Selection of source-modulation waveform for improved signal-to-noise

Signal-to-Noise Ratio in Atomic Absorption Spectrometry. G. M. Hieftje. Department of Chemistry, Indiana University, Bloomington, Ind. 47401. B. E. Ho...
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Table 111. Recovery of Te Spikes by CoprecipitationProcedure

Sample Telluride

Te added, ng 200 400

Sphalerite

800 20 40 80

Te found, ng 190 380 760 18

45 85

Error, ng - 10 - 20 -40 -2 +5

$5

Error,

2 -5.0

-5.0 -5.0 -10.0 $12.5 +6.2

Table IV. Analysis of Samples Sample Procedure Te found Se solution, 1 pg/ml (purified) Direct extraction, std curve 1 .7 ng/ml Se metal Direct extraction, std curve 4 , 3 pprn SeO? Direct extraction, std curve 2 . 9 ppm SeOCle Direct extraction, std addns 0.38 ppm HzS04 Direct extraction, std addns 57 ppb Sphalerite, A. L. Davis Mine (Ill.) Coprecipitation, std curve 130 ppb Galena, Blue Diggings Vein (Ill.) Coprecipitation, std curve 55 ppb

the sample solution were spiked with known amounts of tellurium, and the recovery from the coprecipitation process was determined by comparison to a standard curve. These results appear in Table 111. To establish the validity of the sulfide ore analyses, four 1-gram samples of sphalerite were weighed into 250-ml round bottom flasks, spiked with 0, 0.2, 0.4, and 0.8 ml of 0.1 pg/ml tellurium standard, and treated as described in the procedure for sphalerite. The recovery of the tellurium spikes as determined by comparison to a standard curve is shown in Table 111. Other samples of low, unknown tellurium content were analyzed by the procedures outlined. The results of these determinations are summarized in Table IV.

Delves Cup Method. Since the development of the sampling boat technique, a modification of the same principle with even greater sensitivity has appeared. It was developed for the determination of lead in blood and consists of a small nickel cup, which is inserted into the flame under a n openended ceramic tube, aligned so that the beam from the hollow cathode lamp passes through it. The volatilized material enters the tube through a hole above the cup and is momentarily retained, thereby increasing the sensitivity. The Delves cup method is described in detail by Fernandez and Kahn (16). The technique was tried for tellurium after MIBK extraction and showed an astounding sensitivity of 0.5 ng. Since the reagent blank encountered in the coprecipitation procedure, however, was a n order of magnitude greater than this, the extra sensitivity was redundant, and the technique was not pursued further. When direct extraction is applicable, however, the Delves cup method would provide an ultra-sensitive tool for measurement. ACKNOWLEDGMENT

The author wishes to thank W. T. Schrenk and W. D. Edwards for their interest and helpful consultation. Grateful acknowledgment goes to D. L. Beaty for his experimental assistance and B. L. Perry of the Mining Division of OzarkMahoning Company for his cooperation in furnishing ore samples. The support and encouragement of 0. K. Manuel is especially appreciated. RECEIVED for review July 20, 1972. Accepted October 6, 1972. This work was financed in part by NDEA Title IV Fellowship and a National Science Foundation Grant, NSFGA-12099. (16) F. Fernandez and H. L. Kahn, At. Absorption Newslett., 10, 1 (1971).

Selection of Source-Modulation Waveform for Improved Signal-to-Noise Ratio in Atomic Absorption Spectrometry G. M. Hieftje Department of Chemistry, Indiana Unicersity, Bloomington, Ind. 4740 I

B. E. Holder, A. S. Maddux, Jr., and Robert Lim Unicersity of California, Lawrence Livermore Laboratory, Livermore, Calif. 94550

Electronic modulation of a hollow cathode light source with a sine wave, a square wave, and a Pseudo-random binary sequence has shown that significant differences exist in detection efficiency, signal-to-noise ratio, and practical utility, depending on the choice of waveform. Sauare-wave modulation in which the hollow cathode lamp is never completely turned off provides greater stability than that produced by a completely on/off system. Square-wave modulation/detection also permits greater signal-detection efficiency than is possible with a sinusoidal waveform. The use of a pseudorandom binary sequence for modulation/detection was also evaluated and appears to be of limited utility in atomic absorption spectrometry.

SINCETHE EARLIEST application of atomic absorption spectrometry to chemical analysis, it has been realized that modu238

e

lation of the primary light Source is a useful and often essential technique for improving sensitivity and precision and for minimizing flame background and emission effects (1-3). Even in early studies, electronic ( 4 ) and mechanical ( 5 ) means were used for source-modulation in ways similar to those used in modern instruments. Since that time, a great deal of effort has been devoted to improving detection _

I

(1) A. Walsh, Spectrochim. Acta, 7, 108 (1955). (2) M. L. Parsons and J. D. Winefordner, Appl. Spectrosc., 21, 368

(1967). ( 3 ) J. D. Winefordner, W. J. McCarthy, and P. A. St. John, J. Cliem. Edrc., 44, 80 (1967). (4) G. F. Box and A. Walsh, Spectrochim. Actu, 16, 255 (1960). (5) B. J. Russell, J. P. Shelton, and A. Walsh, ibid., 8, 317 (1957).

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systems for the modulated signal (6-8) and to developing modulation techniques not involving the source intensit) (9-11). However, aside from studies concerning the source reliability (IZ),very little has been done in optimizing modulation or in establishing the method of implementation. In conventional systems, chopper modulation or simple electronic modulation is usually employed with a selectively tuned or a lock-in amplifier detector. Because of either physical limitations or inconvenience, it has been difficult in the past to undertake investigations wherein the modulation/ demodulation operations could be studied and optimized. In the study presented herein, it has been found that the modulation process can itself be the dominant source of noise and serve to obscure an atomic absorption signal. Thus, the final signal characteristics depend significantly on the modulation type and waveform; by use of the optimum technique, signal-detection efficiency can be increased and instrument cost can be reduced. In this study, electronic modulation of a hollow cathode light source with a sine wave, a square wave, and a pseudorandom binary sequence has shown that significant differences exist in detection efficiency, signal-to-noise ratio, and practical utility; and the differences depend on the choice of waveform. It has been determined that square-wave modulation in which the hollow cathode lamp is never completely turned off provides greater stability than that produced by a completely on/off system, and this technique permits greater detection efficiency than is possible with sine-wave modulation. Operation of the hollow cathode in a pulsed mode is also considered; if it is used with a suitable detection system, it is predicted to yield higher signal levels and improved lamp lifetime over that obtained with square or sine-wave modulation systems. Also, a new modulation technique is introduced that involves the use of a random or pseudo-random binary sequence to modulate the light source. The modulated signal has an apparently random pattern identical to the original sequence. By using the original sequence to demodulate the signal after conventional detection, one can separate the signal from any accompanying noise. Although this technique theoretically would enable greater signal-to-noise enhancement than conventional lock-in techniques, practical considerations are expected to limit its application to systems in which a considerable amount of interference noise of unknown frequency is present. MODULATION AND DEMODULATION PROCESSES

To present a unified approach to the choice of a source modulation scheme in atomic absorption spectrometry, we briefly discuss here the processes of modulation and demodulation. In this discussion, we consider only amplitudemodulated signals. Signal Modulation and Recovery. In an instrument system such as an atomic absorption spectrometer, the signal that is obtained and related to concentration usually carries a great (6) R. R . Alfano and N. Ockman, J. Opt. Soc. Amer., 58,90 (1968). (7) T. Coor, J . Chem. Ediic., 45, A583 (1968). (8) D. J. Fisher, R. W. Stelzner, and H. C. Jones, Chem. Instrum., 2 , 51 (1969). (9) W. Lang, Microchirn. Ichnoanal. Acta, 5 , 796 (1964). (10) W. Snelleman, Spectrochim. Acta, 23B, 403 (1968). (11) W. Marinkovic and T. J Vickers, ANAL. CHEM.,42, 1613 ( 1970). (12) J. C. Burger, W. Gillies, and G. K. Yamasaki, Westinghouse Prod. Eng. Memo. ETD-6403 (1964).

deal of noise that has been introduced by the flame, the detector, the electronics, and the light source. By uniquely encoding the desired signal-for example, by chopping the light source-and by efficiently decoding the signal during detection with, for example, a lock-in amplifier, the noise can be quite efficiently reduced. This is realized because the noise, in order to be observed, would have to have the same coding signature as the signal, The signal can be conveniently encoded by impressing its amplitude on a carrier wave of some form, in a fashion similar to that employed in AM radio systems. Alternatively, this can be thought of as altering the signal by the carrier wave to produce a wave having the form of the carrier but with an amplitude related to the signal level. This procedure, called modulation (13), is exactly that used in mechanically- or electronically-chopped atomic absorption spectrometers. The waveform that is impressed on the signal during modulation is generally termed the modulation function-that is, the modulated signal can be obtained by multiplying the original signal level by a modulation function of unit amplitude. The ideal modulation function is assigned a unity peak amplitude and an average value of zero. It is important to realize at this point that the modulation function can have any waveform and is limited only by instrumental restrictions such as frequency response, ease of generation and detection, and signal-recovery convenience. The process of recovering the original signal from the modulated waveform is called demodulation and is discussed in more detail below. In designing an instrument to utilize modulation, two important considerations hold. First, to most efficiently minimize noise, the signal should be modulated as early as possible in the instrument. Any noise present on the signal at the point of modulation will be modulated along with the signal, so that it, too, will be detected. When the signal is modulated as early as possible, the least amount of noise will be included. Of course, it is also important that the modulation function and the device causing the modulation be free of noise, to prevent its unwanted introduction onto the signal. Second, it is important that a clean, noise-free modulation function be available for use in the demodulation system; it has been said that, for optimum signal recovery, the modulation function should have exactly the same waveform as the modulated signal (14). However, this is shown to be unnecessary and even undesirable in some cases. T o satisfy these criteria, an atomic absorption spectrometer such as that shown schematically in Figure 1 can be designed. Figure l a is a block diagram of a generalized atomic absorption instrument that uses light-source modulation for signal improvement ; Figure l b indicates the arrangement of the physical systems (hollow cathode, monochromators, etc.) that were assembled for this investigation. The correspondence between the various blocks or combination of blocks in (6) to provide the functions indicated in ( a ) is fairly obvious. Figure l b shows that modulation is imposed at the earliest possible point in the instrument: at the power supply of the hollow cathode light source. This, of course, requires an electronic modulation system, since a light chopper would have to be inserted after the light source. In a choppermodulated instrument, noise originating in the hollow cathode lamp or in its power supply will be fully carried through the system. This is not true for the electronically modulated system, as we discuss in greater detail below. Also, when (13) N. S. Black, “Modulation Theory,” Van Nostrand, Princeton, N.J., 1953. (14) D. J. Fisher, Chem. Instrum., 2, 1 (1969).

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p H 7 1 Modulator

absorption ~ight-

source

H b-7 Spectralre lect ion

system

(photomultiplier) Transducer

system

Electronic Reference waveform

1

-

I

Readout system (recorder, etc .) output a.

Figure 1. (a) Block diagram of a generalized source-modulation atomic absorption system; (b) block diagram of the physical systems used in this work .irr

Optics

c

4 (square, sine, PRBS, etc.)

b.

Frequency

Frequency f

0

Figure 2. Frequency spectra of original signal and signal modulated with a sine wave of frequencyfo electronic modulation is used, no limitation is imposed on the waveforms of the modulation or demodulation functions. In order to more fully understand the effect of modulation, it is helpful to examine the signal transformations that occur within the instrument in Figure 1. These are illustrated in Figure 2. Generally, the original signal information will be found in a narrow band of frequencies (Af) near zero (that is, dc). This is equivalent to saying that an instrument must have a response time chosen to satisfy practical operating criteria ; this response time implies a finite frequency bandpass. In the process of modulation, the signal information is moved to symmetrical positions about the frequencies existing in the waveform of the modulation function. For example, with simple sine-wave modulation, the modulated signal will have a spectrum such as that shown in Figure 2, where the modulated signal information is located symmetri240

cally about the modulation frequency f ~ .For square wave, pulse, random, or pseudo-random modulation, of course, the process is similar, although the spectra become more complex. The important point here is that, through modulation, the signal is given a distinct spectral signature that distinguishes it from noise which is not modulated. Note also that, although phase is not portrayed in Figure 2 , the phase relationships of all frequencies in the modulated signal can also be used in separating the signal from noise. Therefore, because each waveform possesses its own characteristic frequency components and phase relationships, a unique waveform is a desirable characteristic of the modulation function. Demodulation performs the reverse process of modulation. Ideally, the original signal can be exactly recovered by modulation followed by demodulation; this is symbolized by the reverse arrow in Figure 2 . When demodulation is performed correctly, all frequency components in a modulated signal are recombined exactly in the correct phase to generate the original signal information (Af). During demodulation, it is essential that all traces of the modulation waveform be removed. If this condition is not met, the residual modulation waveform will appear to be noise. This problem and the demodulation process are described below. Instrumental Implementation. The primary light source can be modulated through either electronic or mechanical means, with the former preferable, as discussed above. Either technique is relatively simple to implement with hollow

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Figure 3. Schematic diagram of a simple analog demodulator. M ( t ) : modulation function; S(t): information signal

signal I

Refer’ence

cathode discharge lamps; commercially available systems illustrate this. Other sources are also occasionally used for atomic absorption (or atomic fluorescence), however, and it is equally desirable to employ modulation in these situations. Mechanical chopping of other sources is, of course, the same as that which would be used with a hollow cathode lamp. Electronic chopping has long been used with Osram lamps (1.5) and has recently become possible with high-intensity electrodeless discharge tubes (16,17). In simple sine-wave or square-wave modulated systems, a commercial lock-in amplifier (synchronous detector, phasesensitive detector) can serve as a demodulator (7, 18). However, for application to complex waveforms, a more general demodulator can be constructed as illustrated in Figure 3. The instrument in Figure 3, consisting of an analog multiplier and a low-pass filter, is essentially a lock-in amplifier without a tuned filter on either the reference or signal input. This instrument can also be considered to be a single-point correlator with zero delay (19). In Figure 3, the modulated wave is represented by the product of the original signal S(t) and the modulation function M(r). Remembering that the modulation function has a frequency considerably higher than that of the signal information, which is essentially dc, one sees that multiplying the modulated signal M(t)S(t)by the modulation function M ( t ) gives a product that, after averaging, has a value that is just the original signal multiplied by a constant, the constant being equal to the mean square of the modulation function. Thus .____

Output = [ ~ ( t ) l[*~ ( t )=] kS(t)

(1)

The efficiency of signal recovery in a typical demodulator such as shown in Figure 3 is governed by several factors, including the degree to which the instrumental components approach the ideal, the efficiency of the low-pass filter in eliminating components of the modulation function from the demodulated signal, and the value of the mean square, [M(t)12. It is important to realize at this point that any noise accompanying the signal into the detector in Figure 3 will not be demodulated, since it will produce a zero average. This can be best realized by remembering that the modulation function has an average value of zero. Therefore, any noncoherent function that is multiplied by this function will also have a zero time average. Only the atomic absorption signal, which has been impressed on a carrier of identical waveform, will generate a nonzero average. The problem of completely eliminating the modulation function from the demodulated signal is especially acute in atomic absorption flame spectrometry (AAS) because of the unusual requirement of subtracting two large photometric (15) R. C. Mackey and S. A. Pollack, Appl. opt., 2, 542 (1963). (16) P. C . Wildy and K. C . Thompson, Analyst (London), 95, 562 (1970). (17) K. C. Thompson and P. C. Wildy, ibid., p 776. (18) L. C . Caplan and R. Stern, Reu. Sci. Znstr~tm.,42, 689 (1971). (19) P. J. Garforth, Electron. Znst. Digest, 6 (8), 7 (1970).

signals. Because the amplitude of the modulation waveform is equal to that of the (large) photometric signal, it is quite likely for some residual modulation function to remain after demodulation and thus appear to be noise. Further, the rather short time constants commonly used in AAS aggravate this situation. In the studies presented herein, it is found that this “noise” is responsible for many of the differences in detection efficiency observed for various modulation waveforms. EXPERIMENTAL

Instrumentation. The instrumental system used in this study is essentially that shown schematically in Figure 1. The modulated power supply for the hollow cathode lamp was constructed expressly for use in this work (20). Its design allowed a broad range of modulation functions to be used in either a linear (ripple) or a 100% mode. The term “ripple” as used here refers to anything less than 100% modulation; that is, the source is never completely extinguished. Onehundred per cent modulation implies a fully on/off form of modulation. The optical system used was that of a Jarrell-Ash Model 82-536 atomic absorption unit with a slit width of 100 pm. A multielement (Ca-Mg-AI) hollow cathode lamp, Westinghouse Type WL 22930, was used throughout, with the calcium 422.7-nm line being observed. Although differences exist in the behavior of hollow cathode lamps for various elements, we expect the observations made on this lamp to be applicable to all hollow cathode lamps and, to a great extent, to all sources used in atomic absorption spectrometry. For detection, a 1P28 photomultiplier was used at an applied potential of 600 V. The photomultiplier output current was converted to a proportional voltage by a suitable photometric preamplifier and passed to the demodulator. By monitoring the photomultiplier output under high signal-tonoise ratio conditions, it was ascertained that the modulated light intensity from the hollow cathode lamp followed the modulation function waveform quite well. Only the squarewave modulation produced a noticeable difference, with the hollow cathode radiation having a somewhat slower risetime than the modulation function. A demodulator, similar to that shown in Figure 3, was used to decode the modulated signal from the photomultiplier and was designed and assembled from components, using a linear, analog multiplier and an active single-pole RC lowpass filter (21) with a time constant selectable from zero to 100 sec. With this system, the signal-to-noise improvement and elimination of residual modulation function obtained by using the various modulation techniques could be conveniently compared. Modulation/demodulation waveforms were obtained from a function generator or a noise generator depending on the waveform to be used. Signal-to-Noise Ratio Measurement. Signal-to-noise enhancement in atomic absorption flame spectrometry is unusual in that, rather than requiring a small signal to be extracted from noise, this technique requires that two very large signals, (20) B. E. Holder, R. Lim, A. Maddux, and G. Hieftje, ANAL. CHEM.,44, 1716 (1972). (21) “Philbrick Application Manual,” Nimrod Press, Inc., Boston, Mass., 1966, pp 74-8.

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a.

For the investigation of drift and intermediate-frequency ise, the demodulator output was passed to a stripchart :order having approximately a 0.1-sec time constant. Inmediate-frequency noise was then taken as ' i sof the peak.peak excursions in the recorder trace (22). Provided that a sufficiently long noise record is taken, this technique provides a 99% confidence of obtaining the true rms noise level. Drift was observed from trends in the recorded trace. For the determination of higher-frequency noise power, an rms voltmeter was used. By obtaining a true rms value for both high- and low-frequency noise, the signal-to-noise ratio can he calculated for each case merely by dividing the (dc) signal level obtained at the demodulator output by the rms noise. This procedure has been found to produce the required accuracy in the measurement of both signals and noise. To more easily distinguish between the various techniques to be studied, the signal-to-noise ratio at the demodulator input was intentionally degraded by offsetting the monochromator wavelength adjustment. This is not an unexperienced occurrence in real situations and will serve to emphasize differences that are observed in signal-to-noise enhancement capability. With this intentional offset, the modulated input signals bad the appearance of the oscilloscope photographs of Figure 4 for sine-wave, square-wave, and pseudo-random modulation, respectively. T o obtain these traces, the modulated hollow cathode radiation was measured directly at the preamplifier output, using appropriate gain for the measurement. Throughout this study, the sine- and square-wave modulation frequencies were set at 310 Hz, to minimize interference by power lines. RESULTS AND DISCUSSION

(a) Sine-wave modulated source: (b) squarewave modulated source; (c) pseudo-random binary sequence modulated source. Vertical sensitivity: .- .. . .. . . . scale: 2 msecldivision

m e mcmenr ire) ana rransmitted (P)light intensities, be suhtracted from each other to obtain a signal which must be distinguished from noise. Because Pa and P are usually measured at different times separated by at least several seconds, drift in the measurement system becomes very important. Also, large detected signal-to-noise ratios for P or Pobecome less impressive when the signal values are subtracted. Therefore, small differences in signal-to-noise ratios, which are obtained for the detected hollow cathode radiation by using the various modulation forms discussed below, are more significant than would initially be apparent. For this reason, considerable care was necessary in the measurement of the ratios and, to improve clarity, a distinction was made between low-frequency (drift) and high-frequency noise. 242

To most easily evaluate the use of various modulation functions, results obtained hy using sine-wave modulation are first interpreted and compared to thoseobtained with square wave 100% and ripple modulation. The potential utility of pulse modulation is next considered. Finally, the advantages and limitationsof usinga pseudo-random pulse sequence for modulation are investigated and compared to the other techniques. Sine-Wave Modulation. If a sinusoidally modulated signal and a sine-wave reference are introduced into the demodulator of Figure 3, the output of the multiplier will he a sine-squared wave with an amplitude proportional to the original signal level. Without the use of a low-pass filter, this wave appears as the dominant component of the noise, as shown in Table I. However, when the low-pass filter is used, the wave provides an averaged output equal to the original signal level times the mean square of the sine-wave modulation function (see Equation l). For a sine wave, the mean-square value is 'I2the peak value, so that, for an ideal modulation function, the demodulator output will he half the original signal level. This argument also assumes a perfect low-pass filter, that is, that the ac portion of the sine-squared wave is completely removed by filtering. In Table I, we see that a significant time constant is necessary to remove this ac portion, which, if not removed, is seen as noise. SquareWave Modulation. For a square-wave-modulated input and a square-wave reference, the unfiltered output of the multiplier in Figure 3 will ideally be a dc level. This can be readily understood by recalling that the modulation function, which acts as a reference wave, has only values of +1 and -1 and is in phase with the modulated signal, which has values of + S a n d --S, when S is the original signal. Multiplication of these waves therefore will ideally produce a constant level of S, apparently obviating the need for a filter. (22) V. D. Landon, Proc. IRE, 50 (Feb. 1941).

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In practice, it is found that neither modulation nor demodulation is perfect and that the multiplier output value exhibits spikes a t the times when the signal and reference waves change phase. The unfiltered noise measurement in Table I includes this spike “noise” contribution from the modulation waveform. Even when this noise contribution is included, the signal-to-noise ratio (unfiltered) is higher for square-wave modulation/demodulation than for the corresponding sinewave case. There are two reasons for this: the spikes that appear at the output of the unfiltered demodulator produce less noise than the sine-squared wave obtained earlier; also, for the square-wave situation, the output signal level is approximately equal to the peak amplitude of the modulated signal S , whereas sine-wave modulation produced a value of S12. The spikes occurring in the demodulated square-wave, of course, reduce its value slightly, so that the ratio of the two signals is not exactly 2 . These factors combine to produce a significantly greater signal-to-noise ratio for square-wave than for sine-wave modulation. Even when a 100-msec filter is employed in the demodulator, square-wave modulation is observed to provide a more noise-free output. This occurs because the modulation function is the dominant form of residual noise in this system and the fast-rising spikes resulting from square-wave modulation are more readily removed than the relatively low-frequency sinusoidal modulation function. If sine-wave modulation is employed, it is important here t o realize that a square-wave demodulation function can still be used, with the result having a n efficiency between that obtained with sine-wave modulation,’demodulation and squarewave modulation/demodulation. When a square wave is used to demodulate a sine-wave-modulated signal, the result will be a level having the average value of the sine wave, which is 0.636 of the peak value. This point has considerable practical significance, because square-wave demodulation can be per formed with a nonlinear switching (binary) circuit ; therefore, instrument complexity can be reduced and reliability increased. This principle is used to advantage in some commercial lock-in amplifiers with squaring circuits at the reference input. Ripple Modulation. ‘To facilitate cornparison, the signal was modulated 100% in both the preceding cases by turning the hollow cathode source completely o n and off. Although this procedure produces the greatest variation in signal and therefore the greatest final signal level after demodulation, it can be shown that, for hollow cathode lamps, and probably for most sources, a significant practical advantage can be gained by employing less than 100% modulation. Considering the generalized instrument in Figure 1, it can be seen that turning the source on and off effectively places the point of modulation after the hollow cathode lamp, which is a situation similar to that found in mechanically chopped instruments (23). Therefore, any noise or drift originating in the hollow cathode or its power supply will not be eliminated. In addition, it has been found that the on/off shock produced in hollow cathode lamps generates further instability and shortens lamp lifetime (12). This problem can be reduced by using less than 100% modulation. If the lamp is never completely extinguished during modulation, the modulated light intensity will appear as a ripple on the constant “on” level and will have a n amplitude more dependent on the modulation-function amplitude and less dependent on the absolute light intensity or on the lamp characteristics. To study this behavior, we examined the drift in light intensity common during warm-up of hollow cathode lamps -

(23) H. L. Kahn and W. Slavin, Appl. Opt., 2, 931 (1963).

Table I. Signal-to-Noise Ratios Obtained with Various Modulation Functions output Modulation No filter 100-msec filtera function Sb N c SIN Sb Nc SIN Sine wave 3.3 2.26 1 . 4 6 3 . 2 0.0060 533 Square wave 6 . 4 1.18 5.42 6.3 0.0031 2032 Filter time constant. * S = Signal in volts. c N = Noise in volts rms.

(24). By use of a square-wave modulation function, the stability of the demodulated waveform was recorded for both full (100%) and ripple modulation (90%) and is seen in Figure 5. For comparison, the stability of a sine-wave ripple-modulated signal is also included. The traces in Figure 5, showing the warmup characteristics of the lamp, were taken after the hollow cathode lamp was turned off for 30 min. As expected, the stability of the ripple-modulated signals is significantly greater than that obtained with 100% modulation. This increase in stability is expected to be especially useful during warm-up of single-beam atomic absorption spectrometers, but it is also expected to be useful in increasing the stability after the sources have reached equilibrium. In Figure 5, the sine-wave signal was increased in amplitude somewhat, to facilitate its comparison with the other traces. Pulse Modulation. It is common practice in modulation procedures to employ a symmetrical modulation function such as a sine or square wave. In a commercial lock-in amplifier with a tuned input, it is in fact undesirable to demodulate a n unsymmetrical waveform, such as a pulse train, because of the lower amplitude of the signal component at the tuned reference frequency. However, for an untuned detector such as that in Figure 3, the advantages of higher lamp output available with pulsed operation (25) can be enjoyed. Because of a current limitation in the hollow cathode power supply, this aspect was not examined experimentally. However, because atomic absorption signals can be shown to be proportional t o the intensity of the primary source ( 2 6 , 2 7 ) ,this mode of amplitude modulation is worthy of note. Also, it can be expected that ripple modulation, as described in the preceding section, will probably not be advantageous in the pulsed operation of hollow cathode lamps. As recently found by Cordos and Malmstadt (28), the low duty cycle nature of intermittently-pulsed hollow cathode lamps reduces cathode heating and thereby enhances stability and increases lamp lifetime so that “ripple” operation would likely be superfluous. Pseudo-Random Pulse Modulation. In Fourier-transform nuclear magnetic resonance spectrometry, random or pseudorandom pulses have been used to provide increases in signalto-noise ratio and greater freedom from saturation effects (29, 30). Despite the apparent advantages of this approach, no application has yet been made to other spectrometric tech-

(24) W. Slavin, “Atomic Absorption Spectroscopy,” Interscience, New York, N.Y., 1968, p 11. (25) J. B. Dawson and D. J. Ellis, Spectrochirn. Acta, 23A, 565 (1967). (26) C. Th. J. Alkemade, Appl. Opt., 7, 1261 (1968). (27) P. J. T. Zeegers, R. Smith, and J. D. Winefordner, ANAL. CHEW,40 (13), 26A (1968). (28) E. Cordos and H. V. Malmstadt, ANAL. CHEW 45, 27 (1973). (29) R. R. Ernst, J . Mag. Res., 3, 10 (1970). (30) R. Kaiser, ibid.,p 28.

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Time

a.

time constant Time

j

b. To.1”

1

b.

0.75 sec

Figure 6. Low-frequency noise comparison of demodulated light signals obtained from square-wave and pseudo-random modulation (a) Square-wave modulation ; (6) pseudo-random modulation

C .

I

Source turned on

Time

Figure 5. Variation in demodulated light intensity during warm-up of hollow cathode lamp for various modulation waveforms (a) Square-wave “ripple” modulation; (6) sine-wave “ripple” modulation; (c) square-wave 100 modulation. Demodulator time constant: 1 sec

niques. The unique character of a random or pseudo-random sequence is expected to reduce the likelihood of any noise having the same characteristic and would therefore seem to offer a nearly ideal modulation function. This was investigated by using a pseudo-random binary sequence to modulate the hollow cathode lamp. It has been found that, in conventional atomic absorption spectrometry, pseudo-random source modulationjdemodulation provides a negligible improvement in signal-to-noise ratio over that obtained using a square wave, and practical considerations make it unlikely that the technique will be widely used in this application. In this work, a noise generator was used to modulate the hollow cathode lamp supply and also to serve as a reference signal for demodulation. The resulting modulated photometric 244

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signal, then, contains a broad spectrum of frequency components and has much of the characteristics of random noise, except that only two amplitude levels exist (zero and the signal level), and that, after a finite time, the modulation pattern is repeated. For this study, a pattern with a sequence length of 1024 clock pulses was chosen with a clock frequency of 300 Hz. This has the effect of spreading the signal information over a broad frequency range from 300 Hz to approximately 0.3 Hz (31). Demodulation of this wave, then, reconstructs the signal exactly but discriminates against all noise with any pattern other than that of the sequence. Two advantages would be expected with this technique. The first advantage is that, with the signal spread over a broad frequency range, the spectral characteristics of the noise in the spectrometric system become less important. In real atomic absorption spectrometers, a considerable amount of interference noise will probably be present (32), often at unknown frequencies (33). These strong contributions at specific frequencies arise from such sources as the 60-Hz power line but can also be generated at other unexpected frequencies from high-voltage spark generators and other periodic devices. If sine- or square-wave modulation is inadvertantly used at any of these frequencies or their harmonics, a considerable amount of the noise will appear at the demodulator output. This probability is considerably reduced when a pseudo-random sequence is used as the modulation function. The second advantage expected from pseudo-random modulation arises from its unique waveform. White noise, which ~~~

~

~~

(31) G. A. Korn, “Random Process Stimulation and Measurements,” McGraw-Hill, New York, N.Y., 1966, Chap. 7. (32) T. Coor, J . Chern. Educ., 45, A533 (1968). (33) V. G. Mossotti, Abstracts, 161st National Meeting, American Chemical Society, Los Angeles, Calif., March, 1971, paper No. 28.

NO. 2, FEBRUARY 1973

is present in all systems, especially those with quantum detectors (%), has some contribution at all frequencies, including those at which the sine- or square-wave modulation function is located. This noise will be demodulated along with the signal. Because it is less probable for any noise to have exactly the waveform (that is, to have exactly the same spectral power andphase distribution) as the pseudo-random sequence, less noise can be demodulated (35),thereby providing a greater signal-to-noise enhancement. The degree to which these effects are important can be seen in Table 11 and in Figure 6. In Table 11, the noise observed at the demodulator output has been recorded with both square-wave and pseudo-random modulation. For convenience, the signal level was set equal for both techniques but was different from that employed for the data displayed in Table I . It is seen that the signal-to-noise enhancement obtained in the absence of strong interference noise is approximately the same for either square-wave or pseudo-random modulation. This was borne out by the long-term drift traces obtained at a lower signal level and displayed in Figure 6. This result arises from the fact that, although the pseudorandom sequence is able to effectively discriminate against noise, a rather long demodulator time constant must be employed to fully realize its advantage. Because of its stochastic nature, the sequence contains longer pulses (that is, lowerfrequency components) than does the square-wave at the same clock frequency. These lower frequencies require longer time constants to fully eliminate the residual modulation function which, if not eliminated, appears as noise. With such a long time constant, the effective bandpass of the demodulator becomes smaller (7), so that square-wave modulation also becomes more and more effective. Therefore, although noise is more efficiently removed with pseudo-random modulation, the demodulated sequence itself acts as noise, to produce a worse signal-to-noise ratio than is obtained with simple square-wave modulation, especially with a long time constant. For situations such as those found in atomic absorption spectrometry, where the detected signal is large compared to noise, the pseudo-random technique offers little advantage over conventional modulation in discrimination against white noise. When a small amount of interference is present at or near the modulation frequency of the square wave, however, the attainable signal-to-noise ratio is reduced considerably, although this is not the case for pseudo-random encoding, as is shown in the last column of Table 11. The added noise was chosen at a frequency slightly removed from the square-wave frequency, to make it appear as noise. If the noise were of the square-wave frequency or nearer to it, it would appear as a signal enhancement or as a slower variation in the signal, with a frequency equal to the difference between the noise and square-wave frequencies (13). As such, it could remain undetected but still cause an error in the detected signal level. Because of this, it becomes apparent that one important application of pseudo-random or random modulation would be in situations in which a considerable amount of line or interference noise of unknown frequency is expected. If, of course, the interference noise frequencies are known, it would (34) M. L. Franklin, G. Horlick, and H. V. Malmstadt, ANAL. CHEM., 41, 2 (1969). (35) Y . W. Lee, T. P. Cheatham, Jr., and J. B. Wiesner, Proc. IRE, 38, 1165 (1950).

Table 11. Comparison of Pseudo-Random and Square-Wave Modulation (S = 1.7 V) 10-msec filter, N

(with No 10-msec 100-msec 1-sec filter filter Modulation filter filter N N function Na N Square wave 0.018 0.0024 (310 Hz) 3.9 0.13 Pseudo-random sequence 3.5 0.15 0.036 0.0042 a N = Noise in volts rms.

added 300-Hz

noise) 0.93 0.17

be simpler to select the square-wave frequency accordingly. Because of the additional expense and complexity of the pseudo-random system, its use cannot otherwise be justified for signal-to-noise improvement. Practical Considerations. The tuned prefilter incorporated into most commercial lock-in amplifiers is not necessarily desirable in atomic absorption applications. The tuned filter serves not to increase the signal-to-noise enhancement capability of the lock-in detector but rather to prevent the input amplifiers or multiplier from being saturated by noise in situations wherein the signal is very small (7). Because the detected signal in atomic absorption spectrometry is always much greater than the noise level, noise-saturation can never occur, so the tuned filter is superfluous. Therefore, for use in atomic absorption measurements, we suggest that a detection system such as that shown in Figures 1 and 3 be considered. This system provides a greater degree of versatility in selection of the modulation and demodulation functions and would permit a reduction in the cost of the detection system. From the considerations presented in this paper, it is clear that pseudo-random modulation would be expected to provide greater signal-to-noise enhancement than either sine- or square-wave modulation, but this expectation is not practically realized. Also, it is apparent that the added cost and complexity of the instrumentation necessary for pseudorandom modulation will not be justified except in specific cases involving high levels of interference noise. In comparing the methods of modulation used in this investigation, we see that the greatest practical advantage lies in the use of square-wave ripple modulation, for it provides improved source stability and lifetime, and it permits high demodulation efficiency. The low-pass filter is then most efficient in removing modulation ripple, and the instrumentation is simple. Therefore, for most conventional applications, this technique is recommended for use in atomic absorption spectrometry. RECEIVED for review July 31, 1972. Accepted October 10, 1972. One of the authors (G. M. Hieftje) gratefully acknowledges support of a part of this work by the National Science Foundation (Grant No. NSF G P 24531). Work performed under the auspices of the Atomic Energy Commission. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the US.Atomic Energy Commission to the exclusion of others that may be suitable.

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