22 DERIVATIVE SPECTROSCOPY Anal. Proc. Derivative Spectroscopy and its Applications in Analysis The following are summaries of the seven papers presented at a Joint Meeting of the Scottish, North East and North West Regions and Special Techniques and Joint Pharmaceutical Analysis Groups held at Heriot-Watt University, Edinburgh, on March 19th, 1980. Derivative Spectroscopy : Theoretical Aspects. Thomas C. O'Haver Plenary Lecture Department of Chemistry, University of Maryland, College Park, Md. 20742, USA The derivative technique is becoming increasingly popular in analytical spectrophotometry 'as a resolution enhancement technique, to facilitate the detection and location of the wave- lengths of poorly resolved components of a complex spectrum: and as a background correction technique, to reduce the effect of spectral background interferences in quantitative analytical spectrophotometry.2 A significant disadvantage to the derivative technique, however, is that the signal to noise ratio (SNR) becomes worse at progressively higher derivative orders3 The purpose of this paper is to investigate on a theoretical basis the effect of differentiation on SNR so as to provide the experimenter with a rational approach to the optimisation of SNR in derivative spectroscopy.Consider an experimental spectrum that has been measured by a discrete sampling technique and consists of a series of amplitudes (or absorbances, in absorption spectrometry) taken at discrete, equally spaced wavelength increments a,, a2, a3, a4, . . ., where a, represents the amplitude at wavelength 1, and so on.Consider that this series consists only of noise, i.e., that there is no signal. Let us assume that the noise is independent of the amplitude of the signal, has a white spectral distribution and a Gaussian amplitude probability distribution and that each element in the series is statistically independent of its neighbours. The noise may therefore be expressed as the standard deviation of all the elements in the series, which we will give the symbol oo, the subscript referring to the "zeroth"-order derivative. It can be shown that each element in the nth derivative calculated by the method of successiveJanuary, 1982 DERIVATIVE SPECTROSCOPY 23 differences is a linear combination of n + 1 adjacent elements from the original (zeroth order) series and the weighting coefficients are given by the binomial coefficients of order n : 92 n! & = (-1P * (n - ai+m m=O where d; is the ith element of the nth derivative.The standard deviation of the nth-order derivative can be calculated by the usual rules for error propagation and is simply the weighted quadratic sum of the standard deviation of its terms: The signal depends on the shape of the spectrum. The derivatives of Gaussian and Lorentzian bands have been evaluated analytically.4 We define the “signal” as the difference between the largest (most positive) and the smallest (most negative) value of the derivative. Relative SNRs defined in this way for the first four derivatives of Gaussian and Lorentzian bands are listed in Table I, where W is the number of points in the peak full-width at half-maximum (FWHM).Note that the SNR decreases rapidly with increasing derivative order when W is large. Typically, W must be at least 5-10 to define the width and height of the peak adequately and it is often much larger. If W = 10 the relative SNRs of the first four derivatives of a Gaussian band are 0.2, 0.032, 0.008 and 0.0017. Clearly, if W is large, the SNR of the higher derivatives will be very poor even if the SNR of the original spectrum is good. TABLE I RELATIVE SIGNAL TO NOISE RATIOS OF UNSMOOTHED DERIVATIVES Band shape* Derivative (-A 7 order Gaussian Lorentzian 0 1 1 1 2.021 w 1.84lW 3 8.101 v-3 16.71 W8 4 17.81 W 641 W4 2 3.261 W2 4.11 ws * W = number of points in the FWHM of band. How, then, is it possible to use the derivative technique effectively? The answer is that all practical differentiation techniques include some degree of Zow-pass jltering or smoothing to control the increase in noise that is the inevitable result of differentiation of a noisy signal.Smoothing is also sometimes used in normal (zeroth order) spectroscopy, but its value there is largely cosmetic; the degree of SNR improvement that can be achieved by smoothing is limited, typically 2- to &fold. However, it turns out that smoothing is much more important in derivative spectroscopy; that is, the obtainable degree of SNR improvement is much greater than in normal spectroscopy. The reason for this is that the increase in noise caused by differentiation is largely due to an increase in high-frequency noise, the process of differentiation being effectively a kind of high-pass filtering. Thus, the extra noise is especially easy to reduce by a low-pass smoothing process.The process of smoothing involves a convolution of the data series with a smoothing function consisting of a set of weighting coefficients. Each point in the smoothed array is a linear combination of a group of adjacent points in the original series each multiplied by a weighting coefficient. The different types of smooths differ only in the way the coefficients are calculated. The simplest type of smooth is the equally weighted sliding average, in which the weighting coefficients are equal. Each point in the smoothed series is the simple average of N adjacent points in the original series, where N is the smooth width.The value of the smoothing co- efficients is therefore simply 1/N. The effect of smoothing a peak-type signal is both to reduce noise, which is desirable, and to distort the signal, which is undesirable but unavoidable. The distortion is seen as an attenuation in peak height and a slight increase in peak width. The extent of this distortion24 DERIVATIVE SPECTROSCOPY Anal. PYOC. depends on the ratio of the width of the smooth to the FWHM of the peak, which is called the smoothing It was seen in Table I that the SNR decreases as the derivative order increases. Therefore, it is logical that the amount of smoothing would have to be increased as the derivative order is increased in order to control this SNR degradation.This must be done, however, not by increasing the smoothing ratio but rather by increasing the number of times that the smoothing is passed throagh the data series. Fig. 1 shows the trade-off between attenuation and SNR for the second derivative of a Gaussian band smoothed by one, two and three passes of a sliding average smooth. This plot shows that three passes of the smooth give a better trade-off between SNR improvement and attenuation than one or two passes. In general, it can be shown that for the nth derivative, n + 1 passes are required and the standard deviation of the final series is . . (2) where n is the derivative order and N is the number of points in the smooth. It can be seen from the denominator of this term that the noise reduction with increasing N will be greatest for the higher derivatives.Similarly, the standard deviations of the zeroth, first and second derivatives with, respectively, one, two and three passes of an N-point quadratic-cubic smooth6 are found to be 1.7aO/.t/N, ~ c T ~ / N ~ . ~ and 2 2 0 , / N ~ . ~ . For a given value of N , the quadratic-cubic is less effective at reducing noise but also causes less peak attenuation than the simple sliding average. We have found that, as for the sliding average smooth, the quadratic-cubic smooth also requires n + 1 passes for the nth derivative. Using the above analysis to calculate the noise, the effect of smoothing on the SNRs for any given band shape can be easily evaluated by determining the p2ak-height attenuation caused by smoothing noiseless model bands.The trade-off between attenuation and SNR as a function of smoothing ratio is illustrated in Fig. 2 for the second derivative of a Gaussian band smoothed by three passes of a sliding-average smooth. The optimum SNR occurs at a smoothing ratio of about 1.5, at which point the peak-height attenuation factor is about 0.1. 3 2 .^ o 1 4- 2 $ 0.5 0 0 .- c, 0.2 C G) z 0.1 1.0 0.8 0.6 0.4 0.2 Attenuation factor Fig. 1. The trade-off between signal to noise ratio and peak- height attenuation for the second derivative of a Gaussian band smoothed by one, two and three passes of a sliding average smooth, showing that three passes is always better than one or two. 1 .o 0.9 .O 0.8 2 0.7 .? 0.6 0.5 0.4 6 0.3 c. Q) ix 0.2 0.1 0 1 2 3 Smoothing ratio Fig.2. Attenuation factor and relative signal to noise ratio as a function of smoothing ratio for the second derivative of a Gaus- sian band smoothed by three passes of a sliding average smooth.January, 1982 DERIVATIVE SPECTROSCOPY 25 Although the peak-height attenuation caused by smoothing will not cause a systematic error in a relative analytical method calibrated by appropriate standards, excessive attenuation is undesirable for two reasons. Firstly, in many real applications the measured band will be accompanied by a background signal that is less strongly attenuated by smoothing than the measured band itself, thereby reducing the signal to background ratio. Secondly, smoothing increases the width of the peak and reduces the effective spectral resolution. Inasmuch as the usual reasons for using the derivative technique in the first place are to reduce the effect of spectral background and/or to improve the effective spectral resolution, smoothing acts in the opposite manner and, if overdone, can cancel the advantages offered by the derivative method.Thus it will always be advantageous to consider the trade-off between SNR im- provement and peak-height attenuation as smoothing ratio is increased. This can be done conveniently by plotting SNR versus attenuation, with smoothing ratio being the “hidden parameter.” Such plots for the zeroth, first and second derivatives of Gaussian and Lorentzian bands with eight-point FWHM smoothed with n + 1 passes of sliding average and quadratic- cubic smooths are shown in Figs. 3,4 and 5.From an inspection of these figures we can make the following observations : 1. The achievable relative SNR improvement (relative to the SNR without smoothing) is much greater for the derivatives than for the normal (zeroth derivative) spectrum. Had the peak width W been larger than 8, the difference would have been even more dramatic. 3 2 .- E l 2 .g 0.5 S 0 Y - 0.2 iTj 0.1 S m 0.05 1.0 0.8 0.6 0.4 Attenuation factor .- 0 2 +-’ 2 al 1.0 0.5 .- 0 +-’ - P .$ 0.2 Q) P al .- 2 0.1 - LT 0.05 Fig. 3. The trade-off between signal to noise ratio and attenuation factor for the zeroth, first and second derivatives of a Gaussian band with an eight-point FWHM smoothed by one, two and three passes (respec- tively) of a sliding average smooth. 1.0 0.8 0.6 0.4 Attenuation factor Fig.4. As Fig. 3, except for a quadratic- cubic smooth. 1.0 0.8 0.6 0.4- Attenuation factor Fig. 5. As Fig. 4, except for a Lorent- zian band, quadratic- cubic smooth. 2. With sufficient smoothing, the SNR of the derivatives can exceed that of the unsmoothed normal spectrum (relative SNR = l.O), although this occurs at progressively greater attenuation as the derivative order increases. Ultimately, the SNR of the derivatives can exceed that of the normal spectrum smoothed to optimum SNR, but this occurs only at rather drastic attenuations. 3. The effect of differentiation on SNR depends on the peak shape, type of smooth and especially on the smoothing ratio. However, for the most commonly used smoothing ratios in the range 0.2-0.5, the previously stated generalisation’ that the SNR decreases by a factor of 2 for each stage of differentiation is supported approximately.26 DERIVATIVE SPECTROSCOPY Anal.Proc. 4. The quadratic-cubic and sliding average smooths achieve about the same ultimate SNRs, but the quadratic-cubic gives a better trade-off between SNR and attenuation by about a factor of 2. 5. Gaussian and Lorentzian derivatives exhibit the same general behaviour, but Lorentzian derivatives suffer significantly more attenuation when smoothed to a given SNR improve- ment. (As expected, bands with mixed shapes exhibit intermediate behaviour.) These conclusions can be demonstrated and supported by differentiation and smoothing of realistic computer-generated noisy model bands. Fig. 6A shows an isolated single Gaussian band with a 50-point half-width and an r.m.s.SNR of 100. The noise is white. The second derivative, without smoothing, is shown in Fig. 6B. The SNR of this derivative is predicted (Table I) to be 100 (3.26/502) = 0.13, so it is no surprise that a signal cannot be detected here. Figs. 6C, D and E show the result of progressively larger amounts of sliding average smoothing, Fig. 6. Graphic examples of the effect of differentiation and smoothing on the signal to noise A : Original (zeroth derivative) B: Second deriva- C: Second derivative after two passes of an 11-point sliding average D: After three passes of an 11-point sliding E: After three passes of 25-point sliding average smooth, ratio and peak height of- the second derivative of a Gaussian band.band; Gaussian; 50 point FWHM; signal to noise ratio = 100; white noise. tive, without smoothing. smooth, greater vertical scale expansion than B. average smooth, same scale as C. same scale as C. showing both the effect of the number of passes and the smoothing width. The trade-off between SNR improvement and attenuation is evident. In Fig. 6E the smoothing ratio is 0.5. The SNR can be calculated by multiplying the SNR without smoothing (0.13, from Table I) by Nn+Oa5 and multiplying the result by the attenuation factor (0.63, from Fig. 2) : (0.13)(3125)(0.63) = 2.6 x lo2 Thus the derivative in Fig. 6E has been smoothed to a SNR better than that of the original (unsmoothed) spectrum. Fig. 7 demonstrates that with even more smoothing (smoothing ratio = 1.0 for sliding average smooth) the SNR of the smoothed derivatives equals that of the optimally smoothed original spectrum.However, the figure also illustrates why this is not usually a useful goal; the width of the central maximum of the second derivative has been broadened by smoothing to such an extent that it is now no narrower than the smoothed original peak, i.e., the resolu- tion advantage of the second derivative has been neutralised by smoothing. The same be- haviour has been observed up to the sixth derivative and is probably general for all derivative orders. The advantage of the quadratic-cubic smooth over the sliding average, which is its better trade-off between distortion and SNR improvement, is especially important when the balance between those two factors is critical, as in the example in Fig.8. The spectrum (Fig. 8A) consists of two overlapping Gaussian components of equal width separated by slightly less than their FWHM. The right-hand component has half the intensity of the left-hand com- ponent. In this example, the second derivative mode is used in resolution-enhancement service in order to detect and locate the position of the smaller (right-hand) component. That this is feasible under ideal conditions is demonstrated by Fig. SB, which is the theoretical shape of the second derivative without noise and without smoothing. The two minima correspond closely to the positions of the two components in the original spectrum. However, the separation of these two components is close to the The r.m.s. SNR is 100 (white noise).January, 1982 DERIVATIVE SPECTROSCOPY 27 Fig.7. Zeroth, first and second derivatives of a noisy Gaussian band smoothed to nearly maximum signal to noise ratio, illustrating that smoothing to such a large extent avoids the SNR degradation of differentiation but also cancels the resolution advantages of the higher derivatives. Sliding average, smoothing ratio = 1.0. theoretical minimum for resolution of Gaussians in the second derivative.* In such a case, the broadening effect of smoothing is especially troublesome. Figs. SC-J show second derivatives of the original noisy spectrum smoothed with sliding average (Figs. SC-J) and quadratic-cubic (Figs. 8H- J) smooths with different smoothing ratios. Theeffect of broadening and loss of effective spectral solution is evident, particularly for the sliding average smooth.The superiority of the quadratic-cubic smooth is clear, as it gives about a factor of two lower distortion and better SNR than the sliding average. On the other hand, the quadratic- cubic smooth requires more computation time than the sliding average, both because the required smoothing ratios are about twice as large and because the computations themselves are more complex, requiring N multiplications and N additions, whereas the sliding average requires only N additions and one multiplication. In general, the selection of the optimum smoothing ratio depends on the purpose for which the derivative technique is used. In using the even derivatives for resolution enhancement purposes, relatively small smoothing ratios (of the order of 0.2 for the sliding average or Normal Ideal shape (SNR = 100 unsmoothed) noise or smoothing of 2nd derivative without Normalised second derivatives C f Sliding beverage I smooths Three-passes smoothing ratio given Quadratic-cubic smooths -+ Fig.8. Effect of smoothing ratio and smooth type on the trade-off between signal to noise ratio and effective resolution. A : The original spectrum, consisting of two overlapping Gaussian bands of equal width and a 2: 1 intensity ratio separated by 0.8 of their width; white noise, SNR = 100, unsmoothed. B: The theoretical shape of the second derivative, without noise and without smoothing. The two minima correspond to the two components in the original band. C-G: Second derivatives of the original noisy spectrum, smoothed with three passes of a sliding average smooth, smoothing ratios 0.1, 0.15, 0.2, 0.3 and 0.5.H-J: Same, but with quadratic-cubic smooths, smoothing ratios 0.4, 0.5 and 0.6. The quadratic-cubic smooth is seen to offer a better trade-off between SNR and distortion. All derivatives are normalised to the same height.28 DERIVATIVE SPECTROSCOPY Anal. Proc. 0.5 for the quadratic-cubic) will assure that very little loss in effective resolution will result. In this case a significant loss in SNR will have to be tolerated. In quantitative analytical applications, in which the derivative technique is used to remove or reduce a broadly curved background, significantly larger smooth ratios may be profitably employed, typically 0.5 for the sliding average and 1.0 for the quadratic-cubic.Larger smoothing ratios will yield little SNR improvement at the expense of considerable further peak attenuation and broadening. I t is rarely advisable to smooth to the optimum SNR. In quantitative work the aim in selecting the smoothing ratio is to optimise the trade-off between random measurement errors caused by the noise and the measurement errors, random and systematic, caused by the presence and variability of the background. If the shape and variability of the back- ground can be predicted, then in principle it should be possible to arrive at a truly optimum smoothing ratio that minimises the sum of noise errors and background errors. The width W of the measured spectral peak, here expressed as the number of points in the FWHM, is determined by the spectral scan rate and, in a digital system, by the data sampling rate.It can be shown that if the smoothing ratio is held constant, the SNR is proportional to 4 W for all derivative orders. Therefore, the values of SNR given in Figs. 3, 4 and 5 for an eight-point wide peak can be converted into any other peak width W by multiplying by dW/S. The usual way of changing W is to change the spectral scan rate. If the scan rate is changed at a constant data sampling rate, W changes inversely with scan rate and thus SNR is inversely proportional to the square root of scan rate. If the data rate is changed in proportion to the scan rate, W remains constant but the averaging time varies inversely with the data rate and noise varies with the square root of the averaging time.Therefore, in this case also the SNR is inversely proportional to the square root of the scan rate. The same holds for real-time differentiators; as the scan rate is changed and the system response time is varied to keep the smoothing ratio constant, the band width varies directly with scan rate, and the noise varies inversely with the band width. This result is significant because it is contrary to the expectation based on signal amplitude alone; if the scan rate is increased, the derivative output signal increases but, if the smoothing ratio is kept constant, the SNR decreases. On the other hand, because one generally uses smoothing ratios below the maxi- inum SNR, increasing the scan rate at a constant differentiation response time will increase the SNR because the smoothing ratio is increased. References 1.2. 3. 4. 5. 6. 7 . 8. Butler, W. L., Methods Enzymol., 1979, 56, 501 and references cited t‘nerein. Talsky, G., Mayring, L., and Kreuzer, H., Angew. Chem., Int. E d . Engl., 1978, 17, 735. Cahill, J. E., Am. Lab., 1979, 11, 79. Morrey, J . R., Anal. Chem., 1968, 40, 905. Enke, C. G., and Nieman, T. A., Anal. Chem., 1976, 48, 705% Savitzky, A,, and Golay, M., Anal. Chem., 1964, 36, 1627. O’Haver, T. C., and Green, G. L., Anal. Chem., 1976, 48, 312. Pavlath, A. E., and Millard, M. M., AppZ. Spectrosc., 1979, 33, 502. Higher Derivative Methods in Ultraviolet - Visible and Infrared Spectrophotometry Anthony F. Fell and Geoffrey Smith Department of Pharmacy, Heriot- Watt University, Edinbwgh, EH1 2HJ About 60 years ago Lord Rutherford suggested the first derivative for more sensitive mass spectrometric detection of gas excitation potentia1s.l In 1953, the concept of second and higher derivative detection was patented by two British industrial chemist^,^-^ who first demonstrated the usefulness of higher derivatives in analytical spectroscopy, as discussed later by Martin.5*6 Morrey’s classic essay on the properties of computer-generated derivative functions’ and Butler’s computer work on fourth and higher derivative spectra*-1° coincided with the adventJanuary, 1982 DERIVATIVE SPECTROSCOPY 29 of low-noise operational amplifiers.These led to the high-quality electronic differentiators used in early work on derivative luminescence spectroscopyll 9 1 2 and on derivative infrared spectroscopy.13 More recently, there have been several studies in the biomedical area based on second or higher derivatives of ultraviolet - visible absorption spectra.14-18 The renaissance of interest in derivative spectroscopy is such that the method has been patented again, to give an elegant device for low-noise derivatives up to eighth order.lg Theoretical studies, however, indicate that for resolution enhancement in the ultraviolet - visible range, the most useful derivatives will be second or fourth order.20 These can be generated by careful combination of commercial units for accurate quantitative analysis.21 9 2 2 Recent developments in microcomputer tech- n01ogy~~ permit good quality higher derivatives and enable the derivative method to be simplified, In this paper, the rationale for developing analytical methods based on higher derivative spectroscopy is discussed with reference to applications in the biomedical sciences.Principal Features of Derivative Functions The basic properties of derivative functions have been discussed elsewhere in the context of spectroscopy.' 920924 The derivative technique is, however, perfectly general in its application, and can be used equally for chromatographic or densitometric data, e.g., gas - liquid chromatography (GLC), high-performance liquid chromatography (HPLC) or densito- metric scans of thin-layer plates or electrophoret~grams.~~ >26 Although the first derivative has been more widely known for the detection and characterisation of spectroscopic peaks,27 it turns out that the second and higher even derivatives of absorbance or signal intensity (d2A/dA2, d4A/dA4, .. .) are potentially more useful where Gaussian or Lorentzian functions approximate the data profile. By contrast, in cases where titration curves, reflectance data or thermal analysis curves are recorded, the odd derivatives are used to transform the disperse inflection to a peak for interpretation. The present discussion is concerned with the even derivatives of Gaussian or Lorentzian curves, which are seen as bipolar functions of alter- nating sign, flanked by satellites equal in number to the derivative order. The centroid coincides with the original peak, whose band width decreases progressively with derivative order.This is the key to the potential enhancement of resolution of overlapping bands. Significantly, the derivative process discriminates against broad bands, emphasising sharper features to an extent that increases with increasing derivative order, because for Gaussian or Lorentzian bands the amplitude, Dn, of the nth derivative is inversely related to the original band width, W , raised to the nth degree: Thus, for two coincident bands of equal intensity, the derivative amplitude of the sharper band (X) is greater than that of the broader band (Y) by a factor that increases with in- creasing derivative order (Fig. 1) : This feature, first reported in 19708928 and recently discussed by Cahi11,29 may account for the increase in effective detection sensitivity often observed in second and fourth derivative ~pectra.8.l~ 930 scattering and higher order polynomial interference in spectroscopy, or drifting base lines in chromatograms, are progressively suppressed as a logical consequence of the derivative technique.20 Derivative transformation does not intrinsically increase the information content of spectroscopic or chromatographic data (in fact some information is lost, e.g., constant factors).Rather does the derivative method permit more satisfactory discrimination against inter- ference, and emphasise subtle features of the data by presenting them in a new and visually more accessible way. Greater resolution of overlapping bands, reduction of systematic errors caused by matrix interferences and a sensitive qualitative profile for compound characterisa- tion can be conferred by careful application of the higher derivative method.Other types of background disturbance, such as RayleighAnal. Proc. 30 DERIVATIVE SPECTROSCOPY Strategy for Method Development In essence, the development of a derivative spectroscopic assay is little different from a regular spectroscopic assay. The principal requirements remain assay linearity, accuracy, reproducibility, analyte independence of matrix and satisfactory comparison with an accepted referee method. Any difference arises from the greater number of instrumental variables to be controlled, depending on the derivative module employed. The electronic analogue RC device computes the derivative with respect to time, as the spectrum is scanned at constant speed, S(dh/dt) : dtn - dh” [:In The “true” wavelength derivative is linearly related to the time derivative recorded, the magnitude of which is directly affected by scan speed and spectral band width.For qualitative work, the second or fourth derivatives offer a convenient method for enhancing sharp spectral features (Figs. 2 and 3), although for broad peaks the highest practicable derivative order is usuaIIy second. The lowest derivative order required for the analytical objective should be selected. When using analogue electronic or microcomputer derivative modules, the spectral displace- ment in the direction of scanning is a function of differentiator time constant, scan speed and peak half-width. Clearly, for comparison purposes, the same instrumental conditions must be used for qualitative work. dnA dnA -- First, however, the order of derivative should be considered.Fig. 1. Effect of derivative cu 6 0 3 ‘0 0 1 .O 0.8 Q 0.4 0 220 250 250 300 hln m orde; (zeroth, second and fourth) Fig. 2. Zero-order and second-deriva- on the relative amplitudes of two tive spectra of diphenhydramine hydro- coincident (a) Gaussian or (b) chloride (DPH). 750 p g ml-l in water, Lorentzian bands, X and Y, of equal of matrix M diluted 1 + 3 with water, intensity and band-width ratio 1 : 3. and of diphenhydramine in diluted Curve S represents the combined matrix (DPH + M). The derivative peak. amplitude used for assay is coded D285. In background correction, if a particular matrix interference overlapping the analyte peak approximates a quadratic, the second derivative reduces it to a constant, while the nth is required for an rcth degree polynomial, P: P = a, + aJ + a,h2 + .. . + a,hn dnP dhn -- - n!an Thus, the polynomial of degree n is reduced to a constant in the nth derivative and eliminatedJanuary, 1982 DERIVATIVE SPECTROSCOPY 31 in the (n + 1)th derivative. In fact, the constant leads to displacement of the whole deriva- tive spectrum, a feature readily compensated for by measuring graphically between the derivative peak itself and an adjacent satellite peak. Having established the minimum derivative order required to eliminate a matrix interference, the appropriate peak amplitude measure must be selected, there being several measurement options as discussed by O'Haver and Green.12 There may, of course, be several peaks associated with a particular analyte.Normally a series of standards is set up with the matrix at constant concentration, and the linearity of each peak amplitude measure is examined. An interaction study is performed, where the analyte level is kept constant while the matrix concentration is varied from 0 to 120% (Fig. 4). The best amplitude measure is selected on the basis that it is least affected by the matrix variation, and that it gives the best calibration statistics. The basis of quantita- tion in derivative spectroscopy remains the assumption that the Beer - Lambert law is obeyed over the range of interest: d"A d"e - - -.cb at h [dhn dh" where A is absorbance, E is molar absorptivity (1 mol-l cm-l), c is concentration (moll-l).and b is path length (cm). - + Q x *s O U - 1 .o 0.8 0.4 0 DPH 220 250 300 Alnm E E 100 2 8 50 0 50 100 mg per 100 ml 0 10 20 30 % VIV Fig. 4. (a) Calibration and (b) interaction graphs for diphenhydramine hydrochloride (DPH) in matrix diluted 1 + 3 with water. The concentration of matrix in the calibration graph was 25% V / V . The concentration of DPH in the interaction graph was - - 600 pg ml-l. Fig. 3. Zero-order and fourth-derivative spectra of diphenhydramine hydrochloride (DPH) , 750 pg ml-l in water, and of matrix diluted 1 + 3 with water (M). As an example, the derivative ultraviolet assay of diphenhydramine hydrochloride (DPH) in a multi-component, coloured sucrose vehicle typifies the approach developed in the authors' laboratory. The fine structure of the aromatic nucleus is readily apparent in the second and fourth derivative spectra of the pure aqueous solution (Figs.2 and 3). Dilution of the dosage form with water (1 + 3) yields the matrix at 25% concentration; addition of varying amounts of DPH to the formulation matrix and measurement of each second derivative amplitude indicated that all were linear with concentration up to 1250 pg ml-l (Fig. 4). An interaction experiment with the matrix varying from 0 to 30% V/V in the diluted sample showed that for a constant DPH level of 600 pg ml-l the best amplitude measure was that at 265 nm (to the long wavelength satellite). Using a Perkin-Elmer Model 200 spectrophotometer, the scan speed (120 nm min-l), slit width (2 nm), derivative module gain or time constant (No.5 ; Hitachi 0507 module), the32 DERIVATIVE SPECTROSCOPY Anal. Proc. absorbance scale and the test concentration range were adjusted for optimum signal to noise ratio. Comparison of results for a batch by the derivative method with the official USP XIX procedure (which involves time-consuming extraction and back-extraction steps) gave com- parable recoveries (94.3 and 93.9y0, respectively) and no significant t-test difference (n = 12). The relative standard deviation was 1.4y0, compared with 2.2% (n = 12) by the USP XIX assay.31 As in all quantitative derivative assays, the method must be externally standardised using (aqueous) standards in bracketting sequence to minimise the effect of drift. For this particular formulation, the method is rapid and accurate.Clearly, if the formulation were changed, the interaction study would have to be re-examined. Although the present discussion has concerned the “analyte-rich” situation typical of pharmaceutical and similar production systems, the derivative spectroscopic method is potentially applicable at the trace amount level as illustrated by some recent toxicological studies on paraquat in cases of poisoning,30 where the detection limit was reduced 10-fold by exploiting the second derivative approach. There are many instances in biochemical and environmental analysis where the derivative technique may, conceivably, be found useful. Future Projections Rapid progress in microcomputer technology is leading to high-quality, low-noise derivative modules,23 which may exploit the Savitzky - G01ay~~ or the Fourier transform method.33 The microcomputer permits data manipulation to give automatic peak amplitude measure- ment between defined spectral features.The presentation of “satellite-free” higher derivatives is also a feasible proposition. Automatic multi-component mixture analysis by the matrix inversion method in derivative domain is now possible by microcomputer. This approach relies on an appropriate archive of derivative spectra, which may also be used for rapid con- firmation of identity, as recently demonstrated in a commercial linear diode array spectro- photometer.34 Qualitative characterisation in the derivative domain will be useful in infrared spectroscopy, where the second derivative method has already found application in plastics and fibre and where theoretical studies indicate that fourth and higher derivatives should be useful for resolution enhancement .20 Use of the second and higher derivatives in HPLC and GLC will permit improved resolution of overlapping peaks21 725 s3’ and present interesting possibilities for densitometric scanning of electrophoretograms and TLC plates.26 938 s30 The development of multi-channel spectro- photometers coupled with the widespread availability of instruments with derivative capability, and their rapid acceptance by the analytical community, will lead to further interesting applica- tions of this refined and versatile technique.Thanks are expressed to Perkin-Elmer Ltd., Beaconsfield, Buckinghamshire, for the generous loan of equipment.The authors also acknowledge the skilled assistance of I. E. Aitchison (Department of Computer Science, Heriot-Watt University) and Mrs. Ann E. Mair (Western General Hospital, Edinburgh) and stimulating discussions with Dr. B. P. Chadburn, G. L. Collier, Dr. A. E. Martin, Dr. J. N. Miller, Professor T. C. O’Haver and A. C. M. Panting during the course of this work. 1. 2 . 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. References Dymond, E. G., Proc. Camb. Phil. SOC., 1923-25, 22, 405. Singleton, F., and Collier, G. L., “Improvements in or Relating to Spectroscopes,” BY. Pat., 760729, Collier, G. L., and Singleton, F., J. Appl. Chem., 1956, 6, 495. Collier, G. L., and Panting, A. C. N., Sfiectvochim. Acta, 1959, 14, 104.Martin, A. E., Nature (London), 1957, 180, 231. Martin, A. E., Spectrochim. Acta, 1959, 14, 97. Morrey, J . R., Anal. Chem., 1968, 40, 905. Butler, W. L., and Hopkins, D. W., Photochem. Photobiol., 1970, 12, 439. Butler, W. L., and Hopkins, D. W., Photochem. Photobiol., 1970, 12, 451. Butler, W. L., Methods Enzymol., 1979, 56 (Part G), 501. Green, G. L., and O’Haver, T. C., Anal. Chem., 1974, 46, 2191. O’Haver, T. C., and Green, G. L., Anal. Chem., 1976, 48, 312. Keighley, J. H., and Rhodes, P., Proc. Inst. Elect. Rad. Eng., 1971, 22, 397. Ichikawa, T., and Terada, H., Biochim. Biophys. Acta, 1977, 494, 267. Talsky, G., Mayring, L., and Kreuzer, H., Angew. Chem., Int. Ed. Engl., 1978, 17, 785. 1956.Januavy , 1982 DERIVATIVE SPECTROSCOPY 33 16. 17.18. 19. 20. 21. 22. 23. 21. 25. 263. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. Fell, A. F., Proc. Anal. Div. Chem. Soc., 1978, 15, 260. Balestrieri, C., Colonna, G., Giovane, h., Irace, G., and Servillo, L., Eur. J . Biochem., 1978, 90, 433. Jones, K. G., and Sweeney, G. D., Clin. Chem. (Winston-Salem), 1979, 25, 71. Talsky, G., “Gerat zum Auswerten von Messkurven,” Ger. Offen., 2806826, 1979. Fell, ,4. F., U V Spectrom. Group Bull., 1980, 8, 5. Fell, A. F., UV Spectrom. Group Bull., 1979, 7, 5 . Ishii, H., and Koh, H., Nippon Kagaku Kaishi, 1980, 203. O’Haver, T. C., and Smith, A., Am. Lab., 1981, 13, 43 O’I-Iaver, T. C., Anal. Chem., 1979, 51, 91.4. Fell, A. F., Anal. Proc., 1980, 17, 512. Okamura, K., Clin. Chzm. Acta, 1979, 96, 273. Shibata, S., Angew. Chem., I n t .Ed. Engl., 1976, 15, 673. Gulyaev, R. A., and Litvin, F. F., Biofizzka, 1970, 15, 670. Cahill, J . E., A m . Lab., 1979, 11(11), 79. Fell, A. F., Jarvie, D. R., and Stewart, &I. J., Clin. Ch9m. (Winstotz-Sa!em), 1981, 27, 286. Fell, A. F., to be published. Savitzky, A., and Golay, M. J . E., Anal. Chem., 1964, 36, 1627. Horlick, G., Anal. Chem., 1972, 44, 943. James, G. E., “UV/Vis Application Note,” No. 1, Hewlett-Packard, Palo Alto, Calif., 19SO. Pump, W., and Woltjes, D., Kunststoffe, 1979, 69, 317. Maddams, W. F., and Tooke, P. B., Macvomol. Scz., in the press. Zelt, I>. T., Owen, J . A,, and Marks, G. S., J . Chromatogr., 1980, 189, 203. Machold, W., Meister, A., and ,4dler, K , Photosynthetica, 1971, 5, 160. Cottrell, C. T., “Derivative and Log Spectrophotometry,” SP8 Series Accessories Applications, €’ye Unicam, Cambridge, 1980.Numerical Methods for Generating Derivative Spectra Peter Gans Department of Inorganic and Structural Chemistry, The University, Leeds, L S 2 9 J T We begin by assuming that the spectrum is available in the form of s pairs of numbers xi, yi (i = 1, 2, . . ., s). The simplest method (I) for generating the derivative spectrum is to fit a polynomial of degree h (order k , k = h + 1) to k data points at a time. Secondly (11), a polynomial of degree h can be fitted by the method of least squares to m data points at a time, when m > k . Lastly (111), a spline function of degree h can be fitted to all s data points by the method of least squares. I t is convenient, but not essential, that the data be evenly spaced along the x axis, i.e., xi+l - xi = constant = Ax.The convenience lies in the simplification of the algebra intro- duced into methods I and 11. For the former we obtain the expressions dy - Yi+l - Yi-1 - __--__ 2Ax k:= 3: - ax d2y - Y&L- 2Yi + Yi-1 _- d X 2 - (Ax) (3) for the simplest cases, k = 2 and 3. to equation (1) and, as can be seen, it is no more difficult to compute. extended and applied to spectra by Butler and H0pkins.l For method I1 we consider the simple case, k = 3 and m = 5. result from the algebraic solution of the least-squares equations. For the first derivative equation (2) is to be preferred The method has been Equations (4) and (5) dy ~ 1 (- 2Yi-2 - Yi-1 + Yi+l + 2YiS2) dx lOAx gJ ~.1 (2Yi-2 t Yi-1 - 2Yi 3- Yi+l + dx2 7Ax2 (4) It is clear that these equations contain the terms in equations (2) and (3) and additional terms arising out of the extra points used, which should give a better approximation. The method34 DERIVATIVE SPECTROSCOPY Anal. PYOC. was developed for chemists by Savitzky and Golay,2y3 and has been widely used. The Savitzky - Golay tables require that m be odd, but this is not essential; if m is even the derivatives can be calculated at the points mid-way between the data points by a similar technique. To compare the various methods, let us determine the derivatives of the functiony = x2/2 + x at x = 2, given values of y that are subject to various levels of noise as shown in Table I. The derivatives are shown in Table 11.TABLE I SIMULATED DATA X .. 0 1 2 3 4 Noise . . . . 0.2 0 0.2 -0.2 0.2 Y * . . . 0 1.5 4 7.5 12 y + noise . . 0.2 1.5 4.2 7.3 12.2 Data 1 y + noise/2 . . 0.1 1.5 4.1 7.4 12.1 Data 2 y + noise/4 . . 0.05 1.5 4.05 7.45 12.05 Data 3 y + noise/8 . . 0.025 1.5 4.025 7.475 12.025 Data 4 The significance of these results is as follows. As the noise tends to zero, the derivatives obtained by the Savitzky - Golay technique converge towards the noise-free values of 3 and 1 more rapidly than the derivatives obtained by other methods. For that reason method I1 has been the method of choice, even though it imposes the experimental restriction of equally spaced data points. Methods I and I1 share the characteristic that a low-degree polynomial (e.g., a parabola for k = 3) is fitted to a subset of the data consisting of k and m points, respectively.An advantage of this is that the methods can be applied to real-time differentiation of spectra: some manufacturers offer method I1 in microprocessor-based attachments for spectrophoto- meters. The disadvantage of method I1 is the lack of long-range continuity in the calculated derivative. Also, the choice of m must be subjective. TABLE I1 DERIVATIVES CALCULATED NUMERICALLY Data 1 2 3 4 g, equation (1) 3.1 or 2.7 3.3 or 2.6 3.4 or 2.55 3.45 or 2.525 $, equation (2) 2.9 2.95 2.98 2.987 5 2, equation (4) 2.98 2.99 2.995 2.997 5 - ::, equation (3) 0.4 0.7 0.85 0.925 2 dx2' equation (5) 1.085 7 1.042.9 1.021 4 1.010 7 Continuity is built into method 111, the spline function method. A spline function of degree 12 consists of a number of pieces each of which is a polynomial of degree h and the pieces are joined end-to-end at places on the x axis that are termed knots (or nodes).The function and its derivatives up to that of order h - 1 are continuous throughout the spectrum; the derivative of order h is constant within each polynomial piece, but changes discontinuously at the knots. The spline function is constructed as a linear combination of basis functions, which are defined completely by the knots, using the principle of least squares, and the derivatives are obtained directly from the spline function. All s data points are used so that the spline function and its derivatives (which are also spline functions) have the defined property of continuity throughout the spectrum.We have explored various schemes for knot placement with splines of degree 3, 4 and 5 and have applied the method to the analysis of Raman spectra. The signal to noise ratioJanMary , 1982 DERIVATIVE SPECTROSCOPY 35 (SNR) tends to increase as the number of knots is decreased, so that a scheme that places knots according to need is preferred to a scheme of regularly placed knots. We have attempted to make the choice of number of knots and placement scheme automatic, determined by objective criteria. The results obtained on equally spaced data indicate that the spline function method is more objective and generates derivative spectra with a higher SNR than the Savitzky - Golay method. The enhanced resolution of the second derivatives has been successfully utilised to aid the qualitative analyses of the Raman spectra of cyano - silver complexes dissolved in liquid amm~nia.~ Initial attempts to understand these spectra using the Savitzky - Golay method were vitiated by the relatively poor SNR.References The main reason for this is clearly the use of all the data simultaneously. 1. 2. 3. 4. Butler, W. L., and Hopkins, D. W., Photochem. Photobiol., 1970, 12, 439 and 451. Savitzky, A., and Golay, M. J. E., Anal. Chem., 1964, 36, 1627. Steinier, J., Termonia, Y . , and Deltour, J., Anal. Chem., 1972, 44, 1906. Gans, P., Gill, J . B., Griffin, M., and Cahill, P. C., J . Chem. SOC. Dalton Trans., 1981, 968. Square-wave Wavelength Modulation System for Use in Atomic Spectrometry” J. Sneddon, L. Bezur, R.G. Michel and J. M. Ottaway Department of Pure and Applied Chemistry, University of Strathclyde, Cathedral Street, Glasgow, G1 1XL In atomic spectroscopy, wavelength modulation can be used to measure derivative spectra but a more important application is for background correction when an atomic line is super- imposed on a continuum background signal. Thus, the technique has been used for background correction in atomic-emission spectrometry using electrothermal atomisers,l ,2 flame^^-^ and plasmas,’ ,* in continuum-source atomic-absorption spectrometryg-12 and to a lesser extent in continuum-source atomic-fluorescence spectrometry.13 ,14 In many of these instances, the application of wavelength modulation has provided sig- nificant advantages, In carbon furnace atomic-emission spectrometry, detection limits were improved substantially,l in some instances by several orders of magnitude, using a quartz refractor plate mounted on a mechanical oscillator and placed near the entrance slit of a 0.75-m monochromator.In one of the early applications, Snelleman et aL3 demonstrated that the spectral interference of CaOH emission bands and/or a continuum can be minimised in the measurement of barium in a dinitrogen oxide - acetylene flame, Improvements in the detection limits of alkali and alkaline earth elements in the presence of many matrix ions were also reported and both effects were achieved by a quartz plate, vibrating at 145 Hz, and mounted behind the entrance slit of the monochromator. Epstein and O’Haver5 used a plane-parallel quartz refractor plate mounted on the shaft of a limited rotation torque motor to achieve correction for spectral interferences due to line, band and continuum radiation in flame emission spectrometry.Another interesting application in flame emission was the reduction in the interference of CH band emission on the determination of al~minium.~ One of the more important recent applications of wavelength modulation has been to background correction in continuum-source atomic-absorption spectrometry.ll ?12 A quartz refractor plate was mounted at the entrance slit of an kchelle polychromator and used to achieve simultaneous multi-element atomic-absorption analysis with automatic background correction in all channels. In the literature referred to above, wavelength modulation has invariably been achieved by employing an oscillating refractor plate. The refractor plate is usually positioned at or near the entrance slit of the monochromator and is made to oscillate about the vertical axis using commercially available scanning motors.The result of this is that the wavelength is scanned sinusoidally. Such a waveform is also highly suited to the production of derivative atomic spectra. O’Haver et aZ.15 have described computer modelling studies designed to national Confercnce on Analytical Chemistry (SAC 80) a t the university of Lancaster in June, 1980. * The system described in this paper was also demonstrated a t a Workshop Session at the Fifth Inter-36 DERIVATIVE SPECTROSCOPY Anal. Proc. determine the effects of the nature of the modulation waveform and amplitude, the shape of the modulated line and the signal processing technique used.Sinusoidal and square-wave modulation of Gaussian, triangular and Lorentzian line profiles were treated and the results indicated that the shape of the line profile has little effect, but that square-wave modulation offers a signal to noise ratio advantage approaching 2 in the 2F mode, compared with sinusoidal modulation, for a system limited by background carried photon shot noise. Koirtyohann et a1.l6 have also demonstrated experimentally that square-wave modulation gives an improve- ment over sinusoidal modulation. The improvement appears to be greater for the second compared with the first harmonic mode and increases if larger plate amplitudes are required. With scanning motors, square-wave oscillation is more difficult to achieve than sinusoidal oscillation at frequencies suitable for atomic spectrometry.Commercial equipment is avail- able,16 however, which incorporates sufficient control over the position of the refractor plate to achieve square-wave modulation at a frequency of 17 Hz. In recent reviews of wavelength modulation applied to atomic spectroscopy, O'Haverl' y18 has indicated that the oscillating refractor plate whether operated in sinusoidal or square waveform is the only current method of generating wavelength modulation. We have recently describedlg a new mechanical arrangement that incorporates a rotating quartz mechanical chopper and that results in the wavelength being repetitively scanned with a square waveform.The construction of this system and applications to atomic spectroscopy investigated to date are reviewed in this paper. When the standard refractor plate goes through an oscillation, the angle of incidence of the dispersed radiation from the monochromator at the plate changes continuously, and the spectral intensity distribution at the exit slit is modulated over a discrete wavelength interval in a sinusoidal waveform. The displacement, d, at any time is given by d = ta(n - 1)/n, where t (mm) is the thickness of the plate, cc is the angle of incidence of the light beam at the refractor plate in radians and n is the refractive index of the quartz plate. As t is constant for the quartz refractor plate, d depends only on a.The rotating quartz chopper operates on the same principle, except that in order to vary d, a is maintained constant and t is varied. The chopper was constructed of four quartz quadrants of varying thickness, mounted at an incident angle of 45" to the light beam at either the entrance or exit slits of the monochromators used. Two opposite quadrants were made of quartz of equal thickness (2.5 mm), and the other two were made of greater (4.0 mm) and lesser (1.0 mm) thickness. When the two identical quadrants were in the optical beam, light at the analyte atomic wavelength, AA, was allowed to pass through the exit slit. The other quadrants, when present in the optical beam, gave displacements to (AA + Ah) and (AA - Ah), respectively, and allowed the back- ground signal to be measured on each side of the atomic line.The modulation interval is therefore 2AX and its magnitude depends on the dispersion of the monochromator used. A detailed description and the incorporation of this system in two different spectrometers have been published elsewhere.lg~Z0 To date the rotating mechanical chopper has been used to achieve automatic background correction in flame atomic-fluorescence spectrometry,lg 921 flame emission spectrometryz1 and carbon furnace atomic-emission spectrometry.20922 Using a 300-W xenon arc as a continuum light source, correction for background signals caused by scatter and flame emission has been demonstrated in atomic-fluorescence measurements of a wide range of elements in an air - acetylene flame. Correction for flame emission background signals superimposed on atomic emission has also been demonstrated with the same instrument with the light source switched off.A new system has also been incorporated into a high-resolution echelle spectrometer used for the measurement of sensitive carbon furnace atomic-emission signals.20 In this instance, platform atomisation in an HGA-72 atomiser was used and the improvement in detection limits was achieved by a combination of factors derived from the use of the platform, high-resolution spectrometer and wavelength modulation system. The separate contributions of each factor have yet to be identified. However, the modulation system clearly offers the potential for automatic correction of background from molecular emission and matrix scatter, as well as continuum radiation from the graphite tube.The square-wave wavelength modulation system has been shown to give excellent back- ground correction in all three techniques mentioned above, when used for the determination of trace elements in clinical materials.lg~21~22 Detection limits of 20-30 pg ml-l for chromium and manganese have been used to develop simple direct methods for the determination ofJanuary, 1982 DERIVATIVE SPECTROSCOPI’ 37 these elements in blood and/or urine using carbon furnace atomic emission.22 The mechanical arrangement is no more complex than the traditional rotating glass choppers used for in- tensity modulation in spectrometric measurement. Application to continuum-source atomic- absorption measurements has yet to be demonstrated, but should be no more complicated than the above systems.It may also present a simpler means of background correction than the oscillating refractor plate for emission systems exhibiting complex spectra, such as the inductively coupled plasma. 1. 3. 1. 6. S . 9. 10. 11. 12. 13. 14. 15. 16. 17. 1s. 19. 30. 31. “ 2 . 7 -. a . - 1 References Epstein, &I. S., Rains, T. C., and O’Haver, T. C., Appl. Spectrosc., 1976, 30, 324. Hutton, R. C., Ottaway, J . M., Epstein, M. S., and Rains, T. C., Analyst, 1977, 102, 658. Snelleman, W., Rains, T. C . , Yee, K. W., Cook, H. D., and Menis, O., Anal. Chem., 1970, 42, 394. Rains, T. C., and Xenis, O., Anal. Lett., 1974, 1, 715. Epstein, M. S., and O’Haver, T. C., Spectrochim. Acta, 1975, 30B, 135. Syder, R.J., and Hieftje, G. M., Anal. Chprn., 1976, 48, 535. Iiawaguchi, H., Okada, M., Ito, T., and Mituike, A., AmaZ. Chirn. Acta, 1977, 95, 143. Rose, O., Mincey, D. W., Yacynych, A. M., Heineman, W. R., and Caruso, J . A, AnalJfst, 1976,101, 753. Zander, A. T., O’Haver, T. C . , and Keliher, P. N., Aazal. Chern., 1976, 48, 1166. Snelleman, W., Spectrochzm. Acta, 1968, 23B, 403. Harnley, J . M., and O’Haver, T. C., Anal. Chem., 1977, 49, 2187. Harnley, J . M., O’Haver, T. C., Golden, R., and Wolf, W. R., Anal. Chem., 1979, 51, 2007. Fowler, IV. K., Knapp, D. O., and Winefordner, J. D., Anal. Chem., 1974, 46, 601. Lipari, F., and Plankey, F. W., Anal. Chem., 1978, 50, 386 O’Haver, T. C., Epstein, M. S., and Zander, A. T., Anal. Chem., 1977, 49, 458. Koirtyohann, S. K., Class, E.D., Yates, D. A,, Hinderbnrger, E. J., and Lichte, F. E., Anal. Chet?z., O’Haver, T. C., Anal. Chem., 1979, 51, 91A. O’Haver, T. C., “Contemporary Topics in Analytical and Clinical Chemistry,” Plenum, New York, Illichel, R. G., Sneddon, J., Hunter, J . I<., Ottaway, J . M., and Fell, G. S., Analyst, 1981, 106, 288. Ottaway, J. M., Bezur, L., and Marshall, J., Awlyst, 1980, 105, 1130. Ottaway, J . M., Hall, M. L., Michel, R. G., Sneddon, J , , and Fell, G. S., in “Trace Element Analvtica Chemistry in Medicine and Biology,” Walter de Gruyter, Berlin, New York, 1980, p. 255. Ottaway, J. M., Bezur, L., Fakhrul-Aldeen, R., Frech, W., and Marshall, J., in “Trace Element Analytical Chemistry in Medicine and Biology,” Walter de Gruyter, Berlin, Yew York, 1980, p.575. 1977, 49, 1121. 1979, p. 1. Derivative Fluorescence Spectroscopy J. N. Miller and T. A. Ahmad and A. F. Fell Defircrtment of Chemistry, Lozdghborough University of Technology, Loughbovough, Leicestershire, LE11 3T U Ihpnvtment of Pharmacy, Heriot- Watt University, Edinburgh, E H 1 2HJ Fluorescence spectroscopy finds its main applications in two fields : (i) biochemical studies, including clinical, pharmacological and pharmaceutical analysis, and (ii) environmental analyses. These fields have in common a number of experimental problems; in particular, they both require extremely sensitive analytical methods (because of the small samples and/or low analyte concentrations) and they also demand highly selective techniques (because of the extreme complexity of the samples).The sensitivity of fluorescence spectroscopy is well established : picogram concentrations of strongly fluorescent solutes can be determined using modern instruments. I n principle, the selectivity of fluorimetry should also be superior to that of absorption spectroscopy, as each solute can be characterised by two wavelengths, those of excitation and fluorescence. In practice, this advantage is often more apparent than real, as the large band widths of fluorescence signals often yield strongly overlapping spectra. Additional selectivity can be obtained by combining fluorimetry with separation techniques or with biochemically specific methods, or by the use of modified forms of spectroscopic analysis. Amongst the latter, derivative methods have recently received much a t t e n t i ~ n .l - ~ A further approach, not possible in absorption spectrometry, is that of synchronous scanning fluorimetry* 9 5 ; combination of the derivative and synchronous methods was suggested by John and SoutarS6 Derivative fluorescence spectroscopy, both alone and in combination with38 DERIVATIVE SPECTROSCOPY Anal. Proc. synchronous scanning, has thus far been largely applied to environmental analysis. This paper describes some applications in the field of analytical biochemistry. Experimental Derivative luminescence spectra (second derivative in this study, unless otherwise stated) can be obtained from conventional excitation , fluorescence and synchronous spectra by electronic (ie. , analogue) differentiation or by numerical (digital) methods. In the work described here the former approach was exemplified by the use of a Fluoricord spectrofluori- meter (Baird-Atomic, Braintree, Essex), in conjunction with a Hitachi derivative module (Model 200-0507, obtained from Perkin-Elmer, Beaconsfield , Buckinghamshire) ; this fluori- meter generated spectra that were uncorrected for instrumental characteristics.Derivative spectra computed numerically were obtained using a Perkin-Elmer MPF 44B spectrofluori- meter equipped with a DCSU-2 microprocessor unit ; this unit was sometimes used to generate corrected spectra in addition to derivative spectra. All spectra were obtained at room temperature using samples of the highest available purity; water was distilled at least twice from a silica still.Results and Discussion The major benefits of derivative techniques are expected to lie in the increased resolution of overlapping spectral bands and in the enhancement of relatively minor spectral features. Both of these advantages are well demonstrated in Fig. 1, which shows the fluorescence excitation spectrum of fluorescein, and the second derivative of the same spectrum. A further advantage is illustrated in Fig. 2, where it is shown that a fluorescence peak superimposed on a sloping base line (in this instance fluorescein in a blood serum sample with high background fluorescence) can be readily separated from the background signal. However, it is important to note that the effectiveness of derivative spectroscopy is a function of the band width of the zero-order spectrum : spectra with large band widths will, other circumstances being equal, yield less intense derivative signals than spectra with narrow band widths.This point is 250 350 450 5"3 I l n m Fig. 1. Fluorescence excitation spectrum of fluorescein (A! = 510 nm) and its second derivative obtained using the DCSU-2 unit. 3 Vnrn Fig. 2; Zero-order and second-derivative (DSCU-2) spectra of fluorescein in a diluted serum sample. In the zero-order spectrum the fluorescein fluorescence peak (A! = 515 nm) overlaps the serum background (A! = 465 nm), but the second-deriva- tive spectrum allows the fluorescein to be deter- mined without background interference. Excitation wavelength : 400 nm.January, 1982 DERIVATIVE SPECTROSCOPY 39 well illustrated in Fig.3, which illustrates a broad fluorescence band with a sharp Raman scattering band superimposed on i t ; thc second derivative spectrum shows the Raman band clearly, but the fluorescence band is scarcely detectable. In these circumstances the synchronous scanning approach may be extremely valuable. This method involves scanning both the fluorimeter monochromators simultaneously with a fixed wavelength difference between them. The result is the production of a spectrum with a much narrower band width.5 Synchronous spectra may therefore be capable of conferring increased selectivity on their own, but in other instances the additional resolution provided by derivative spectroscopy is necessary. These principles have been applied to the solution of a well known problem in analytical biochemistry, the detection of tyrosine fluorescence in the presence of tryptophan.These two amino acids have very similar excitation spectra, and their fluorescence spectra overlap strongly. In addition, as the molar absorptivity of tryptophan at 280 nm is about four times greater than that of tyrosine, a solution of tryptophan is approximately 2.25 times as fluorescent as an equimolar solution of tyrosine excited at the same wavelength [the quantum yields are (4f)trp = 0.12 and (4f)tyr = 0.211. When the two amino acids are incorporated in the same protein molecule, the identification of tyrosine fluorescence is made even more difficult by two further factors: there is a blue shift in the fluorescence maximum of the tryptophan residues (i.e., increasing the spectral overlap) and the tyrosine fluorescence intensity is reduced by energy transfer and quenching effects.An extra problem is the small Stokes shift of tyrosine (Aex- m 280 nm; Afl. m 303 nm), which may introduce interference by Rayleigh and Raman scattered light signals.' Thus, although it is easy to detect tryptophan fluorescence in the presence of tyrosine (e.g., by using excitation wavelengths longer than 295 nm, when 400 500 600 )i/n rn Fig. 3. Derivative spectro- scopy emphasising spectral features with narrow band widths. In the zero-order spectrum a fluorescamine- labelled amino acid ( A t = 480nm) is overlapped by a Raman peak (A = 420 nm); in the second-derivative (DSCU-2) spectrum, only the Raman signal is clearly defined.Excita- tion wavelength = 370 nm. I 300 400 300 400 hdnm Lr.Jnm Fig. 4. Use of synchronous scanning to produce well defined derivative spectra ; (a) fluorescence emission spectrum of tryptophan (-20 pg ml-l) and its second derivative (DSCU-2, excitation wave- length 287 nm) ; (b) synchronous spectrum. of the same solution (AA = 58 nm) and its second derivative. The double-headed arrows show that the synchronous spec- trum has less than half the band width of the conventional spectrum.40 DERIVATIVE SPECTROSCOPY Anal. Proc. tyrosine does not absorb) the detection of tyrosine fluorescence in the presence of tryptophan may be exceedingly difficult. The problem is not only important in its own right (e.g., in studies of protein photochemistry and structure), it also exemplifies many of the problems encountered in numerous other fluorimetric assays in biochemistry.A similar problem, that of resolving tyrosine and phenylalanine fluorescence, has been satisfactorily resolved using derivative spectroscopy alone.8 This approach is not available when tryptophan is under study, because of the large band width (about 65 nm at half-height) of tryptophan fluorescence : even intense zero-order fluorescence spectra yield only weak (second) derivative spectra. The synchronous spectrum of tryptophan, obtained at a mono- chromator wavelength difference (Ah) of 58 nm, has a band width of only about 25 nm, and hence yields excellent second-derivative spectra (Fig. 4). In an earlier papers it was shown that tyrosine and tryptophan might be resolved by synchronous spectroscopy alone, Ah values of less than 15 nm giving spectra characteristic of tyrosine, and Ah values of greater than 60 nm giving spectra characteristic of tryptophan.An example of the quantitative applica- tion of this procedure, both with and without the use of derivative methods, is given in Fig. 5 . An alternative and less cumbersome approach is to use a synchronous scanning interval, which reveals both tyrosine and tryptophan components; these components can then be resolved using second-derivative spectroscopy (Fig. 6). This separation can be achieved 0 2 4 6 8 1 0 TyrIpM Fig. 5. Determination of tyrosine in the presence of tryptophan using (a) syn- chronous and (b) second- derivative synchronous fluori- metry (AA = 10 nm).All solutions were made up so that the total Tyr + Trp concentration was 10 p ~ . I n (b) the 2 D ~ line uses the long-wavelength satellite of the derivative spectrum to measure intensities, and the 2 D ~ line the short-wavelength satellite . 230 330 21 0 310 hexjnm 111111- 260 360 270 370 hernjnm Fig. 6. Resolution of tyrosine and tryptophan fluorescence using derivative synchronous spectroscopy with AA values of (a) 30nm and (b) 60nm. For details, see text. either at moderate Ah values (about 30 nm) or at much larger AX values (70 nm). In the latter instance use is made of a small but well defined peak that appears in the excitation spectrum of tyrosine at 234 nm. These methods have also been used with success in resolving three- component mixtures (phenylalanine, tyrosine and tryptophan) and in studies of proteins.January, 1982 DERIVATIVE SPECTROSCOPY 41 For example, in agreement with earlier results obtained using more complex technique^,^^"-' the tyrosine contribution to the fluorescence of lysozyme was found to be very small, whereas the tyrosine contribution to human serum albumin fluorescence was substantial.A number of other mixtures of biologically active materials have been studied and these results will be reported separately.ll Conclusion The advantages of derivative spectroscopy are just as applicable in fluorimetry as in In fluorimetry the additional device of synchronous scanning is Derivative synchronous spectra will Using second-derivative spectra, A number of fields in which derivative Replacement of the chromatographic step in many quantitative analyses that currently utilise HPLC or TLC to provide selectivity.Clearly there will be instances where closely similar materials cannot be resolved spectroscopically,l2 but equally there will be many cases where existing procedures can be improved upon. (iz) Combinations of derivative spectroscopy and phosphorimetry, especially at room temperature.13 Room-temperature phosphorescence (RTP) is of considerable value in, for example, environmental analyses, but RTP spectra are less sharply featured than those obtained at 77 K. Derivative methods will yield more characteristic spectra of added value in qualitative and quantitative analysis. These molecules or fluorophores exhibit changes in their fluorescence wavelengths and intensities as their environments change, on binding to a macromolecule, for e~arnp1e.l~ In such instances derivative methods could distinguish between probe molecules in different environments, and this approach would be of great importance in the study of drug - protein binding interactions, and in the development of fluorescence immunoassays.Studies of this type are proceeding in the authors’ laboratory. (iv) No great technical difficulty attaches to the determination of fourth-derivative (and higher order) spectra. These will merit further study, although the complexity of the derivative spectra themselves and signal to noise ratio problems may offset the potential advantages of still greater discrimination and resolution 0btainab1e.l~ absorption spectroscopy.of help in studying solutes with broad band spectra. thus be of special value in resolving difficult mixtures. quantitative analysis should present few problems. luminescence spectroscopy will be valuable can be identified. (i) These include : (iii) The use of derivative fluorimetry in combination with fluorescence probes. We thank the Medical Research Council for provision of funds to buy the recording spectro- fluorimeter, and Dr. C. S. Lim for generous assistance. References 1. O’Haver, T. C., in Wehry, E. L., Editor, “Modern Fluorescence Spectroscopy,” Plenum, New York, 1976. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 18. Green, G. L., and O’Haver, T. C., Anal, Chem., 1974, 46, 2191. O’Haver, T. C., Clin. Chem., 1979, 25, 1548. Lloyd, J . B.F., Nature Phys. Sci., 1971, 231, 64. Lloyd, J . B. F., J . Forensic Sci. Soc., 1971, 11, 83. John, P., and Soutar, I., Anal. Chem., 1976, 48, 520. Miller, J . N., Prog. Biophys. Mol. Biol., 1974, 28, 41. Terhaar, D. A., and Di Cesare, J . L., Perkin-Elmer Fluorescence Report, 1979, NO. F2-71. Miller, J . N., Proc. Anal. Div. Chem. Soc., 1979, 16, 203. Miller, J . N., and King, L. A., Biochim. Biophys. Acta, 1975, 393, 433. Miller, J. N., and Fell, A. F., in preparation. Fell, A. F., and Miller, J . N., unpublished work. Vo-Dinh, T., and Gammage, R. B., Anal. Chim. Acta, 1979, 147, 261. Edelman, G. M., and McClure, W. O., Acc. Chem. Res., 1968, 1, 65. Cahill, J . E., 30th Pittsburgh Conference, Cleveland, Ohio, 1979, Abstract No. 174.42 DERIVATIVE SPECTROSCOPY Anal.PYOC. Derivative Spectroscopy in the Laboratory: Advantages and Trading Rules Brian P. Chadburn Perkin-Elmer Ltd., Beaconsfield, Buckinghamshive The derivative technique is useful for extracting both qualitative and quantitative information from spectral curves composed of unresolved bands. However, its application involves the choice of two new parameters, and an inappropriate choice can artificially limit the advantages of the technique and lead to an excessive reduction in the signal to noise ratio. In this study, the advantages of derivative spectroscopy are considered and the trading rules involved in its application in ultraviolet - visible spectroscopy are discussed. Derivative spectroscopy is a simple yet powerful technique for enhancing the fine structure of spectral curves.l It involves plotting the first, second or higher order derivative of a spectrum with respect to wavelength rather than the spectrum itself.Usually, the derivative is obtained by an electronic RC or microcomputer device in series with the spectrophotometer and plotted as the spectrum is scanned. This process acts as a filter that favours the short- range changes in spectrum. The result is an enhancement of fine structure, which is accom- panied by a decrease in the signal to noise ratio (S/N). The technique is especially useful in areas such as the visible and ultraviolet spectra of liquid solutions, which usually have high signal to noise ratios but are lacking in structure. In this present paper the advantages of the derivative technique are identified and the trading rules between S/N, derivative order and the wavelength range over which the derivative is averaged are discussed. Advantages When the even derivative spectrum is plotted, two general advantages result.The first is an effective enhancement of resolution, which can be extremely helpful when a solution contains two or more components whose spectra overlap. This effective enhancement of resolution will often result in a separate feature for one or more of the components, which can then be used for quantitative measurements. The second general advantage is a dis- crimination in favour of the sharper features of a spectrum.2 Through this discrimination effect the signal from that component of a solution whose spectrum contains the sharpest structure will be enhanced relative to the signals from the other components whose structure is broader.This effect is useful for selectively eliminating interference by broad-band con- s tituents . Trading Rules The following equation can be derived for S/N for nth derivative spectrum : where the subscripts 0 and n indicate the zero-order and nth derivative spectrum, W is the full band width at half-maximum (FWHM) and AA is the wavelength range over which the derivative is averaged, and is assumed to be small relative to W. The optimum values of n and AA will vary with each application, and this must be determined by trial and error. Ah should be set as high as the required discrimination and resolution permit in order to obtain good S/N. While this will distort the derivative shape, the linearity of the derivative signal with concentration is not affected.Instrumentation The advent of microcomputer ultraviolet - visible spectrophotometers has realised numerous benefits in terms of a faster set-up procedure and more accurate results. Using the numerical keyboard entry, any value for the ordinate minimum and maximum readings can be con- veniently used for the recorder scale. Derivative spectroscopy on a modern microcomputer instrument is now a standard feature, with the inherent flexibility and convenience of aJanuary, 1982 DERIVATIVE SPECTROSCOPY 43 numerical keyboard entry for many of the parameters. The derivative technique is useful in those situations where resolution enhancement can greatly increase the fingerprinting use of ultraviolet spectra and sometimes will separate components in a mixture.This discrimina- tion effect separates spectra with sharp structure from broad interferences for both identifica- tion and quantitation. Although UV spectra have been considered explicitly in this study, the conclusions apply to any other composite curves such as infrared spectra and chromato- grams. Both the advantages and the noise increase with derivative order; the second derivative is almost always more useful than the first derivative. In addition to greater resolution and discrimination, the characteristic second-derivative minimum at the peak of an individual sub-band is easier to identify than the first-derivative shape. The applicability of the higher derivatives is often limited by noise and fine structure in the background.The derivative must be generated by averaging over a finite wavelength range. This wavelength range should generally be about half the width (FWMH) of the sub-bands when resolution is desired, and about equal to the FWMH for the best S/N in quantitative work, where a broader interference is to be suppressed. The distortion of the derivative by these large values is more than com- pensated for by the ability to trade the large resultant S/N for greater matrix suppression. Current developments in analytical instrumentation point to the increased use of the derivative method in spectroscopy and chromatography. References 1. 2. O’Haver, T. C., and Green, G. L., Int. Lab., 1975, 5(3), 11. Cahill, J .E., Int. Lab., 1980, 10(1), 64. Extending the Applications of Derivative Spectrophotometry Christopher T. Cottrell Pye Unicam Ltd., Cambridge The absorbance peaks encountered in ultraviolet - visible spectrophotometry are by nature normally broad, owing to the overlap of the many molecular transitions taking place. For this reason, the precise determination of A,,,. of a broad peak or resolution of multi-component mixtures where peak overlap is present can be difficult. The systematic error encountered with background or sample turbidity can cause similar problems, unless care is taken prior to sample measurement. Many techniques have been proposed for overcoming or reducing these analytical problems, e.g., mathematical correction, variation of measurement wavelength and adaptation of instrumentation.Unfortunately, they all suffer from a variety of compromises, such as time, cost and possibility of introducing errors in the interpretation of the data. One of the more elegant alternatives is the application of derivative spectrophotometry, which was first described by Hammond and Price1 in 1953 and was soon followed by the work of Morrison2 and French et aZ.3 Theoretical aspects of the technique were described by Giese and French4 and derivative orders of second and higher were discussed by Martin.5 Further studies by O’Haver and Green6 concerned the performance of the technique when applied to various band overlap situations, complemented by a discussion of the possible systematic and random errors associated with various methods of measurement .’ The types of presentation obtained by the application of first to fourth derivatives on a variety of peak configurations have been extensively reviewed.8-11 Various instrumental methods have been developed for the generation of derivative spectra.6s10J2 The approach adopted in the design of the Pye Unicam derivative accessory module was that of electronic differentiation of the spectrophotometer analogue output.It was found that this principle allowed the full advantages of the derivative technique to be applied, particularly the ability of using a number of accessory modules in series to generate derivatives up to fourth order, as well as allowing the presentation of derivative spectra at a fixed wavelength for applications such as densitometry and kinetics, etc.Because the derivative signal is, in fact, obtained with respect to time rather than wave- length, the wavelength scanning speed significantly affects both the amplitude of the derivative44 DERIVATIVE SPECTROSCOPY Anal. Proc. spectrum and also the effect of background noise. Thus, increasing the scanning speed will present a more rapidly changing absorption signal to the derivative circuit, with a significant improvement in the apparent signal to noise ratio. Applications and Advantages of Derivative Spectrophotometry Derivative spectrophotometry offers a convenient solution to a number of well defined analytical problems, such as resolution of multi-component systems, removal of sample turbidity, matrix background and enhancement of spectral details.The following briefly describes the major advantages of the application of derivative techniques in ultraviolet - visible spectrophotometry. Applications of derivative techniques in other areas where significant improvements in both analytical performance and speed of analysis can be expected are discussed. Derivative spectrophotometry offers an extremely valuable means of resolving fine detail barely visible in the normal, zero-order, spectrum. For liquid samples, second and fourth derivative orders are the most convenient owing to their ease of interpretation. For resolution of gaseous sample spectra, however, the second derivative is likely to be the most usefu1.13-15 The first derivative for the precise determination of sample maximum absorption wavelength can be very useful, especially when dealing with broad absorbance peaks, where accurate and precise estimations of the latter can prove to be something of a cornpromise.ls-l8 One of the classic analytical problems for any worker in the field of ultraviolet - visible spectrophotometry is the resolution of a number of components in a mixture. For applications of this type, the use of second and fourth derivatives offers considerable advantages.Where small peaks or shoulders appear on the side of a sloping major component background, increasing derivative orders will progressively flatten the major peaks to almost a straight line and resolve the minor components more sharply. Increasing derivative orders will also increase the apparent band sharpening and will, therefore, provide an increase in analytical sensitivity.Most publications concerning derivative ultraviolet - visible spectrophotometry have featured the application of the technique to multi-component resolution and this, in itself, aptly demonstrates the importance of this approach. Derivative techniques have been successfully applied to biological16 and biochemical problems, particularly amino acidslO 3 1 9 s20 and proteins,20-22 and to inorganic1* and pharmaceuticalll systems. Thus, when scanning in the derivative mode, the gradually increasing turbidity will not cause any marked change in the spectrum and will therefore be substantially eliminated, allowing the absorbing component to be readily resolved. This effect of the derivative on sample turbidity suggests a wide variety of applications particularly in water analysis,lO the analysis of pharma- ceutical preparationsll and the examination and measurement of components in biological matrices.23 - 26 Turbidity generally produces an absorbance that increases as wavelength decreases. Extended Applications of the Derivative Technique The derivative technique can also enhance spectral detail generated by methods other than straightforward ultraviolet - visible spectrophotometry. Colour measurement, liquid chroma- tography and densitometry are areas where derivative spectrophotometry can, if applied with care, provide improvements in both qualitative and quantitative information, and significantly reduce analysis time. The technique of colour measurement using an integrating sphere is now an accepted means of obtaining diffuse or total reflectance using tristimulus values and chromaticity co-ordinates, biased for the accepted illuminants and observer angles.In certain situations, the application of the derivative method can provide a useful means of accentuating small differences in detail. The enhancement of analytical detail from HPLC records using the first-derivative approach has been reported using a rapid-scanning diode array spectrometer% to identify small amounts of benz(a)anthracene co-eluting with chrysene, in a reversed-phase separation of atmospheric particulate^.^^ The application of second and fourth derivatives and the implications of the method for quantitation of HPLC data have recently been proposed and demon~trated.~~,~~ The effect of applying the second derivative to a zero-order liquid chromatogram has been examined in our laboratories, using a Pye Unicam LC-XPD pump, SPS-150 spectrophotometer and the liquid chromatography accessory.8 A 2O-pl sample of a mixture of polynuclearJnnzinry, 1982 WATER RESEARCH CENTRE TECHNICAL REPORTS 45 aromatics in an acetonitrile - water eluent was separated using a Partisil 10-ODs-2 column with detection at 245 nm.The application of the second derivative produced an apparent 10-fold improvement in sensitivity. The application of derivatives may prove to be an extremely convenient means of obtaining improved resolution if it has been found impossible to improve conditions further by chromatographic means. The application of derivative spectrophotometry as a means for expanding analytical detail in densitometry has been described by Machold et aL31 and 0kamu1-a.~~ Machold et al.separated various chlorophyll protein complexes by polyacrylamide gel electrophoresis and enhanced the spectral scan detail of fixed pigment-complex zones using the second derivative. Okamura used the second derivative of absorbance versus distance to resolve the ill components in the globulin fraction of human serum proteins, previously separated by cellulose acetate membrane electrophoresis. Lsing a cell compartment densitometer, described by Crane,33 the derivative technique has been applied to a variety of samples, including an autoradiograph obtained by the electrophoretic separation of a complex mixture of radioactively labelled (33S) proteins.The second derivative significantly improved the apparent resolution by reducing the effect of the background and sharpening the absorbance bands such that quantitation could be readily attempted.8 The possibility of applying derivative densitometry to normal acrylamide gels, and more interestingly unstained gels, measured in the ultraviolet region, is being investigated further. The added advantage of being able to scan the zone of interest at a fixed point in the gel with second or fourth derivative recording suggests a powerful new analytical tool for the haematologist. References 1. 3. 4. 5. 6. S. 9. 10. 11. 12. 13. 14. 15. 16. 17. I S . 19, 20. 21. 22. 23. 24. 25. 26. 2 7 . 2s 29. 30. 31. 32. 33. > -. I . Hammond, V. J . , and Price, It'. C. J., J . Opt. Soc. Am., 1953, 43, 924. Morrison, J . D., J . Chem. Phys., 1953, 21, 1767. French, C. S., Church, A. B., and Epplev, R. IV., Cavnepie Inst. Wash. Yeavb., 1954, 53, 182. Giese, A. T., and French, C. S., Apil: Spectrosc., 1955, 9, 78. Martin, A. E., Spectrochim. Acta, 1969, 14, 97. O'Haver, T. C., and Green, G. L., Int. Lab., 1975, 6(5). 11. O'Haver, T. C., and Green, G. L., Anal. Chem., 1976, 48, 312. Cottrell, C. T., "Derivative and Log Spectrophotometry," SP8 Series Accessories Applications, Pye Unicam, Cambridge, 1980. O'Haver, T. C., Clzn. Chem., 1979, 25, 1548. Talsky, G., Mayring, H., and Kreuzer, H., Angew. Chem., Int. Ed. Engl., IS Fell, 4. F., Proc. Anal. Div. Chem. Soc., 1978, 15, 260. 178, 17, 783. Gunders, E., and Kaplan, B., J . Opt. SOC. Am., 1965, 55, 1094. Grum, F., Paine, P., and Zoeller, L., Appl. Opt., 1972, 11, 93. IVilliams, D. T., and Hager, R. N., Appl. Opt., 1970, 9, 1597. Hager, R. N., Anal. Chem., 1973, 45, 1131.4. Shiga, T., Shiga, K., and Kuroda, M., Anal. Biochem., 1971, 44, 291. IVahbi, A. M., and Ebel, S., Anal. Chim. Acta, 1974, 70, 57. Shibata, S., Angew. Chem., I n t . Ed. Engl., 1976, 15. 673. Fell A. F.. I . Pharm. Pharmacol.. 1979. 31. 23P. , ~~ ~ Fell, A. F.: "CrV Spectrom ~ r o u p E u i . , 1979; 71 5. Natsushima, >I., Inoue, I., and Shibata, K., Anal. Biochem., 1975, 65, 362. Brandts, J . F., and Kaplan, L. J , , Biochemistry, 1973, 12, 2011. Schtnitt, .I., J . Clin. Chem. Clin. Biochemistry, 1977, 15, 303. Tones, K. G., and Sweenev, G. D., Clin. Chem., 1979, 25, 71. gotten, D., Instvum. Are&, 1975, 25, 14. French, C. S., and Harper, G. E., Carnegze Inst. Wash. Yearb., 1957, 56, 281. Crane, R. T., "Colour Measurement," SP8 Series -4ccessories Applications, Pye Unicam, Cambridge, Milano. >I. I.. and Grushka. E.. 1. Chromatoev.. 1977. 133. 352. 1978. Fox, li. and Staley, S. w., x n a l . Chem.,s1976, 481 992: Fell, A. F., Anal. Proc., 1980, 17, 512. Machold, O., Meister, -4., and Adler, K., Photosynthetica. 1971, 5, 160. Okamura, K., Clin. Chim. Acta, 1979, 96, 273. Crane, R. T., "Densitometry," SP8 Series Accessories Applications, Pye Unicam, Cambridge, 1978. Water Research Centre Technical Reports The following recently published reports are AIedmenham Laboratory (P.O. Box 16, Henley available from the LVater Research Centre, Road, Medmenham, Marlow, Buckinghamshire,46 EQUIPMENT NEWS SL7 2HD) or Stevenage Laboratory (Elder Way, Stevenage, Hertfordshire, SGl 1TH) : TR 15 I The Calculation of Equilibrium TR 158 TR TR Trace Metal Speciation and Solu- bility in Aqueous Systems by a Computer Method, with Particular Reference to Lead. 52 Calculation of Lead Solubility in 53 Use of Chelsting Ion-exchange TR TR Water. 59 60 Artal. PYOC, Resins for the Determination of Trace Metals in Drinking Waters. A Survey of Polycyclic Aromatic Hydrocarbon Levels in British Waters. Organic Micropollutants in Drinking Water. A Review of Photo-oxidation for the Determination of Total Organic Carbon in Water.