Waveform Effects in Wavelength Modulation Spectrometry 1.C. O’Haver,” M. S. Epstein,’ and A. 1.Zander2 Department of Chemistry, University of Maryland, College Park, Md. 20740
Results are described of some studies In computer modellng of wavelength modulation spectrometry which were undertaken to determine the effect of the waveform and amplltude of modulation, the shape of the modulated line, and the type of signal processlng technique used. Sinusoidal and squarewave wavelength modulation of Gaussian, triangular, and Lorentrian line profiles is treated. A soflware lock-in amplifier simulator is used for slgnal processing both In the first harmonlc (1F) and second harmonlc (2F) modes. The results Indicate that the profile shape has llttle effect, but that square-wave modulation offers a signal-to-nolse ratlo advantage by approximately a factor of 2 In the 2F mode compared to slnusoidal modulation, for a system llmited by background-carried photon shot noise.
In recent years, the technique of wavelength modulation has become increasingly used for the improvement of signal-tonoise ratio (SNR) andlor for the compensation for spectral interferences in atomic emission (I-3), atomic absorption (4-6) and atomic fluorescence (7-9) spectrometry. Of continuing concern in these applications is the effect of the waveform, amplitude, and frequency of wavelength modulation on the signal amplitude and on the SNR. Optimization of these parameters is usually performed empirically, if at all. Yet these parameters may play an important role in overall system performance. For example, some workers have reported a loss in SNR and a corresponding degradation in detection limits when a wavelength modulation system is compared to fixed-wavelength systems (4,9) while others report an improuement (2, 6). Whether SNR is increased or decreased by wavelength modulation, or by any other kind of modulation for that matter, depends on the trade-off between the reduction in noises (or other interfering signals) and the inevitable reduction in signal amplitude caused by modulation ( I O ) . Both of these factors depend on the choice of modulation parameters. Furthermore, in wavelength modulation atomic absorption, the signal amplitude reduction must be taken into account in the calculation of absorbance (6). The purpose of this paper is to describe the results of some experiments in computer modeling of wavelength modulation which were undertaken to determine the effect of the waveform and amplitude of modulation, the shape of the modulated line or band, and the signal processing technique used. The model is based upon sinusoidal and square-wave wavelength modulation of spectral emission bands of Gaussian, Lorentzian, and triangular shapes with signal processing by a wide-band synchronous (lock-in) amplifier system tuned to the first or second harmonic of the wavelength modulation frequency. The objective is to determine the signal amplitude loss and the optimum wavelength modulation interval for maximum signal and for maximum signal-to-noise ratio under various conditions of modulation waveform, band shape, and noise type. Present address, Institute for Materials Research, Analytical Chemistry Division, National Bureau of Standards, Washington, D.C. 20234. Present address, Department of Chemistry, Indiana University, Bloomington, Ind. 47401. 458
ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
The type of wavelength modulation of concern here might be called large-amplitude modulation, to distinguish it from the small-amplitude wavelength modulation often used in derivative spectrometry (11).In wavelength modulation derivative spectrometry, modulation amplitudes small compared to the widths of the spectral bands must be used in order to obtain undistorted derivatives. In the present treatment, on the other hand, it is assumed that the object is to obtain a measure of the intensity of the band or line, while rejecting “background” signals. Large modulation intervals, equal to or greater than the width of the measured band, are found to provide the best SNR in this case. MODULATION WAVEFORM In most of the published applications of wavelength modulation to atomic spectrometry, the waveform of wavelength modulation has been sinusoidal ( I , 5, 9) or square (12, 13). Lock-in amplifiers are usually employed for signal processing; and, most often, the detection system is tuned to the second harmonic of the applied wavelength modulation frequency (2F mode) in order to more effectively reject interference from sloping spectral background distributions ( I ) . For a sinusoidal modulation waveform, the wavelength, A, a t time t is given by AX - AX A = X+ -sin cot = x +-sin 0 2 2 where r; is the center of the wavelength modulation interval, AX is the peak-to-peak amplitude of wavelength modulation, w is the angular frequency of modulation, and 0 (0 = cot) is the modulation phase angle. For square-wave modulation in the IF mode, the wavelength modulation-waveform is defined as: X = r; AX12 for a = 0 to R, and X = X - AX12 for 0 = T to 2 a as shown in Figure lb. For operation in the 2F mode, a 3-step waveform (Figure IC)would be required, as deficed by X = X for 0 = 0 to ir/4,3a/4 to 5 ~ 1 4and , 7 ~ 1 to 4 2 ~X ;= X - AX12 for 0 = a14 to 3 ~ 1 4and ; X = 1 AX12 for 8 = 5n/4 to 7x14.
+
+
BAND SHAPE The shape of the spectral intensity distribution across which the wavelength is being modulated depends upon the true shape of the line or band as well as the slit function of the monochromator. Such shapes will usually be Gaussian, Lorentzian, triangular, or some mixture thereof, and thus each of these shapes is used in this treatment. For a Gaussian emission profile superimposed on a linear background, the intensity Z(X) at wavelength X is: dZ (2) Z(X) = ZO exp - (114 In Xo)2 2)6X2] + - dX -X+ZB
[
where Zo = peak intensity, XO = line center, 6h = full width a t half maximum of line, dZ/dX = slope of the background, and Ig = a constant related to the intensity of the background. Since we will be using only linear signal processing techniques, we may consider the background terms separately later on. Thus Equation 2 reduces to (3)
For the Lorentzian profile: (4)
a.
and for the triangular profile:
b. The signal waveforms I ( 0 ) produced by sinusoidal modulation across each of the above profile shapes is given by substituting Equation 1 into Equations 3 , 4 , and 5:
C.
d.
e. f.
9. where we have used the notation I(B)s,cto represent the signal waveform produced by sinusoidal modulation across a Gaussian profile (Figures If and g). For square wave modulation, the signal waveform I(B)sQ will be a square wave of peak-to-peak amplitude nearly equal to lo,assuming that AX is sufficiently large (See Figures I d and e). Detailed expressions need not be given in this case. In some cases i t will be useful to know the auerage signal intensity I T ) with sine or square modulation:
I(B)s4"aPe
=
Y'I0
(10)
Approximate values of I(e) are indicated for the signal waveforms in Figures le, f, and g. For the background, the I ( 0 ) signal is I ( ~ )=BI B dI/dX Ah/2 sin 0) for sinusoidal modulation.
+
+
(x
SIGNAL PROCESSING By far the most commonly used method of measuring the amplitude of the signal in modulation spectroscopy is synchronous (lock-in) amplification. The response of a lock-in amplifier to an ac input signal depends not only upon the amplitude of the ac input but also upon its waveform. For a lock-in amplifier with no pre-detection filtering (i.e., with a "wideband front end"), the signal waveform giving the largest response for a given peak-to-peak input amplitude is a square wave; a sine wave of the same peak-to-peak amplitude gives a response 36% lower. The signal waveform produced by a sinusoidal wavelength modulation waveform depends on the shape of the spectral intensity distribution; but in general, such signal waveforms will be less efficient than a square wave for a wideband front-end lock-in system ( 1 3 ) . A wide-band front-end lock-in amplifier acts like a switched inverter (with a gain which is positive or negative depending on the modulation phase angle) followed by a n averaging
h. i Figure 1. Illustration of the phase relationship between the various waveforms involved in wavelength modulation spectrometry (a) Sinusoidal wavelength modulation waveform, I F and 2F modes: (b) squarewave wavelength modulation waveform for I F mode; (c) square-wave wavelength modulation waveform for 2F mode; (d)signal waveform, /(8), for 1F mode square-wave modulation, large AX, f AX12 = XO; (e) I(@ for 2F mode square-wave modulation, large AX, A_= XO: (f) I(@ for 1F mode sinusoidal modulation of a Gaussian profile, Xo - X = 0.6 SX,AX = 1.5 6X; (9) (0) for 2F mode sinusoidal modulation of a Gaussian profile, X = XO, AA = 2 6X: (h) unfiltered output of software-simulated lock-in amplifier with wide-band front end, phased for maximum positive output signal, 1F mode. Input signal is shown in t (i) Same as h but in 2F mode, with input waveform shown in g
low-pass filter (10).The output signal, E, of the lock-in amplifier is given in the 1F mode by E ~ =F 2iT
[ l T I ( 6 ' ) d H- Jz'I(0)dO] 0
7r
(11)
where G is a constant factor which depends on the lock-in amplifier sensitivity range setting and the photomultiplier sensitivity and load resistance. The integration limits, which determine the phase relationship between the signal and reference waveforms, have been selected so that the limits of the positive integral (0 to T) are centered on the most positive region of the signal waveform I(6'). This corresponds to "phasing" the lock-in for maximum positive output signal. (See Figure lh.) In the 2F mode, the reference waveform frequency is doubled. Again, the integration limits are chosen for maximum positive signal: ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
459
-I
0.3
0'5
t
1 -
O 0.oI 2 I
0
0 1.0
2.0
3.0
AX Flgure 2. Simulated lock-in output signals in 2F mode for sinusoidal wavelength modulation of Gaussian (-), Lorentzian (- -) and triangular (. .) profile shapes, as a function of the wavelength modulation amplitude AA, expressed as a ratio to the profile full width at half maximum,
-
6A
G
15
AA
20
25
30
[- l;y I(0)dO + i5*'4 I(0)dO r/4
I(0)dO
+
Flgure 3. Simulated lock-in output signals in the 1F mode for sinusoidal wavelength modulation of a Gaussian profile, as a function of AA, for three values of A Xo (the separation between the center of the modulation i n t e r v a 2 and the profile center ho).This illustrates the interaction between A - A. and the optimum AX
=
3x
=2a
IO
bA
0
E2F
05
Lgr" */4
I(0)d0]
(12)
to about 261. (This is significant because it means we need not be concerned about the shape of the modulated profile, but only its width, in the optimization of AA.) However, the value of the maximum signal is 0.275 GI0 for the Gaussian and triangular profiles but is 0.21 GZo for the Lorentzian. The signal loss compared to square-wave modulation is given by the ratio of the E values:
In this case i t is clear that the maximum 2F signal will be obtained when the modulation interval is centered on the spectral profile, i.e., when = Ao. Thus, the symmetry of Z(0) allows us to consider only the region between 0 and a12 (See Figure li):
x
EZF=
5[
I(0)dO - Jn/4 r i I(O)d0] z
(13)
For square-wave signal waveforms, Figures I d and e, Z(0) is constant between the integration limits in each of the integrals in Equations 11and 13; Z(0) = I Ofor the positive integrals and Z(0) = 0 for the negative integrals in the limit of large AX. Thus, Equations 11 and 13 reduce to the same value:
and
For sinusoidal wavelength modulation, the values of E and E ~ depend F on AX and the profile shape and must be evaluated for each case. For the background terms we have d l AX ( E ~ F )=B0.63 -dA 2
(EZF)B =0 (17) by substitution of I ( e ) B into Equations 11and 12, respectively. As expected, a linear sloping background is rejected in the 2F mode, but not in the 1F mode. RESULTS AND DISCUSSION Equations 9,11, and 13 were evaluated by numerical integration using programs written in FORTRAN IV for the Univac 1106 a t the University of Maryland Computer Center. Plots of E Z Fvs. AA of the three profile shapes are given in Figure 2. In each case the maximum signal occurs at a AA equal 460
ANALYTICAL CHEMISTRY, VOL. 49,
NO. 3,
MARCH 1977
Thus, square-wave modulation has a signal amplitude advantage of about a factor of 1.8 in the 2F mode. In the 1F mode, the optimum AX depends on - 10,as shown in Figure 3 for the Gaussian profile. The overall maximum signal is 0.38 GI0 in this case and is obtained a t AA = 1.5 dA and Xo - A = 0.60 6X. For square wave modulation, the 1F signal is again 0.5 GIo, a 25% advantage. In order to determine the effect of wavelength modulation on signal-to-noise ratio, the nature of the dominant noise must be considered. The only noise type for which one would expect modulation to improve the SNR, compared to an unmodulated dc system, is background-carried fluctuation noise consisting mostly of drift, llf, or other low-frequency components. Examples of such noise types include source intensity fluctuation noise and background emission or absorption fluctuation noise in absorption measurements and background emission fluctuation noise in emission measurements. In systems limited by these noises, the SNR will be improved only if the reduction in noise caused by modulation exceeds the reduction in signal amplitude. Such improvements in SNR have been observed in graphite atomization atomic emission (2) and continuum-source atomic absorption spectrometry (6),where the improvements have been of the order of 5- to 100-fold. However, if other noise types are dominant, the SNR will not be improved. If signal-carried fluctuation noise is dominant, the noise will be reduced by the same factor as the signal amplitude and the SNR will not be changed. If continuum background shot noise is dominant, the noise will not change; and the SNR will be reduced by the same factor as the signal, which could be as much as a factor of 4 for 2F sinusoidal modulation. If signal-carried photon shot noise is dominant, the noise will be reduced by the square root of the factor by which the average signal intensity I-) is reduced, as evaluated by Equations 9 and 10. For square-wave modulation, I ( 0 ) is
x
reduced by 0.5 (Equation lo), so the SNR is reduced by the factor 0.7. For sinusoidal modulation, the maximum SNR is about one-half of that of an unmodulated dc system and is attained a t a Ah of 2.5 6h, slightly larger than the Ah for maximum signal. Thus we see that the SNR of a wavelength modulation system may be anywhere from a factor of 4 worse than to many times better than an unmodulated system, depending on the contribution of the various noise types to the total system noise. The SNR differences between sine and square-wave modulation depend on the nature of the dominant noise remaining after modulation and are also easily calculated. Thus, in a system limited by background-carried photon shot noise, e.g., source photon shot noise in wavelength-modulation continuum-source atomic absorption (6), the 2F sine-Gaussian modulation SNR is lower by 0.55 than that of a square-wave modulated system. In a system limited by signal-carried photon shot noise, e.g., emission or fluorescence spectrometry with a low-background atomizer, the factor is 0.7. These differences are of course less significant in the 1F mode.
ACKNOWLEDGMENT We are grateful to Mike Failey for help with the computer programming. LITERATURE C I T E D W. Snelleman, T. C. Rains, K. W. Yee, H. D:Cook, and 0. Menis, Anal. Chem., 42, 394 (1970). M. S. Epstein, T. C. Rains, and T. C. O'Haver, Appl. Spectrosc., 30, 324 (1976). F. E. Lichte and R. K. Skogerboe, Anal. Chem., 44, 1321 (1972); and 45, 399 (1973). W. Snelleman, Spectrochim Acta, Part 6,23, 403 (1968). R . C. Elser and J. D. Winefordner, Anal. Chem., 44, 698 (1972). A. T. Zander, T. C. O'Haver, and P. N. Keliher, Anal. Chem., 48, 1166 (1976). C. P. Thomas, Ph.D Dissertation, University of Maryland, College Park, Md., 1972. T. C. O'Haver, 165th National Meeting of the American Chemical Society, Dallas, Texas, April 10, 1973. W. K . Fowler, D. 0. Knapp, and J. D. Winefordner, Anal. Chem., 46,601 119741.
i . C . O'Haver, J. Chem. Educ., 49, A131 (1972). R. N. Hager, Jr., and R. C. Anderson, J. Opt. SOC. Am., 60, 1444 (1970). R. K.Skogerboe, P. J. Lamothe, G. J. Bastianns,S. J. Freeland, and G. N. Coleman, Appl. Spectrosc., 30, 495 (1976). S. R. Koirlyohann, E. Hinderberger,and F. E. Lichte, "The Influence of Wave Form on Refractor Plate BackgroundCompensation in Emission Analysis", Paper No. 187, Third Annual FACSS Bicentennial Meeting, Philadelphia, Pa., Nov. 1976.
CONCLUSION The selection of the optimum conditions for wavelength modulation involves a trade-off between theoretical advantages and practical advantages. On the basis of signal amplitude and, more important, signal-to-noise ratio, square-wave modulation clearly has the advantage if lock-in signal processing is utilized. The SNR advantage compared to sinusoidal modulation can be as much as a factor of 1.8.
RECEIVEDfor review September 27,1976. Accepted December 15, 1976. Financial support provided by the National Science Foundation, Grant ESR-75-02667 (NSF-RANN) is gratefully acknowledged.
Determination of Molybdenum in Seawater by Electron Paramagnetic Resonance Spectrometry Glenn Hanson, Andre Szabo, and N. Dennis Chasteen" Deparfmenf of Chemistry, University of N e w Hampshire, Durham, N.H. 03824
An EPR method for determlning molybdenum In saline waters in the pg/L range is presented. The method, based on the extraction of paramagnetic Mo(SCN)5 Into isoamyl alcohol, is relatively rapid, requires only 10 mL of sample and has a detection limit of 0.46 pg/L Mo and a relative precision of 4.7% at the 11 pg/L level.
The determination of trace elements in water has received increasing attention in recent years. Molybdenum is one element which has been analyzed by a wide variety of methods (1-9). Since the concentration of Mo in seawater is usually in the range of 9-13 pg/L ( 2 ) ,it is necessary to preconcentrate the element before a spectroscopic determination can be made. Determination of Mo in seawater using coprecipitation with hydrous manganese dioxide followed by a spectrophotometric determination as the dithiol complex has been reported ( 1 , 2 ) . This method appears to offer good reproducibility but the process is tedious, time consuming, and requires a large (1 liter) sample. The use of a co-crystallizing agent has been investigated, but as in the coprecipitation method, the process is very time consuming and requires a large sample ( 3 ) .Application of ion-exchange chromatography in conjunction with atomic absorption or spectrophotometry has been studied by a
number of workers (4-6).These methods allow for a more rapid determination than either coprecipitation or co-crystallization, but a large sample is still required for the analysis. The use of a foam separation technique combined with a spectrophotometric determination has been reported (7). In this process the Mo is preconcentrated in 5 min but a large sample, 500 mL, is still required. Chou and Lum-Shui-Chan (8) investigated the use of atomic absorption in conjunction with solvent extraction using 1%oxime in methyl isobutyl ketone for preconcentration. The detection limit is 3 pg/L, in which a preconcentration factor of 20 is employed. The disadvantages of the above system are that it still requires a 100-mL sample and there are interferences, although some of these interferences can be eliminated (9).
We report here an electron paramagnetic resonance (EPR) method which overcomes the above difficulties. The method, a variant of the well known molybdenum determination by thiocyanate (IO), is based on the fact that the Mo(SCN)s complex is paramagnetic and can be detected in very dilute solutions by EPR spectrometry. Trace metal analysis of marine systems by EPR spectrometry has already been suggested by previous work (11). EXPERIMENTAL Reagents. All of the solutions used were prepared with reagent grade chemicals and double distilled deionized water. A 105 mg/L ANALYTICAL CHEMISTRY, VOL. 49, NO. 3, MARCH 1977
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