis for each step In the algorithm Is explained. PLS callbratlon Is shown to be composed of a series of simpllfled CLS and ILS steps. This detalled understandlng of the PLS algorithm has helped to ldentlfy how chemically Interpretable qualltatlve spectral lnformatlon can be obtained from the lntennedlatesteps of the PLS algorithm. These methods for extractlng qualitative Information are demonstrated by use of simulated spectral data. The qualltatlve Information directly available from the PLS analysis Is superlor to that obtained from PCR but is not as complete as that which can be generated during CLS analyses. Methods are presented for selecting optbnal numbers of loading vectors for both the PLS and PCR models In order to optimize the model while simultaneously reduclng the potential for overfittlng the caHbratlon data. Outlier detection and methods to evaluate the statlstlcal slgnlflcance of resuits obtalned from the dMerent cahatlon methods applied to the same spectral data are also discussed.
Partial least-squares (PLS) modeling is a powerful new multivariate statistical tool that has been successfully applied
to the quantitative analyses of ultraviolet (1,2) near-infrared (349, chromatographic (6-8), and electrochemical (9)data. An excellent review of this multivariate statistical method has been presented by Martens (lo), which also includes a number of published papers. Recently Lorber et al. (11) presented a theoretical basis for the PLS algorithm, and Geladi and Kowalski published a tutorial on the PLS algorithm (12). PLS software has also recently been made available by several Fourier transform infrared (FT-IR) instrument manufacturers for quantitative spectral analyses. Since software using PLS techniques is now available, it is important for infrared spectroscopists to understand the PLS method and its relation to methods more commonly used in quantitative IR spectroscopy. Therefore, PLS will be described along with the classical least-squares (CLS) (13-16), inverse least-squares (ILS) (17--19), and principal component regression (PCR) (20-23) multivariate statistical methods which have been applied to quantitative IR analyses in the past. A detailed description and understanding of the PLS algorithm is presented here which indicates that while it is similar to PCR, the PLS calibration can be broken down into steps that separately involve CLS calibration and prediction followed by ILS calibration. Thus PLS has properties which combine some of the separate advantages of CLS and ILS methods while making some potential improvements over PCR. In addition, it will be shown that this detailed understanding of the PLS algorithm helps us identify how qualitative information might be extracted from the intermediate steps of the PLS modeling. This chemically interpretable spectral information available during the PLS calibration and prediction
0003-2700/88/0360-1193$01.50/0 0 1988 American Chemical Society
