Multielement atomic absorption analysis using Hadamard transform spectroscopy with a new computation and superposition procedure

Spectrochimica

Acla.

Vol. 328,

pp. 59 to 69. Pcrpmon

RCU

1977. Rintd

in Nortbem

Ireland

Multielement atomic absorption analysis using Hadamard transform spectroscopy with a new computation and superposition procedure* M. J. KEIR, J. B. DAWSON and D. J. ELLIS Department

of Medical Physics, General Infirmary, Leeds LSl 3EX, England (Receiued 1 June 1976. Reoised 14 September 1976)

AbstrPet-The application of Hadamard transform spectroscopy (HTS) to analytical atomic spectroscopy has been investigated. A theoretical examination of the signal to noise ratio indicates that HTS offers a slight multiplex advantage over single slit scanning of the spectrum for the measurement of intense lines, as in atomic absorption, but is disadvantageous for measuring small signals in atomic emission and fluorescence. Using a simple HT spectrometer Mg and Pb were determined simultaneously by flame atomic absorption spectrometry. Sensitivities similar to those of conventional systems were obtained but, owing to instrumental imperfections and a short data collection time, detection limits were worse. Optimum system performance was obtained when the mask interval width was equal to the width of the image of the spectrometer entrance slit. Greater spectral detail was revealed by superposition of a set of computed spectra in which the starting point of each spectrum was displaced from the others by a distance less than the interval width of the Hadamard mask. This approach gave improved spectra without increased instrumental complexity.

HADAMARD transform spectroscopy (HTS) is based on an image encoding procedure and has been used with a single detector for the multiplexing of linearly dispersed infra-red spectra to give an improved signal to noise ratio (SNR) [l-3]. Its use in analytical atomic spectroscopy has been limited. PLANKEY et al. [4] used a HT spectrometer for multielement atomic fluorescence studies and HARWIT et al. [5] imaged the 546.1 nm Hg line when evaluating the performance of their infra-red instruments. In multielement spectrochemical analysis the simultaneous measurement of several atomic line intensities is advantageous and therefore we have investigated the usefulness of HTS as a multiplexing technique for analytical atomic spectroscopy. The purpose of our study was an examination of the fundamental limits of HTS in analytical atomic spectroscopy rather than a comprehensive survey of its performance relative to the wide range of techniques available for multielement spectrochemical analysis. In a study of the latter, in addition to the multiplex advantage, factors such as the range of application of the spectrochemical technique employed and the availability of commercial equipment must be

* Presented in part at the 18th Colloquim Spectroscopicurn

Internationale,

Grenoble,

1975.

[l] E. D. NELSON and M. L. FREDMAN, J. Opt. Sm. Am. 60, 1664 (1970). [2] J. A. DECKER, Anal. Chem. 44, 127A (1972). [3] J. A. DECKER, Appl. Optics 10,510 (1971). [4] F. W. PLANKEY,T. H. GLENN, L. P. HART and J. D. WINEFORDNER,Anal. Chem. 46,1000 (1974). [5] M. HARWIT, P. G. PHILLIPS, T. FINE and N. J. A. SLOANE, Appl. Optics 9, 1149 (1970). 59

60

M. J. KEIR,J. B. DAWSONand D. J. ELLIS

taken into account. The theory and benefits of multiplexing in optical spectroscopy have been discussed by WINEFORDNERet al. [6]. We shall present a mathematical analysis of the SNRs of a single slit (SS) scanning system and of a Hadamard system which predicts that the most appropriate use of HTS is in atomic absorption spectroscopy (AAS). In addition we shall describe a variation in the data processing which facilitates the production of a more detailed spectrum without additional complication of the system. In HTS, the intensity distributioq of the selected spectral range is encoded in the focal plane of the spectrometer by a series of N masks. Each mask consists of a set of rectangular apertures (slots) whose widths and separations are integer multiples of the length of the spectral window divided by N. This dimension is the “interval width” of the mask. The radiation passing through the slots is registered by a single detector. Each of the N masks allows the radiation from a unique set of spectral intervals to fall on the detector. In this way, a set of simultaneous equations can be generated which relate the intensity in the spectral intervals to the total intensities measured by the detector. The solutions of these equations give the intensity of the spectral intervals. The pattern of clear and opaque intervals of a mask is determined by a row in an encoding matrix of “1” s and “0” s where a “1” represents transmission and a “0” obstruction of radiation. The encoding matrix should be regular if unique solutions to the simultaneous equations are to be obtained [7]. A modified Hadamard matrix as shown in Fig. 1 is suitable for this purpose [8]. These matrices have the further advantage of being cyclic. A single mask can be made whose length is (2N- 1) intervals and which is capable of generating each line of the matrix in turn by moving stepwise across the spectrum; each step is equal to the interval width of the mask. Matrix multiplication of the transmitted intensities using the inverse of the modified Hadamard matrix gives the intensity distribution in the observed spectrum. The relationship between the spectral image, the transformed spectrum and the computed spectrum is shown schematically in Fig. 2 for the simple case of N = 3. THEORETICALCONSIDERATIONS It has offers no measured the SNRs

been generally stated e.g., by HARWIT and DECKER [9], that HTS multiplex, or “FELLGET?’ [lo] advantage when the spectrum to be is photon noise limited. We have made a theoretical comparison of to be expected when either a single slit or a Hadamard mask is used

[6] J. D. WINEFORDNER,R. AVNI, T. L. CHESTER,J. J. FITZGERALD,L. P. HART, D. J. JOHNSONand F. W. PLANKEY,Spectrochim. Actu 31B, 1 (1976). [7] I. S. SOKOLNIKOFF and R. M. REDHEFFER,Mathematics of Physics and Modern Engineering, 2nd Edit. McGraw-Hill, New York (1958). [8] N. J. A. SLOANE,T. FINE, P. G. PHILLIPS and M. HARWIT, Appl. Optics 8, 2103 (1969). [9] M. HARWITand J. A. DECKER, Modulation Techniques in Spectrometry, Progress in Optics (Edited by E. WOLF), Vol. 12, Ch. 3. North-Holland, Amsterdam (1974). [lo] P. FELLIGETT, J. Phys. Radium 19, 187 (1958).

Multielement

atomic absorption

61

analysis

Spectral aperture Movement

0101110 1011100 0111001 1110010 1100101 1001011 0010111

Fig. 1. An encoding mask for N = 7 and its corresponding modified Hadamard matrix. The matrix is presented in an oblique form to demonstrate the relationship between the slots in the mask and the rows of the matrix. “a” is the interval width.

to scan the same spectrum in the same total time. We find that in certain cases a multiplex advantage should arise. If & photoelectron events-unit time is the intensity in the ith interval then the SNR of a measurement made by a single slit which stepwise scans the spectral window in total time NC% will be: (SNR,,), = J(Xi 6r)

(1)

Spectral aperture -Movement“ Encoding matrix

Decoding matrix 1 1 -1

+ I -1I-1 1 1I I I

I

&ectral A

Iii43

F 1

c

_B

IL Wavelengths (a)

HT transform

I

r

Calculated

A 1

IL

LB ti

D

Mask position (b)

Fig. 2. Schematic representation of the use of the spectral intensity distributions. (a) A five element distribution. (b) The encoding matrix and the resulting tion. (c) The decoding matrix and the calculated

Wavelength (c)

HTS for the derivation of mask and spectral intensity measured intensity distribuintensity distribution.

62

M. J. KEIR, J. B. DAWSON and D. J. ELLIS

If the same spectral window is scanned by a HT mask of N intervals in the same total time then, from the properties of the HT matrix:

(2) ..

(3)

It follows that the Hadamard interval where:

system gives the greater SNR in any spectral

Xi

/ 2 Xj>&. j-l

This condition (Equation 4) is fulfilled when the intensity in any spectral interval is greater than approximately twice the mean spectral intensity. We therefore expect that when the spectrum under consideration contains only a few intense lines these features will be measured with an improved precision but elsewhere in the spectrum there will be a reduced precision of measurement. This conclusion agrees with the analysis by KAHN [l l] and CHESTER et al. [12] for photon noise limited Fourier Transform Spectroscopy and that of LARSON et al. [13] for similarly limited HTS. Some improvement in the precision of measurements can be expected if redundant spectral regions are obscured. The increased precision in the measurement of intense features should improve detection limits in AAS but the reduced precision of background measurements would worsen those for atomic emission and fluorescence. EXPERIMENTAL

SNR studies The validity of the SNR formula (Equation 2) was examined using a simple HT spectrometer simulator. In this device the image of a pattern of bright lines representing spectral lines was projected onto a rectangular aperture which corresponded to a ‘spectral window’ behind which was positioned a 15 element Hadamard mask. The light transmitted by the mask was registered by a photomultiplier. The effective observation interval, St, was approximately equal to the time constant, 6, of the system (0.1 set). The mask was moved in 15 equal steps across the aperture and the photomultiplier signal corresponding to each position, Pi, was registered by a chart recorder. At each step the intensity, Pi, was measured 10 times at intervals of approximately 0.6 sec. The standard deviation of these values, up,, was calculated for each step. Intensities were measured by the deflection of the recorder pen but the theoretical treatment was in terms of photo-electron events. In order that [ll]

F. D. KAHN, Asfrophys. J. 129, 518 (1959). [12] T. L. CHESTER,J. J. FITZGERALD,J. D. WINJSORDNER,Ad. Chem.48, 779 (1976). [133 N. M. LARSON,R. CROSMLJN and Y. TALMI, Appl. Optics13, 2662 (1974).

63

Multielement atomic absorption analysis

theory and experimental results may be compared, a conversion factor, k, is required. If 4 is the intensity measured as photo-electron events per unit time, the factor may be derived as follows: P, = kl,{; . *.

UP,

=

kJl(I,3)

(3

k = ap,‘lPi.

(6)

If yi is the measured intensity of a spectral interval computed recording of the Hadamard transform, then:

from a chart

yi = kt where xi{ is the corresponding SNR will be:

(7)

number of photo-electron

(SNR,)i =

events. The predicted

yi/(k & Flyi)“’ -

(8)

The value of this expression (Equation 8) at several signal levels was computed, measured directly and compared with that given by a single slit observing the same image. The results are presented in Table 1. The average light intensity over the “spectral window” was 1.48 X 10’ photo-electron events per second. According to the theoretical treatment, light intensities twice the average intensity should be measured with greater precision by HTS than by scanning with a single slit. On this basis the figure in the last two lines of the 2nd and 3rd columns of Table 1 should be less than unity. The theoretical values inevitably fulfil the criterion but experimentally the advantage was not realised until the light intensity was 3 to 4 times the average intensity. In general, the experimental results, though limited, are consistent with the theoretical predictions. ANALYTICAL APPLICATIONS Apparatus

To assess the feasibility of a multi-element atomic absorption instrument based on HTS, an Optica CF4 monochromator was modified and used for Table 1. Comparison of theoretical and experimental SNRs of HT and SS scanned spectra Intensity of simulated spectral line (photo-electron events, set-‘) SNR,, theory SNR,, observed SNR,, observed Ratio SNRss theory SNRHn

Rat;?iiF_

observed

1.35 X 10’ 33 34 2.10

3.71

x 10’ 6.08 x 10’

194 145 190 0.87

355 350 306 0.64

1.31

0.87

64

M. J. #FIR, J. B. DAWSON

and D. J. ELLIS

studies of the simultaneous determination of Pb and Mg by flame AAS. The existing entrance and exit slit system was replaced by a fixed entrance slit and a carriage moving in the plane of the exit slit on which was mounted the Hadamard mask. The latter was 210 Frn thick sheet steel in which were cut the slots forming the mask; this divided an aperture 7.5 mm wide (~12 nm) into 15 intervals each of 0.5 mm width. The detector used was an EM1 9529A photomultiplier. As the mask aperture was small, auxiliary optics were not required to direct the transmitted light onto the photocathode. In conventional HTS systems the mask is moved stepwise across the aperture. In our work, however, the carriage was continuously driven via a linkage to the pen of a chart recorder which moved in response to a linear ramp voltage. The mask traversed the region of spectrum to be encoded at a constant velocity in 0.4 sec. The continuous variation in radiation transmitted by the mask was detected using a photomultiplier tube whose output was presented on a fast response U.V. chart recorder (SE. 3006). The time constant of the recording system was 0.3 msec. The position of the mask was simultaneously recorded on the same chart by means of a photo-electric sensing device. This scanner consisted of a small collimated light source set on one side of the mask carriage and opposite, on the other side of the mask carriage, was a photodiode. A series of small, equally spaced holes drilled in the mask was viewed by the sensor system. As the mask moved, a series of electrical pulses was generated corresponding to the mask position. From the chart trace an accurate estimate of the mask position was obtained for eight points along the scan; more detailed information was derived by linear interpolation between these points. The intensity of the light transmitted by the mask was measured at points on the chart recording corresponding to known positions of the mask. Calculation procedure The matrix multiplications required to derive the spectra from the chart recording of the transmitted light intensity were performed on an electrical analogue-digital calculator designed and built in the laboratory. In this device, voltages proportional to the deflections on the chart record were generated using a linear potentiometer. These voltages were converted into trains of pulses and were simultaneously entered into 15 “up-down” counters. The states of the counters were determined by the requirements of the decoding matrix. Apart from a constant factor, the elements of this matrix are all *l, and the required spectral intensity distribution was then proportional to the residual total in each of the counters after all 15 intensities had been entered. The calculations were carried out by first determining, from the position sensing trace, the 15 points on the chart corresponding to the 15 standard positions of the mask. The amplitudes of the intensity trace at these points were then entered in the calculator. When continuous rather than stepwise scanning is used, a more detailed spectrum may be obtained by repeated processing of the recorded intensity distribution using origins slightly displaced from that of the first mask position.

Multielement

atomic absorption

analysis

65

This approach represents a significant dzparture from conventional HTS systems in both the data acquisition and utilisation process and gives spectral detail which previously has only been obtained with the aid of masks whose interval width is much less than the width of the images of the entrance slit. The resolution of the system is not, however, increased as this is determined by the width of the entrance slit. The measurement procedure was as follows: the first spectrum was computed in the normal manner by sampling the recorded trace at a set of 15 points corresponding to standard positions of the mask. The next set of calculations assumed the first position of the mask to be displaced halfway towards the original second position. Starting from this new origin, each sampled point corresponded to a displacement of one half interval width from the first set. A composite spectrum was then derived by plotting both spectra together on the same set of axes and allowing for the displaced origin of the second spectral distribution; a more detailed spectrum was obtained than would be achieved by plotting either spectrum alone. Further spectral detail was obtained by initiating the sampling of the trace from other displaced origins such as, for example, one quarter and three quarters of a mask interval width. As the number of such sub-interval sets was increased, the spectral detail approached that given by a single slit continuously scanning the spectrum. The limit to the detail is set by the entrance slit width, the radiation intensity and the response time of the system. An example of a Hadamard transform and the spectrum computed by the above procedure is shown in Fig. 3. The advantages of continuous scanning over conventional stepwise scanning arise from matching the mask interval to the width of the image of the entrance slit and are: (i) for photon noise limited spectra, Equation 3 indicates that the optimum SNR is obtained; (ii) the number of mathematical operations required to give the same level of detail is proportional to the number of measurements in the former approach and to the square of the number in the latter; (iii) the mask is easier to make because the interval width does not need to be made smaller than the entrance slit width to reveal the available spectral detail. Observations

The scanning HT Spectrometer was used to study the simultaneous determination of Pb and Mg by flame atomic absorption. The spectral region 288.G 271.5 nm was encoded to accommodate the resonance lines of Pb at 283.3 nm and Mg at 285.2 nm emitted by two d.c. operated hollow cathode lamps. The radiation from these was combined using a semi-silvered mirror and then passed through an air-&Hz flame burning on a water cooled, 7-cm long path burner before entering the monochromator. Figure 4 shows four examples of spectra obtained while making analytical measurements with the system. Spectra c and d were used to compute the background intensities to be subtracted from the resonance line intensities. Intensities less than twice the mean intensity, indicated by the horizontal lines in Fig. 4, will be measured

66

M. J. KEIR, J. B. DAWSON and D. J. ELLIS Position

Mask

sensw

position

(b)

280

270 Approximate

wovelength.

nm

Fig. 3. (a) The recorder traces of the Hadamard Transform of a spectrum from the combined radiation from Pb and Mg hollow cathode lamps and of the position sensor output. (b) The spectrum derived from a single set of measurements on the trace shown in (a). (c) The spectrum derived from the inclusion of data derived from a further seven sets of measurements on the same recorded trace.

with less precision by HTS than by SS scanning. The non-resonance line of Pb at 280.2 nm can be used to correct for non-specific absorption by the sample vapour but this facility was not used in this study. A set of standard solutions of Pb and Mg in concentrations of 420 pg/ml Pb and 0.1-0.5 pg/ml Mg in 0.1 N HNO, was prepared and used to obtain the calibration curve for the simultaneous detection of Pb and Mg shown in Fig. 5. The data points are the mean of four observations, hence points below the detection limit for a single measurement may be plotted with confidence. From these measurements, sensitivities of 1.0 pg/ml and 0.028 pg/ml for 1% absorption by Pb and Mg respectively were obtained. The detection limits, expressed as the concentration equivalent to twice the standard deviation of a measurement at zero concentration, were 9.7 pg/ml for Pb and 0.16 pg/ml for Mg. While the detection limits were worse than those of a conventional flame system of measurement, the sensitivities were comparable with those usually obtained. No attempt was made to optimise the instrumental

Multielement atomic absorption analysis

(c)

67

(d)

Approximate

wavelength,

nm

Fig. 4. Spectra derived by HTS. (a) Spectrum of flame emission. (b) Spectrum of flame with Pb and Mg hollow cathode lamp emission. (c) Spectrum (b) with Mg 285.2 nm line removed by absorption. (d) Spectrum (b) with Pb 283.3 nm line removed by absorption. - - - - 2 x mean intensity.

parameters. The curvature of the Mg calibration is probably a consequence of defects in the encoding system and inaccurate background subtraction. With a view to possible improvements in the system, the sources of fluctuations were investigated. To facilitate the analysis it was assumed that the contribution of each source was random and independent of other sources. The results of these calculations are summarized in Table 2. The data are presented in concentration units to facilitate comparison with the measured detection limit figures. In a perfect system, at the spectral line intensities used in this study, fluctuations in the photo-electron event rate would set detection limits of 0.05 pg/ml for Mg and 2.0 pg/ml for Pb. The difference between the observed and limiting detection limits are attributable to fluctuations in the flame and in the Hadamard system. The former contribution was assessed by using the instrument as a monochromator with the flame operating and aspirating distilled water. The effect of the data reduction process on the overall detection limit of the system was deduced from repeated independent measurements of the recorder traces from 10 scans of the spectrum.

68

M. J. KEIR, J. B. DAWSON and D. J. ELLIS

a

4

8

01

02

12

concn ,

Fig. 5. Calibration

16

03

04

20

Pb

05

Mg

w

pg /mt

curves for the simultaneous

determination

of Pb and Mg.

On completion of measurements using the HT system, the monochromator was restored to its original condition for SS scanning measurements. The monochromator was fitted with a wavelength drive and, using a slit equal to the HT mask interval width, the same spectral interval was scanned in the same total time as in the HT studies. The electronic system, burner and hollow cathode lamps were also the same. The detection limits for a single scan were 0.074 pg/ml for Mg and 4.1 pg/ml for Pb. The corresponding theoretical values calculated from the photo-electron event rate were 0.092 yg/ml and 2.8 pg/ml, respectively. This general agreement between the experimental results and theoretical prediction indicates that under the experimental conditions employed, the stochastic nature of the photo-electron flux is the dominant source of fluctuation in the system. The experimental detection limits of the SS system are approximately half those obtained with the HT system, Table 2. The performance of the HT system is principally limited by inaccuracies in the mask position sensing system. A time constant of 0.3 msec was used with a view to studying transient phenomena. Owing to this short time constant, the effective observation time of Table 2. Analysis of factors determining the flame AA detection limits of Mg and Pb when using HTS. Contributions Element Light source Mg Pb

0.046 1.98

Detection limit (pgiml)

to system “noise” (&ml)

Analog/ Flame Hadamard back- transform Position digital scan ground sensor conversion 0.091 5.0

0.02 1.37

0.163 8.09

0.010 0.55

Sum of individual contributions 0.19 9.8

Observed 0.16 9.7

Applicationof a gaseous-burstagitation technique

69

an HT scan was 2.5 msec and of an SS scan 0.3 msec/spectral interval per scan. These observation times are very much less than those generally used in flame atomic absorption analysis (31.0 set). Consequently by virtue of the limited amount of information collected, the detection limits by our scanning systems must be at least an order of magnitude worse than by a conventional static system. An increase in the observation time in an HT system would improve the fundamental limit set by the randomicity of the photo-electron flux and would also reduce the effect of random flame flicker. Combined with an improved mask position sensing device these changes could lead to simultaneous detection limits for several elements using an HTS system which are no more than a factor of 3 or 4 worse than those by conventional instruments. CONCLUSION Our analysis of the SNRs obtained when imaging a spectrum by Hadamard transform and single slit scanning systems shows that even in the case of source noise, limited spectra some multiplex advantage may be obtained when using HTS for the measurement of peak intensities. Thus HTS is principally of value in AA measurements when relatively intense signals are measured; it produces inferior results when used in atomic emission and fluorescence spectroscopy. HTS is suitable for simultaneous multi-element atomic absorption analysis provided that an appropriate multi-element light souice is available and the spectrometer can accommodate the corresponding spectral range. For use in routine analysis, on-line or built-in computing facilities would be necessary. It is unlikely, however, that, even in the most favourable circumstances, an HT spectrometer can offer advantages which could not be achieved more easily by other means such as a slewed scan spectrometer. As a generally applicable procedure, we have shown that additional spectral detail is revealed by the superposition of a succession of computed spectra whose origins are displaced from each other by distances less than a mask interval width. This can be achieved either by continuous movement of the HT mask, as used in this study, or, more effectively, by sub-interval stepping across the spectrum. This approach requires less computing power than would be necessary if further detail were to be obtained by reducing the mask interval widths. Optimum system performance is obtained when the mask interval width is equal to the width of the image of the spectrometer entrance slit and unwanted parts of the spectrum are obscured. Acknowledgements-We wish to thank the Medical Research Council for a grant to one of us (M.J.K.) and Mr. P. MORAN for technical assistance. We are grateful to The Royal Society for a grant for the purchase of the high speed recorder.