Quantitative Raman Spectroscopy of Highly Fluorescent Samples

Mar 15, 2001 - Calibration using second derivatives gave a prediction error which was approximately twice as large, at 6.5%; however, when data with b...
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Anal. Chem. 2001, 73, 2058-2065

Quantitative Raman Spectroscopy of Highly Fluorescent Samples Using Pseudosecond Derivatives and Multivariate Analysis Antoinette O’Grady,† Andrew C. Dennis,‡ Donal Denvir,† John J. McGarvey,§ and Steven E. J. Bell*,§

Andor Technology Ltd., 9 Millenium Way, Springvale Business Park, Belfast BT12 7AL, Northern Ireland, Avalon Instruments Ltd., 10 Malone Road, Belfast BT9 5BN, Northern Ireland, and School of Chemistry, The Queen’s University of Belfast, Belfast BT9 5AG, Northern Ireland

Intense luminescence backgrounds cause significant problems in quantitative Raman spectroscopy, particularly in multivariate analysis where background suppression is essential. Taking second derivatives reduces the background, but differentiation increases the apparent noise that arises on spectra recorded with CCD detectors due to random, but fixed, variations in the pixel-to-pixel response. We have recently reported a very general method for correcting CCD fixed-pattern response in which spectra are taken at two or more slightly shifted spectrometer positions and are then subtracted to give a derivative-like shifted, subtracted Raman (SSR) spectrum. Here we show that differentiating SSR data (which has inherently higher S/N than the undifferenced data) yields spectra that are similar to those that are obtained from the normal two-step differentiation process and can be characterized as pseudo-second-derivative, PSD, spectra. The backgrounds are suppressed in the PSD spectra, which means they can be used directly in multivariate data analysis, but they have significantly higher S/N ratios than do simple second derivatives. To demonstrate the improvement brought about by using PSD spectra, we have analyzed known samples, consisting of simple binary mixtures of methanol and ethanol doped with laser dye. When the background levels of all samples included in the models were e 10× greater than the intensity of the strongest Raman bands, partial least-squares calibration of the PSD data gave a standard error of prediction of 3.2%. Calibration using second derivatives gave a prediction error which was approximately twice as large, at 6.5%; however, when data with background levels .∼100× larger than the strongest Raman bands were included, the noise on the second-derivative spectra was so large as to prevent a meaningful calibration. Conversely, the PSD treatment of these samples gave a very satisfactory calibration with a standard error of prediction (3.3%) almost identical to that obtained when the most fluorescent samples were excluded. This method clearly has great potential for general purpose Raman analytical chemistry, because it does not depend on specialized equipment, is computationally undemanding, and gives stable and robust calibrations, even for samples in which the luminescence background level fluctuates between the extremes of being practically zero and completely dominating the Raman signal. 2058 Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

A major problem in Raman characterization of many industrial samples is that they give very large interfering luminescence backgrounds that can almost completely obscure the underlying Raman signals. Many experimental strategies have been used to reduce the level of background luminescence, but none has been universally successful, either because they work for only certain sample types or because they are extremely expensive to implement.1-8 This being the case, it is inevitable that in attempting to obtain Raman spectra of a diverse range of sample types, some level of background luminescence will be encountered and a strategy to remove its effects needs to be developed. The level of background luminescence that is regarded as a problem varies significantly across the range of users and uses of Raman spectroscopy. In studies in which the main objective is simply to determine the positions and intensities of the Raman bands, the most common method of removing a sloping background is to subtract a smooth function that is the same shape as the luminescence background.9,10 The time needed to carry out the correction is normally much shorter than that needed to record the spectra or interpret the data generated. However, such manual correction is at best undesirable and at its worst is impracticable for routine chemical analysis by Raman methods. The need for stable and reliable automated background correction for analytical Raman spectroscopy is particularly pressing in multivariate data analysis. It is already clear from other studies, particularly near-infrared (NIR) absorption spectroscopy, * To whom correspondence should be addressed. Tel: 44-(0)2890 274470. Fax: 44-(0)2890 382117. E-mail: [email protected]. † Andor Technology Ltd. ‡ Avalon Instruments Ltd. § The Queen’s University of Belfast. (1) Kagan, M. R.; McCreery, R. L. Anal. Chem. 1994, 66, 4159. (2) Chang, R. K.; Furtak, T. E. Surface Enhanced Raman Spectroscopy; Plenum Press: New York, 1982. (3) Fujiwara, M.; Hamaguchi, H.; Tasumi, M. Appl. Spectrosc. 1986, 40, 137. (4) Fujii, T.; Kamogawa, K.; Kitagawa, T. Chem. Phys. 1988, 148, 17. (5) Kamalov, V. F.; Koroteev, N. I.; Toleutaev, BB. N. In Time-Resolved Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Wiley: Chichester, 1989; Vol. 18, pp 255-300. (6) Matousek, P.; Towrie, M.; Stanley A.; Parker, A. W. Appl. Spectrosc., 1999, 53, 1485. (7) Chase, D. B. J. Am. Chem. Soc. 1986, 108, 7485. (8) Porterfield, D. R.; Campion, A. J. Am. Chem. Soc. 1988, 110, 408. (9) Jegla, J. D.; Lewis, I. R.; Griffiths, P. R. In Proc. XVth Int. Conf. Raman Spectroscopy, Pittsburgh; Stein, P., Asher, S. A., Eds.; McGraw-Hill: New York, 1996; Vol. 2, p 33. (10) Brennan, J. F., III; Wang, Y.; Dasari, R. R.; Field, M. S. Appl. Spectrosc. 1997, 51, 201. 10.1021/ac0010072 CCC: $20.00

© 2001 American Chemical Society Published on Web 03/15/2001

that multivariate data analysis can be used to extract valid quantitative analytical data from spectra with overlapping and unassigned spectral features,11-15 and it has been used for Raman analysis of industrial polymers 16,17 and gasoline blends.18,19 However, the spectra of even these samples, which have only moderate fluorescence backgrounds, must be preprocessed to remove spurious luminescence backgrounds before multivariate analysis can be applied.20 The most straightforward and robust background suppression method for routine analytical applications has been found to be the use of simple second derivatives;20 however, although second-derivative processing of the data has significant computational advantages, it has the severe disadvantage that it emphasizes any high frequency noise on the spectra. This problem can be so severe that the differentiation must be carried out as two sequential differentiation steps with smoothing after each. Unfortunately, it is precisely at the time when second derivatives are needed, that is, at high luminescence levels, that the apparent S/N ratios of the Raman bands will be lowest due to the influence of this same background. There will inevitably be a decrease in the S/N ratio of a given sample if the background level increases (due to increased photon shot noise) but with modern high throughput spectrographs and high sensitivity CCD detectors, the main factor limiting the S/N ratio in the Raman spectra of highly luminescent samples is not the shot noise on the luminescence, which is dominant at low signal levels, but is actually due to random but fixed variations in the pixel-to-pixel response on the detectors. We have recently reported the results of a very general method for correcting fixedpattern response from CCD detectors in which spectra are taken at two or more slightly shifted spectrometer positions and are then subtracted to give a derivative-like shifted, subtracted Raman (SSR) spectrum.21,22 The noise levels in such spectra can be very low, because the major cause of apparent noise in the spectra of luminescent samples arises from irregularity in the detector response, which is canceled when the shifted spectra are subtracted. We have previously concentrated on “reconstructing” the conventional Raman signal from the SSR data21,22 but now report a strategy based on using the SSR data directly in analytical spectroscopy, extracting quantitative information through multivariate (11) Wise, B. M.; Kowalski, B. R. In Process Analytical Chemistry; McLennan, F., Kowalski, B. R., Eds.; Blackie Academic & Professional: London, 1995; pp 259-312. (12) Adams, M. J. Chemometrics in Analytical Spectroscopy; Royal Society of Chemistry: Cambridge, 1995. (13) Workman, J. J., Jr.; Mobley, P. R.; Kowalski, B. R.; Bro, R. Appl. Spectrosc. Rev. 1996, 31, 73. (14) Workman, J. J., Jr.; Mobley, P. R.; Kowalski, B. R.; Bro, R. Appl. Spectrosc. Rev. 1996, 31, 337. (15) Brown, S. D. Appl. Spectrosc. 1995, 49, 14A-31A. (16) Shimoyamo, M.; Maeda, H.; Matsukawa, K.; Inove, H.; Nimomiya, T.; Ozaki, Y. Vib. Spectrosc. 1997, 14, 253. (17) Williams, K. P. J.; Everall, N. J. J. Raman Spectrosc. 1995, 26, 427. (18) Cooper, J. B.; Wise, K. L.; Welch, W. T.; Summer, M. B.; Will, B. K.; Bledsoe, R. R. Appl. Spectrosc. 1997, 51, 1613. (19) Seasholtz, M. B.; Archibald, D. D.; Lorber, A.; Kowalski, B. R. Appl. Spectrosc. 1989, 43, 1067. (20) Everall, N. J.; Davis, K.; Owen, H.; Pelletier, M. J.; Slater, J. Appl. Spectrosc. 1996, 50, 388. (21) Bell, S. E. J.; Bourguignon, E. S. O.; Dennis, A. C. Analyst 1998, 123, 1729. (22) Bell, S. E. J.; Bourguignon, E. S. O.; Dennis, A. C.; Fields, J. A.; McGarvey, J. J.; Seddon, K. R. Anal. Chem., 2000, 72, 234.

analysis rather than reconstructing the conventional data before quantitation. Here we demonstrate that by taking SSR data (which has inherently higher S/N than the undifferenced data) and then differentiating it, we obtain spectra that are similar to the those obtained from the normal two-step differentiation process and can be characterized as pseudosecond derivative, PSD, spectra. In these PSD spectra, the broad background signals are suppressed relative to the much narrower Raman bands in much the same way as is observed for normal second derivatives, and indeed, both types of spectra carry similar spectroscopic information. However, the PSD spectra have significantly higher S/N ratios than the normal second-derivative spectra. This improvement in S/N arises because the first step in generating the PSD spectra, subtracting the shifted spectra, removes the sharp features that are due to the fixed pattern response of the detector. The second step is simple differentiation of these data. In contrast, the normal second-derivative spectra are effectively generated by two sequential differentiation steps, each one of which decreases the S/N ratio on the data. We have used principal component regression and partial-leastsquares analysis of PSD spectra both to demonstrate that this approach can be used to extract accurate and precise analytical data from a simple test system and to investigate the origin and significance of factors that might prevent a satisfactory calibration. The test system that was chosen is a series of simple binary mixtures of ethanol and methanol which have been doped with varying amounts of a highly fluorescent laser dye. The objective is to demonstrate that good quantitative data can be extracted from spectra of the mixtures, even at fluorescence levels that are so high that the Raman bands are practically indistinguishable in the raw data. EXPERIMENTAL SECTION Eleven standard 200-mL methanol/ethanol stock solutions (0100% methanol in 10% increments) were prepared. Sample solutions were prepared by adding 0, 10, 40 or 450 µL aliquots of a fluorescent dye solution (1.27 × 10-5 mol dm-3 rhodamine 640 perchlorate in methanol) to 10 cm3 of each of the stock alcohol mixtures, giving 44 samples with dye concentrations of 0, 1.27, 6.32, and 60.5 × 10-8 mol dm-3. A Brimrose Corporation (BWL-20) frequency-doubled, diodepumped Nd:YVO4 laser operating at 532 nm was used for Raman excitation. Spectra were recorded using a thermoelectrically cooled CCD detector (Andor Technology, model DV401) operating at -70 °C and coupled to a 150-mm spectrograph of in-house design and construction. The spectrograph (resolution of 10 cm-1) was uncorrected for vertical astigmatism so that even point input sources at the slit produced vertical lines >100 pixels high at the detector. The spectra were recorded by binning each vertical column of pixels on the chip. The spectrophotometer was calibrated using the standard band positions of a 50/50 toluene/ acetone mixture. For each solution, a pair of spectra were recorded at the initial position before the spectrometer grating was moved manually from this position by the required-shiftvalue (22 pixels in this case) by monitoring a Hg-emission line from a fluorescent room light in real time. To minimize the signal shot noise and to ensure that the spectra were dominated by fixed pattern response, all spectra Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

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Figure 1. The Raman spectra of unadulterated methanol/ethanol calibration mixtures with compositions as marked.

Figure 2. The Raman spectra of a series of calibration solutions (pure methanol in this case) with increasing amounts of added fluorescent laser dye: a-d, 0-6.07 × 10-7 mol dm-3. Even in spectrum b, the lowest nonzero dye concentration, the fluorescence is at a level at which it should to be suppressed before multivariate calibration. At the highest dye concentration, the Raman signal is practically invisible, because it lies on top of fluorescence that is >100× more intense.

were accumulated to g106 counts. Accumulation times were typically 300-600 s/spectrum. Raman data were exported to Grams/386 (Galactic Industries Inc., Salem, NH) software for data processing. Pairs of spectra recorded at each position were compared to remove cosmic rays before being summed. Spectra of each sample at each of the two spectrometer positions were then subtracted and differentiated (second order Savitsky-Golay, 7 points) to generate the PSD spectra, which were then normalized to the intensity of the Raman signal at column number 919 (see Figure 3). This position was chosen because the spectra of both alcohols have strong Raman signals at this point. Alternatively, second derivatives of spectra taken at one of the two spectrometer positions (second order Savitsky-Golay, 7 points) were taken directly. Finally, the data were 2060 Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

exported to Simca-P 8.0 software (Umetrics AB, SE90719 Umea, Sweden) for multivariate analysis. This software performs an internal cross-validation of data using a “leave one out” rotation approach. Because there are no Raman bands between columns 300 and 760 in the spectra, data from these pixels were eliminated in all multivariate calculations and this region does not appear in the loading plots shown in Figures 5 and 6. RESULTS AND DISCUSSION Figure 1 shows a representative series of the Raman spectra for unadulterated methanol/ethanol calibration mixtures with different methanol/ethanol ratios. In the absence of any added laser dye, the large changes in the spectra and the low backgrounds would make determination of the composition trivial;

Figure 3. Comparison of the high cm-1 (most intense) region of the Raman spectrum of a methanol solution doped with the highest concentration of laser dye (6.05 × 10-7 mol dm-3): (a) SSR spectrum obtained by subtracting two spectra, obtained at slightly different spectrometer grating positions 22 columns apart; (b) pseudosecondderivative (PSD) spectrum, obtained by differentation of the SSR spectrum shown as (a); (c) first derivative; (d) second derivative. The apparent S/N ratio of the PSD spectrum is very much higher than that of the second-derivative spectrum. A clear low-response pixel gives rise to the sharp features at ∼2780 cm-1 on all of the spectra, but other, smaller variations in detector response also contribute to the noise on the first- and second-derivative spectra.

however, the spectral features of interest become more difficult to discern as the level of background fluorescence is increased. Figure 2 shows the Raman spectra of a series of calibration solutions (pure methanol in this case) to which have been added increasing amounts of fluorescent laser dye. The bottom spectrum has zero added dye; the top spectrum is that with the largest dye addition. Even at the lowest nonzero dye concentration, the fluorescence is already at the level where it would be regarded as a problem for multivariate data analysis, but at the highest dye concentration, the Raman signal is practically invisible because it lies on top of the fluorescence that is >100× larger. The background can be suppressed relative to the Raman signal either by taking the first derivative of the spectrum or by subtracting two spectra obtained at slightly different spectrometer grating positions (SSR spectra). Figure 3 compares the first derivative and SSR spectra of a simple methanol solution that was doped with the highest dye concentration. The results of then differentiating these spectra to obtain a true second derivative and

Figure 4. The effect of increasing background level on (a-d) second-derivative and (e-h) PSD spectra of methanol/dye solutions. Dye concentrations range from 0 (a, e) to 6.05 × 10-7 mol dm-3 (d, h). At the lowest dye level, the S/N ratio of the second-derivative spectra is acceptable, but as the luminescence background increases, there is a corresponding fall in the apparent S/N of the secondderivative spectra as the effect of the fixed pattern irregularly starts to become apparent.

a PSD spectrum are also shown in the figure. The apparent S/N ratio of the PSD spectrum is very much higher than that of the second-derivative spectrum. This large improvement is due to the strong suppression of the fixed pattern irregularly on the detector that occurs when two slightly shifted spectra are subtracted from each other. Conversely, the fixed pattern response is emphasized in the second-derivative spectrum, because the regions of low detector response are typically only 1-2 pixels wide and, thus, have highly sloped sides. There is a clear low-response pixel in the spectral region shown in Figure 3, which gives rise to the strong sharp features at 2780 cm-1, but other smaller variations in detector response also contribute to the noise on the first- and second-derivative spectra. It is important to note that these lowresponse pixels are not the manufacturing defects that give rise to dead pixels in poor quality detectors; here, the response of even the worst pixel column is ∼0.993× the response of adjacent columns. It is only because the background level is high that the small drop in response becomes significant as compared to the intensity of the Raman bands. Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

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Figure 5. (a) Loading plot for the first principal component for data set A, which excludes the data from the most heavily doped calibration solutions; (b)PSD spectrum of a 50/50 ethanol/methanol mixture with no added laser dye. The agreement between both is a good indicator of a physically meaningful model; the sharp discontinuity at column 300 in both traces is due to exclusion of data in the center of the spectral range, as described in the text.

The effect of increasing background level on the PSD and second-derivative spectra of the same calibration solution is shown in Figure 4. At the lowest dye level, the S/N ratio of the secondderivative spectra is acceptable, but as the luminescence background increases, there is a corresponding fall in the apparent S/N of the second-derivative spectra as the effect of the fixed pattern irregularly starts to become apparent. At the second highest dye concentration, the largest fixed pattern noise spike at 2780 cm-1 is clearly visible, but at the highest dye concentration, this feature is 0.8× of the intensity of the Raman band at column number 853(2862 cm-1), which is the most intense Raman feature in the entire spectrum. At this dye concentration, the remainder of the Raman bands at lower cm-1 are completely obscured, and even the second most intense band in the spectrum, which is clearly visible in Figure 4a-c now lies among sharp features which are ∼0.7× its intensity. However, the PSD spectra are barely affected right through the range of fluorescence background levels, even at the highest dye concentration the magnitude of the largest “noise” feature at 2780 cm-1 is 0.1× the intensity of the largest Raman feature. The PSD data shown in Figure 4, or rather, the data from the full set of 44 calibration mixtures, could be used for a simple 2062

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calibration based on measuring relative peak heights or areas of the strongest bands, but multivariate analysis is a much more efficient way of extracting the maximum analytical data from the spectra, so we have chosen to follow this route. We have chosen two subsets of the data for analysis. One set, A, which models “normal” data sets in which there is some luminescence, but it does not reach extreme values, included all of the sets except those that were obtained at the highest concentration of added dye. The second set, B, chosen to illustrate how far this method can be extended, included all of the data in the calibration. For both of the data sets, the first analysis step was to scale all of the PSD data to the intensity of the peak at pixel 919. We then examined the contribution to the variance in the data using two and then three principal components. For set A, we found that the data could be satisfactorily fitted by just two principal components, and the cross-validated prediction error was 3.2% with 98.4 and 1.3% of the variance accounted for by the first and second components. The loading plot for the first principal component within this model is shown in Figure 5, where it is compared to the PSD spectrum of a 50/50 ethanol/ methanol mixture with no added laser dye. The agreement between both plots is a good indicator of a physically meaningful model. Under these conditions, for which the fluorescence intensity is up to only 10 times stronger than the most intense Raman bands, the overwhelming majority of the variance is explained by the first principal component. This is important because it shows that the only significant variation between the PSD spectra of the samples, irrespective of the amounts of added laser dye, was the methanol/ethanol ratio. This confirms the observation that the PSD spectra of samples with moderate amounts of laser dye are practically indistinguishable from spectra of pure mixtures with the same composition; that is, the PSD method gives effective background suppression, and the PSD data are effectively univariate. The data in set B would be expected to be much more challenging because it includes data, such as that shown in Figure 2d, in which the luminescence intensity is so high that it almost completely conceals the strongest of the underlying Raman bands. However, the PSD spectra of even these samples contain good quality data, as shown in Figure 4(h). In particular, they are dominated by the Raman signals and low levels of true random noise (photon shot noise), and the contribution from fixed pattern detector noise, although visible, is a very minor component. We have found that even these data can be fitted by just two principal components. The contribution to the variance of the first component (shown in Figure 6) is lower than in the case in set A (80.7% vs 98.4%), but the addition of a second component generates a model which accounts for 99.7% of the variance. Again, this is physically meaningful, because the PSD spectra of the calibration mixtures with the highest amount of added laser dye show some baseline offset due to incomplete suppression of the intense fluorescence background in the subtraction/differentiation process. Inclusion of these data in the set to be modeled would be expected to lead to a minimum-two-component model; however, we would stress that the model here has been generated using just these expected two components. Indeed, any need for additional components would have been an indication of problems within the procedure that were being concealed by the efficiency

Figure 6. Loading plot for the first principal component for data set B, which includes data from all of the calibration solutions, including the most heavily doped set. The plot is similar to that shown in Figure 5 but has a smoothly varying background component.

Figure 7. Calibration plot of observed vs predicted concentration values from the two-component model of the full data set B using PSDs. The RMS prediction error is 3.3%. No satisfactory model could be determined for these samples using second derivatives as the input data.

with which multivariate methods can fit even poor quality data when a large number of components are used. The RMS prediction error for data set B is 3.3%, which is similar to that of set A, and reflects the fact that the reduction in fixed pattern detector response and background flurorescence levels brought about by generating PSD spectra means that the level of background fluorescence in the sample has little effect on the ability of the model to determine the sample composition. The calibration plot of observed vs predicted concentration values for the data set B is shown in Figure 7. We have repeated the analysis using second-derivative data taken from the same spectra used to make the sets A and B that are described above. For the less fluorescent set A, the secondderivative spectra could be used to generate a satisfactory model that was near univariate. The contributions to these variances of

the first and second principal components were 94.5 and 4.3%, respectively; however, even in this set, the RMS prediction error was 6.5% which is approximately twice the 3.2% value obtained by using the PSD method. The success of the second-derivative method is not surprising, because the conditions used in the experiments here (with vertical dispersion of the signal on the CCD) were designed to reduce the effect of fixed pattern irregularity to a much lower level than what is normally found with imaging spectrographs. This in turn translates into lower apparent noise on the fluorescent background and the second-derivative spectra. However, as the fluorescence level increases, for example, in the data set B, the dominant effect of fixed pattern irregularity on the second-derivative spectra becomes obvious and, because it is not a random effect, increasing signal accumulation does not improve the spectra. We have tried Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

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to fit the full data set B with two and three principal components but found that inclusion of the most fluorescent data made it impossible to find a satisfactory model with this number of principal components. We could, of course, increase the number of principal components in the model so that more of the variance was explained, but even with a physically unrealistic model with eight principal components, the prediction error was >50%, and meaningful data could not be extracted from the second-derivative spectra when the most fluorescent samples were included. CONCLUSIONS Multivariate data analysis does not occupy the central position in Raman spectroscopy that it does in NIR spectroscopy. In part, this is probably due to the highly structured nature of typical Raman spectra, which allows conventional univariate analysis to be carried out in a straightforward way. However, as the complexity of the problems addressed by Raman methods increases, it is clear that multivariate methods will become more widely used, which in turn means that the problem of treating moderate fluorescence backgrounds in multivariate calibrations of Raman data will become more pressing. The simplest answer to fluorescence problems is to try to find experimental conditions in which there is low fluorescence and the advantages of FT-Raman instruments for analysis of industrial samples, in particular the dramatic lowering of background fluorescence levels that can be observed, have been discussed extensively since they first became commercially available.7 Only recently has the advantage of the higher sensitivity of dispersive Raman spectroscopy over FTRaman methods received close attention. In particular, the use of far red excitation coupled with multichannel detectors has been shown to be an excellent compromise for many analytes that show strong fluorescence with visible excitation but significantly less when excitation wavelengths > 700 nm are used. However, even when fluorescence levels are reduced by changing excitation wavelengths, it will often be necessary to preprocess the data using second derivatives before they are suitable for multivariate analysis.20 The advantage of the technique described here is that although it is conceptually similar to simple second-derivative spectroscopy, it has the advantage that it minimizes the apparent noise on the signals that arises from the variations in pixel-topixel response that are a characteristic of CCD detectors. These variations, although minor in the raw data, become more significant when second derivatives are used and when the spectra contain Raman bands that lie on top of a broad (nominally smooth) fluorescence background. The experimental conditions used here were designed to minimize the effect of fixed pattern variations by use of a nonimaging spectrograph that smears the signal at each cm-1 over a vertical column of pixels that are then binned together during readout. Under these conditions, low response due to a single pixel is partly averaged out by the higher response of the other pixels that lie in the same vertical column. Indeed, we have found that the fixed pattern irregularity in response drops from ca. (1% for a single row of pixels to ca. (0.1% per vertical column; however, even under these conditions, the fixed pattern response irregularly becomes very significant in second-derivative spectra taken at high background fluorescence levels. In effect, the irregular response sets a ceiling above which meaningful analytical data cannot be extracted from simple second derivatives. As the data in Table 1 2064 Analytical Chemistry, Vol. 73, No. 9, May 1, 2001

Table 1. Summary of the Results of Partial-Least-Squares Calibration of Second-Derivative and PSD Spectra of Two Data Sets, A and B, That Differ Only by the Inclusion of Data from Solutions for Which the Fluorescence Background Is g100× Stronger than the Raman Signala

method

% contribution to variance (component no.)

std error in prediction %

A

PSD second derivative

98.4 (1), 1.3 (2) 94.5 (1), 4.3 (2)

3.2 6.5

B

PSD second derivative

80.7 (1), 19.0 (2)

3.3

sample set

a No satisfactory calibration could be obtained for the full data set using standard second-derivative data pretreatment.

show, in this experiment, the ceiling is relatively high, and fluorescence that is up to 10× stronger than the strongest Raman bands does not prevent sample analysis, albeit with prediction errors twice as high as those of the PSD method. Above this ceiling, the prediction errors are so large that the calibration is meaningless. Under conditions in which the fixed pattern response has not been carefully minimized, that is, with imaging spectrographs, the fluorescence level where meaningful data become difficult to obtain is correspondingly lower, so that with 1% irregularity, even a 5-fold fluorescence/Raman signal ratio will be a severe problem. This agrees with literature reports that show that satisfactory calibrations were only obtained after averaging of spectra or smoothing after each differentiation step, even when background levels were of only the same order as the Raman bands of interest.20 Because uncorrected variations in pixel response of even 1% have a significant effect on quantitative analysis of luminescent samples, any source of variation of this magnitude is important. Although it is normally assumed that all the variation in CCD response arises from manufacturing defects, reductions in response of this magnitude can arise from minor dust contamination on the outer window of the detector (a 6 µm2 shadow masks 1% of a 625 µm2 pixel). This means that even if multivariate calibrations of second-derivative data are established, they are still vulnerable to later adventitious dust contamination, which will cause the appearance of new artifacts on the data. The use of the PSD spectra minimizes the effect of the fixed pattern response to the extent that even at apparently overwhelmingly high fluorescence levels, the PSD spectra are dominated by photon shot noise. With the PSD method, dust contamination becomes less important, because the effect of fixed pattern response is corrected on each spectral run and automatically changes if the form of the fixed pattern is altered, for example, by shadowing due to dust.23 In the data shown here we have deliberately chosen the shift between the spectra to be >2× fwhm of the Raman bands to emphasize the difference between the true second-derivative data and the PSD data. Moving to a smaller shift value makes the PSD (23) In the PSD spectra, the effect of the response irregularity is minimized rather than eliminated, because the absolute magnitude of the signal on a given pixel will be different at different spectrometer positions, but complete elimination would require subtraction of spectra with the same absolute signal intensity.

spectra more closely resemble the second derivatives and also decreases the residual broad signal which results from shifting and differentiation of the broad background fluorescence. We have kept the value large to illustrate that the method does not depend on the use of small shift values, but in cases where the background was changing shape as well as intensity, it would be good practice to minimize the residual background level to reduce the weighting of the broad signals in the calibration. Similarly, we used only binary mixtures of alcohols, because they provide a good illustration of the method, but the method is completely general and it could equally well be used for the analysis of more complex mixtures if required. This PSD method clearly has great potential for general purpose Raman analytical chemistry. It does not depend on

specialized equipment, is computationally undemanding, and gives stable and robust calibrations, even when the luminescence background level of the samples fluctuates between extremes of practically zero to completely dominating the Raman signal. ACKNOWLEDGMENT The authors thank the Teaching Company Directorate for the award of a grant, which made this work possible.

Received for review August 22, 2000. Accepted January 29, 2001. AC0010072

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