(29) "Optical Multichannel Analyzer OMA Operating and Service Manual," MDL 1205A; 6/75, Princeton Applied Research Corp., Princeton, N.J., 1975. (30) D. E. Osten, lnd. Res., 17 (IO), 82 (Oct. 1975). (31) "Photomultiplier Manual," Manual PT-61, RCA Corp., Harrison, N.J., 1970. (32) "Photomultiplier Tubes Catalog," PIT-7008 12/7 1, RCA Corp., Harrison, N.J., 1971. (33) K.W. Jackson, K. M. Aldous, and D. G. Mitchell, Appl. Spectrosc., 28,569 (1974). (34) Y. Talmi, R. Crosmun, and N. R. Larson, Anal. Chem., 48, 326 (1976).
(21) J. A. Dean and T. C. Rains, "Standard Solutions for Flame spectrometry", in "Flame Emission and Atomic Absorption Spectrometry", Vol. 2, J. A. Dean and T. C. Rains, Ed., Marcel Dekker, New York, N.Y., 1971. (22) G. D. Christian and F. J. Feldman, Appl. Spectrosc., 25, 660 (1971). (23) E. E. Pickett and S. R. Koirtyohann, Spectrochim. Acta, Part B, 23, 673 (1968). (24) P. W. J. M. Boumans and F. J. De Boer, Spectrochim. Acta, Part B, 27,39 1 (1972). (25) G. H. Morrison and R. K. Skogerboe, "General Aspects of Trace Analysis", in "Trace Analysis: Physical Methods," G. H. Morrison, Ed., Interscience, New York, N.Y., 1965. (26) IUPAC, Information Bulletin-Number 27, "Nomenclature on Analytical Flame Spectroscopy and Associated Procedures" (1972). (27) C. S. Williams and 0. A. Becklund, "Optics: A Short Course for Engineers and Scientists," Wiley-lnterscience, New York, N.Y., 1972., (28) H. T. Betz and G. L. Johnson, "Spectroradiometric Principles, in "Analytical Emission Spectroscopy," Vol. 1, Part 1, E. L. Grove, Ed.. Marcel Dekker, New York, N.Y., 1971.
RECEIVEDfor review July 26,1976. Accepted September 23, 1976. This work was supported in part by the National Institutes of Health under Grant No. 5 R01 GM 19905-03 and by the National Science Foundatiop through the Cornell Materials Science Center.
Analytical Capabilities of the Selectively Modulated Interferometric Dispersive Spectrometer T. L. Chester' and J. D. Wlnefordner" Department of Chemistry, University of Florida, Gainesville, Fla. 326 1 1
A general signal-to-noise ratlo (S/N) behavlor model Is derived for the Selectively Modulated Interferometric Dispersive Spectrometer (SEMIDS) based on an evaluation of the instrument as a flame atomic emission analyzer. A comparison Is made to a slmllar model derived for a conventional dispersive spectrometer. It is shown that the S/N for SEMIDS strongly depends on the nature of the spectral background and that no significant S/N Improvement Is expected In SEMIDS (as compared to the dispersive spectrometer) for any realistic analytlcal measurement In the UV-vlslble spectral region. However, some Improvement may be realized In the Infrared spectral reglon.
The Selectively Modulated Interferometric Dispersive Spectrometer (SEMIDS) was first described by Dohi and Suzuki (1). It is essentially a Michelson interferometer in which the stationary reflecting mirror is replaced with a rotatable diffraction grating (see Figure 1).As a result, the multiplex nature of the interferometer is eliminated as interference occurs only for the Littrow wavelength of the grating. Slight oscillation of the remaining mirror results in interference modulation of the signal spectral component. Selective amplification of the ac signal component distinguishes it from the remaining dc background. Thus, no interferogram is produced, and no Fourier transform is required. The practical resolving power is nearly equal to the theoretical resolving power of the grating used and is independent of the entrance aperture area (within a limit). Thus, the luminosity-resolving power product for SEMIDS may be much greater than that of a conventional dispersive spectrometer with the same grating. Mechanical tolerances are much less severe for SEMIDS than for the Michelson interferometer (used as a Fourier transform spectrometer) and for the SISAM spectrometer (which is a Michelson interferometer employing gratings in place of both mirrors). Thus, use of SEMIDS is possible in the UV-visible spectral region where it has proved difficult for multiplex systems based on the Michelson interferometer, i.e., the Fourier transform spectrometer ( 2 ) ,and Present address, Procter & G a m b l e Co., M i a m i Valley L a b o r a tories, P.O. Box 39175, Cincinnati, Ohio 45247.
the SISAM spectrometer ( 3 , 4 ) .Investigation of SEMIDS is warranted by a potential Jacquinot (or throughput) advantage of lo2 to lo3compared to single slit dispersive spectrometers used at the same resolving power. SEMIDS was recently investigated for analytical utility in the UV-visible spectral region ( 5 ) .The preliminary conclusions given were that some potential analytical usefulness existed for SEMIDS in those situations where the measurement of faint light signals are of importance, namely, atomic emission, atomic fluorescence, and molecular luminescence. Subsequently, the present careful evaluation of SEMIDS as a flame emission detector has indicated that no signal-to-noise ratio (S/N) improvement results and, in fact, the detection limits obtained using SEMIDS are much inferior to those obtained by conventional spectrometric systems. In addition, considerations of separate spectral bandpasses for the signal and (background carried) noise components in atomic fluorescence spectrometry (AFS) indicate that no improvement in S/N should be expected from SEMIDS, SISAM, multiplexed systems, and other selective wavelength modulation methods for AFS (6). In order to understand the experimental failure of SEMIDS and to predict its behavior in other applications, a S/N behavior model was developed for SEMIDS and is presented in this paper. The model, evaluated for flame emission and experimentally verified, is generally applicable to other analytical spectrometric situations.
THEORETICAL CONSIDERATIONS Signals and noises (in terms of counts; count rates result in the same S/N expressions) for various spectrometric methods of analysis have recently been formulated by Winefordner et al. ( 7 ) .These will be followed to a large extent, but some expansion is necessary to properly describe SEMIDS. Noise Types. Only two types of noises were previously considered ( 7 ) ,photon (shot) noise and l/f (drift or flicker) noise. Photon (shot) noise, N,, in counts, is given by the square root of the number of the counts (due to radiation impinging on the detector) observed (assuming photon counting is used), N , = a ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
113
Table I. Flame Background Noise Characterization for SEMIDS Instrumentation Flame Ar separated C,H,/air flame (see Table IV) Entrance aperture = Exit aperture = 5 mm SEMIDS Photomultiplier 650 V dc applied to RCA 1P28 PM tube Electronics: Preamplifier Transconductance = l o 7 VIA Selective amplifier Frequency = 2 kHz
Table 11. Noise Components in SEMIDS Source
Noise t y p e
Shot
J%G-
Signal
Shot
J Z G 4
Background =
[fs
Whistle
tws(F)
Entrance Aperture
1I1
1 If (X
1 0 0 attenuator)
N
Whistle
E x i t Aperture
Moving Mirror
Beamsplitter
Grating
dispersive spectrometer (SEMIDS) where R is the average photon count rate, in counts s-l (the photon flux reaching the detector is greater than R by l / v c , where 11 is the photocathode efficiency and t is the dynode efficiency factor) and t o is the observation time, in s. The llf noise, Nf, is proportional to the light flux which carries it and is given by (2)
where [f is the proportionality constant (no units) (7). These two noise types are usually sufficient to describe dc measurements, but in SEMIDS, another noise was found to be prominent. For small analyte signals in flame atomic emission, it was expected that the limiting noise in SEMIDS would originate in the flame emission background. Furthermore, because the signal and the small contribution of flame background beneath it (within the signal spectral resolution interval) are interferometrically modulated while the remainder of the flame background emission is not modulated, demodulation of the ac signal results in nearly complete rejection of the low frequency background carried noise. Therefore, it was expected that SEMIDS (for flame emission) would be limited by photon noise on the flame background. An experiment was performed to verify this (obtainable from the authors by writing JDW), and the results are given in Table I. Surprisingly, the limiting noise was found to be proportional to the light flux and therefore could not be photon noise. This noise also certainly was not l/f noise be114
.?1 t w b (si
E-
Figure 1. Schematic diagram of selectively modulated interferometric
Nf = [ & t o
Shot
1s
Noise data Total noise (no optical attenuation) = 1.93 V rms Noise measured with attenuator = 0.233 V rms Calculated shot noise = 0.358 V rms Calculated proportional noise = 1.90 V rms
/n
(Jy)
1I f
Q=2
Gain = 1 0 AC amplifier Gain = 20 Multiplier 10-V ac Input Time constant output x 1 0 Recorder: Span = 1 0 mV
Noise term (in counts)
Detector
ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
+
)(
JRbito
7)
cause it was detected at a high frequency (2 kHz), but rather was most likely due to flame oscillations and other disturbances which are not llf in nature. Some evidence of this is suggested in the noise power spectra recently published by Talmi, Crosmun, and Larson (8),although these authors did not speculate fully on the nature of the noises observed. Most flame sources, and especially turbulent flames, exhibit noise power spectra with large, broad frequency bands which certainly are not l/f in nature and are also certainly not white (indicative partially of photon noise) in nature. Furthermore, Gaydon and Wolfhard (9)have summarized flame noise and flame oscillations. They report that pressure front variations in a flame are responsible for both the audible noise and a closely correlated optical noise. Physical perturbations of the (steady state) flame emission by pressure front variations result in an optical noise which is proportional to both the magnitude of the perturbations and the light flux detected. This noise has previously not been important in laminar flames, especially in separated laminar flames, because of the quiet nature of burning of these flames and the relatively low flame emission background in the flame region usually observed, Le., this noise is usually small relative to the photon noise and to signal carried l/f noise. However, in SEMIDS, the measured flame background light flux is ca. lo6 times greater than that observed with a dispersive spectrometer because of the increased aperture area and collection solid angle in SEMIDS and also because no spectral dispersion occurs in one of the reflecting arms, thus flooding the detector with the complete optical spectrum. The flame backgroundwhile carried shot noise is larger in $EMIDS by d@or the proportional noise is larger by lo6. The ratio of proportional noise to shot noise is increased by lo3 in SEMIDS as compared to a conventional dispersive spectrometer and thus accounts for the observed dominance of proportional noise. In this paper, the high frequency (Le., non-l/f) proportional noise will be called whistle noise. It is probably not limited to flames but may also exist in general in light sources. For example, it is conceivable that oscillatory pressure variations may exist in a CW arc discharge, such as a dc arc or a xenon arc lamp. Following the procedure previously used to evaluate l/f noise (7), the detected whistle noise, N,, in counts, is given by N , = 5,Rt
(3)
where 5, is the proportionality constant ( 4 , 7) for the whistle
noise, and will be called the whistle factor. It is distinguished from &, which is the proportionality constant for l/f noise (previously called (7) the fluctuation constant). Signal. The optical signal in SEMIDS is modulated by the application of two displacement signals to piezoelectric crystals on which the mirror is mounted. If the maximum mirror displacements for each of the applied frequencies are A/4, then signals appear in the frequency spectrum of the detector output in the vicinity of f U and 2f,, where fU is the upper applied displacement frequency. These signals are not phase-locked and must be asynchronously rectified. Any noises which are present are also rectified and lead to an ultimate dc offset due solely to noise. To minimize the rectified noise, an ac selective amplifier (Le., active filter) is employed. However, it may be tuned to one or the other of the signal frequency regions, but not to both. The signal (information) power is divided between these two frequency regions and thus only half of the total signal power is detected. Additionally, another factor of 2 is lost due to the modulation of the (steady state) signal. If Ra, is the photon count rate of a signal in a conventional spectrometer (Le., a sequential slew scan spectrometer, SSS) (7),then the signal, S, in counts, for SEMIDS is
where J is the (geometric) throughput or luminosity improvement of SEMIDS compared to the SSS instrument and t o is the total analysis time. Strictly, it is not correct to describe an analog filtered signal (count rate) with a digital expression (counts). However, Equation 4 is still correct in terms of the signal informing power and has the advantage of simplicity in the arguments to follow. Noise Terms. The various noise terms for SEMIDS are listed by source in Table 11. Detector Noise. Detector noise is not important in SEMIDS when photomultiplier detection is employed. This is due to the high photon flux detected which renders the detector noise negligible. However, other situations may be limited by detector noise and its inclusion in a general model is necessary. However, only detector shot noise will be considered here. Signal Carried Noise. The signal carried shot noise equals the square root of the total number of signal counts observed in a measurement period. Signal carried drift ( l l f )and whistle noises are directly proportional to the signal with proportionality constants Efs and E,,. Background Carried Noise. The background contribution from the mirror is very different from that of the grating due to the dispersion of light from the latter. The spectral bandwidth of the grating arm contribution can be found by ignoring the mirror and beamsplitter altogether and by treating what is left as a spectrometer. Thus W
AA = - d cos 0
f
(5)
where AA is the spectral bandwidth (halfwidth) of the emergent light, w is the width of the apertures (assuming the entrance and exit apertures are equal), f is the focal length of the collimator and focusing lenses (assuming they are identical), d is the groove spacing on the grating and 0 (= arc sin (A/2cl)) is the grating angle. Equation 5 applies directly only when rectangular slits are used in a spectrometer. However, for the purpose at hand, no serious error is encountered by the application of this equation to SEMIDS which uses circular apertures. Thus, the background light contributed from the grating will be assumed to follow a triangular spectrometer function with a bandwidth equal to AA. Let it further be assumed that the center wavelength is not attenuated except
tronsmittonce
I
Transmit tance
I
(b)
Tronsmiftonce
(C)
I
x',
A"
A-
Flgure 2. Spectral background transmittance in SEMIDS. (a) The grating arm contribution. (b) The mirror arm Contribution. (c) Total
by the two interactions with the beamsplitter. Thus, the peak transmittance is 0.25 as shown in Figure 2a. The background contribution from the mirror arm is not dispersed and thus covers the entire optical spectrum. For convenience, it is assumed that the detector spectral response is rectangular with a sharp upper response cutoff at A, and a sharp lower response cutoff at A1 as is shown in Figure 2b. The only attenuation is due to the beamsplitter and the instrument transmittance for this arm is 0.25 over the entire spectrum. Except for the signal wavelength at which interference occurs, the total background is found by summing the two contributions. The result is shown in Figure 2c. The reciprocal linear dispersion for the grating and lens combination in SEMIDS (5) is 8.34 nm/mm. Thus, the bandwidth for 5 mm apertures is 41.7 nm for the grating contributed background. The response bandwidth of the photomultiplier tube used is about 500 nm. Thus, for a white light background, the grating arm contribution to the total background could never exceed 41.71500 or 58%;this will be shown below. The number of background photons for the ith spectral component reaching the detector in the time period t owhich is contributed from the mirror arm is JRbit,/4, where Rbi is the photon count rate for that component with a dispersive spectrometer. The total number of background counts contributed by the mirror arm, C b m , is found by summing over the number of spectral components (spectral resolution intervals), N , in the spectrum,
The contribution to the observed background from the grating is identical except that it is modified by dispersion. The correct contribution results when Equation 6 is multiplied by the spectrometer function of a spectrometer employing the ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
115
same grating, collimating and focusing elements, and apertures as SEMIDS. If this function is S ( h ) ,which equals 1for the center wavelength of the spectrometer bandpass (assuming lOoO/o efficiency), ranges between 0 and 1 for other wavelengths within the bandpass and equals 0 for all wavelengths not within the bandpass, then the grating arm contribution to the observed background, Cbg, is
If S ( h )is replaced by its value, S i , for every wavelength component then
The total number of background counts observed, the sum of the mirror and grating contributions,
0
J
d
II
v) v) h
?
52.
116
ANALYTICAL CHEMISTRY, VOL. 49, NO
is
In most real situations (and especially with flame or plasma sources), the S , contribution will be negligible. For the purpose of establishing trends, no serious error is ever encountered by ignoring Si (S,= 0 for most of the i intervals). The background carried shot noise is the square root of the total number of background counts observed in the measurement period. The background carried l// and whistle noises are proportional to the number of background counts observed. The proportionality constants are &, and &b. The total noise is the quadratic sum of the noise components listed in Table 11. Signal-to-Noise Ratio for SEMIDS. The S/N ratios for the SSS method (sequential slew scan dispersive spectrometric method) and for SEMIDS for the analysis of a single spectral signal are given in Table 111. Comparison of these ratios yields predictions of the potential applicability of SEMIDS as a replacement for the more conventional SSS or SLS (sequential linear scan dispersive spectrometric method) techniques (7). There are two possible advantages for using SEMIDS. First, the signal in SEMIDS is larger than for SSS (or SLS) if the factor J is greater than 4;J is typically lo2 to lo", and thus a substantial improvement in signal gathering efficiency can be realized. Second, the factor ,$fi is significantly reduced in SEMIDS because of the signal modulation. Therefore, in situations where background l/f noise is of major importance, SEMIDS could offer substantial noise reduction. However, it must be emphasized that the background light flux is so greatly increased because of the non-dispersed mirror arm contribution over that of the typical background observed in SSS that whistle noise, which is usually not significant with dc detection systems relative to the observed l / f noise, is greatly increased. The S/N behavior of SEMIDS was investigated experimentally for flame atomic emission. An Ar-separated air/ acetylene flame was used. This flame was chosen because of its combination of good atomization efficiency for most elements and its relatively low background. Details of the burner, flame, and external optics are given in Table IV. I t was found in all cases except for extremely large signals, that the limiting noise was carried on the background signal. In some cases, much of this background signal was due to emission from other lines and bands of the analyte element a t wavelengths other than the one being measured. This was extreme for Ca and Sr because of the very strong emission bands of CaOH and SrOH. However, for every other element near its limit of detection, the limiting noise was due to flame background. The elements investigated were Na, Ca, Sr, Li, Au, Cu, In, Cr, Mg,
ir
II
cbt,
, JANUARY 1977
___ Table IV. Burner, Flame, and External Optics Used for Flame Emission Measurements
___--
Instrumentation Burner
Model 290-010
Nebulizer Capillary burner head flame separator Lens
Model 303-0352
Perkin-Elmer Corp. Norwalk, Conn. Perkin-Elmer Corp. Norwalk, Conn. Laboratory constructed ( 1 0 )
2-in. diameter 2-in. focal length Spectrosil
Esco Optics Oak Ridge, N.J.
Conditions Flame gas flow rates C*H, 1.5 1. min-' Air 9.7 1. m i d Ar 15.5 1. min-l 5 ml min-' Solution flow rate ____--_I _ _ _ _ _ _ _ _ _ _ _ I I _ _
Table V. SSS Background Count Rates of the Ar Separated C,H,/Air Flame Experimental conditions Monochromator, grating, photomultiplier tube and photon counter used are the same components listed in reference 10. Slit height = 1 0 mm Slit width = 1 0 pm Resolution = 1.2 (Manufacturer's figure for the grating and slit width used) Flame (see Table 1V) Experimental results Wavelength, nm
Count rate. s - ~a
200
5
250
25 130 220 350
300 350 400
500 600
650 175
'These figures are corrected for a 20 s-' dark count rate. Ni, and Cd. Detection limits for these elements were lo2 to lo3 X poorer than values obt,ained on a conventional single channel atomic emission flame spectrometer (11). The conclusion of whistle noise dominance on the flame background light for SEMIDS can also be derived from theory once the existence of whistle noise is assumed. Let us compare the background shot and whistle noise terms in the total noise expression, i.e., the squares of the terms in Table 11. For kwh = N = lo4,J = 102, T = 1 s and neglecting Si, a background count rate, Rbi, of only 4 s-l per spectral resolution interval (measured by SSS) equates the two background noise terms for SEMIDS. An average background count rate much lower than this would be necessary to make the background whistle noise negligible with respect to the background shot noise. A much higher count rate would mean that shot noise is negligibly small compared to whistle noise. For example, if the average background count rate is 40 s-l, the square of the whistle noise would be a factor of 10 larger than the square of the shot noise. The background count rate observed for the flame used typically ranges across the UV-visible spectrum from 5 to 700 s-l with an average value of about 300 s-l (as measured by SSS). The details of this measurement are given in Table V. Thus, it is doubtful that shot noise could ever be important in SEMIDS. A typical analytical situation might yield a S/N limited by background shot noise with the SSS method. If the same
t
Signal
0
' W- J Time
L 45s
Figure 3. 589.0 nm Na flame emission for 0.1 ppm solution without (left trace) and with (right trace) a filter to limit the flame background emission. (Time constant = 1 s for both traces. Lower portions of the curves are the blank measurement)
measurement is made with SEMIDS, background whistle noise limitation is most likely. If the background is uniform throughout the spectrum and if Si is neglected, the ratio of the S/N for the two techniques with the above noise restrictions, is
Thus, for the values of &b, N, and T assumed above, SEMIDS will have a significantly poorer S/N than the SSS system. When background carried noise limits the S/N in SEMIDS, conditions may be improved by limiting the bandwidth of this background with a filter. This is demonstrated experimentally in Figure 3. The first trace is the signal for the flame emission of a 0.1 ppm Na solution. The second trace was obtained for the same solution but with an interference filter (589 nm, 8-nm bandpass, Bausch and Lomb, Rochester, N.Y.) placed over the entrance aperture. As long as background light carried noise is the limiting noise, the S/N can be improved by using another filter with a narrower bandpass provided that the peak transmission of the filter is not reduced. However, the S/N for SEMIDS with a narrow filter can lzeuer be higher than that obtained by a filter colorimeter with the same filter if whistle noise for SEMIDS is comparable to the l/f noise for the filter colorimeter. If the same light gathering efficiency is assumed for both a filter colorimeter and for SEMIDS plus the same filter, the signal throughput for the colorimeter will be greater by the factor 4 because no interference or modulation losses occur. If l/fnoise limits the filter colorimeter and whistle noise limits SEMIDS and if .$fi for the colorimeter equals [wb for SEMIDS, the colorimeter will have a higher S/N by the factor 2 because the factor Si will be close to unity over the narrow bandpass of the filter. If signal or background carried shot noise is the limiting noise, the filter colorimeter will be better by the factor 2 4 . Dominance by one of the ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
117
signal carried proportional noises results in similar S/N for both instruments. Thus, the only advantage in using SEMIDS instead of a filter colorimeter is one of wavelength selectivity or resolution rather than S/N improvement. Consideration of the S/N expressions in Table I11 leads to two possible applications where SEMIDS would provide a S/N improvement. First, any measurement which is limited by signal carried shot noise with absolutely no background present can be improved with SEMIDS. The S/N improve(as long as signal carried proporment factor will be tional noise remains negligible in SEMIDS). This factor is the Jacquinot advantage for shot noise limitation. Second, any measurement which is detector noise limited may be greatly improved by SEMIDS (if the same detector noise also limits SSS). In this case, the S/N improvement factor will be J/4. This factor is the Jacquinot advantage for detector noise limitation.
a
DISCUSSION The SEMIDS spectrometer can offer nearly a factor of lo3 increase in the luminosity-resolving power product as compared to a conventional spectrometer employing the same grating. However, this improvement cannot lead to an improved S/N in any measurement which is not limited by detector noise where even a "faint" spectral background is present. Thus, in the UV-visible spectral region, all forms of absorption measurements must be eliminated from consideration as well as all sorts of flame and plasma emission, absorption, and fluorescence measurements. A selectivity advantage is, however, more likely to be achieved than a S/N advantage with SEMIDS. Techniques already providing sufficient selectivity therefore could seldom be improved by using SEMIDS. The only situation in the UV-visible spectral region where SEMIDS could offer S/N improvement is in the measurement of a sparse collection of faint narrow lines or bands requiring a high resolution measurement and with no background present. There is no realistic analytical situation similar to
118
ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
this; however, some use might be found in astronomical spectrometry. By far the most promising application of SEMIDS is for measurements in the infrared spectral region. The usual condition of detector noise limitation would ensure that the Jacquinot advantage would be realized in addition to a resolving power improvement. Therefore, SEMIDS should give performance intermediate to that of conventional infrared spectrometers and Fourier transform spectrometers (in which both the Jacquinot and the Fellgett advantage are realized). Because SEMIDS requires fewer components and requires much smaller mechanical tolerances as compared to the Fourier transform spectrometer, and also because no interferogram is produced thus eliminating the requirement of a computer or a Fourier transform analyzer, the cost of SEMIDS would be substantially lower than that of a Fourier transform spectrometer. Thus, SEMIDS could be a reasonable compromise for laboratories requiring an improved infrared spectrometer but without the budget for a Fourier transform spectrometer.
LITERATURE CITED (1) (2) (3) (4) (5)
(6) (7) (8) (9)
(10) (11)
T. Dohi and T. Suzuki, Appl. Opt., 10, 1359 (1971). G. Horlick and W. K Yuen, Anal. Chem., 47, 775A (1975). P. Connes, J. Phys. Rad., 19, 197 (1958). T. L. Chester, Ph.D. Thesis, University of Florida, Gainesviile, Fla., 1976. J. J. Fitzgerald. T. L. Chester, and J. D. Winefordner. Anal. Chem., 47, 2330 (1975). T. L. Chester and J. D. Winefordner, Anal. Chem., 49, 119 (1977). J. D. Winefordner, R. Avni, T. L. Chester, J. J. Fitzgerald, L. P. Hart, D. J. Johnson, and F. W. Plankey, Spectrochim. Acta, Part 6,31, 1 (1976). Y. Talmi, R. Crosmun, and N. M. Larson, Anal. Chem., 48, 326 (1976). A. G. Gaydon and H. G. Wolfhard, "Flames", Third ed. revised, Chapman & Hall Ltd. London, 1970, pp 158-162. D. J. Johnson, F. W. Plankey, and J. D. Winefordner, Anal. Chem., 47, 1739 (1975). J. D. Winefordner, Ed., "Trace Analysis, Spectroscopic Methods for Eiements", John Wiley, New York, 1976.
RECEIVEDfor review June 30,1976. Accepted October 4,1976. This work supported solely by AF-AFOSR F44620 76 C 0005. One of the authors (TLC) acknowledges the award of a fellowship sponsored by the Procter & Gamble Company.
