Throughput Advantage and Disadvantage in Analytical UltravioletVisible Spectrometry by Considerations of Signal and Noise Spectral Bandpasses T. L. Chester' and J. D. Winefordner' Department of Chemistry, University of Florida, Gainesville, Fla. 326 1 1
The spectral bandwldth of the signal and background components of a light flux depend upon the means of identlfying the signal. Signal selectivity does not necessarlly depend on the slit width of the measuring spectrometer. Thus, the large Jacqulnot advantage usually given to Interferometric and multiplex instruments in comparisons with dispersive spectrometers may not always apply. Treatment of the signal and background as separate nolse sources leads to a slmpie explanatlon of spectrometer performance (i.e., the signal-to-noise ratio) as a function of spectrometer slit width.
In comparisons of signal-to-noise ratios (S/N) for various spectral measurement methods, one of the first simplifying assumptions usually made is that the resolving power is the same for each method. This invariably leads to a large Jacquinot advantage for multiplex and other interferometric instruments because very small slit widths must be used in conventional dispersive spectrometers to achieve the resolving power of a typical interferometer. While this is true in most measurement situations, it is not necessarily true when the analyte signal can be differentiated from any spectral background present by other means ( I ) , thus allowing the use of much larger slits in a dispersive spectrometer.
THEORETICAL CONSIDERATIONS Consider resonance fluorescence of an element excited by a perfect line source. Modulation of this source results in a modulated fluorescence signal. Any emission (not source induced) from another element at a slightly different wavelength is not modulated. Because this emission can be distinguished from the desired signal (in the frequency domain rather than spectrally), the effective resolution of the complete instrument (modulator, spectrometer, and demodulator) is the width of the atomic line regardless of the spectral bandpass of the spectrometer. However, any spectral component striking the detector can carry noise. The total noise will be dependent on the presence of all radiation reaching the detector and on any noise carried by that radiation and therefore will depend on the spectral bandpass of the spectrometer. Thus, as is suggested here, the spectral bandpass of the signal may be different than the spectral bandpass of the noise. If a modulated continuum source is used to excite the fluorescence in the example above, things are now a little different. The spectrometer bandpass must be chosen such that the line of interest is sorted from any others which may be near it. Once this is done, the signal can still be distinguished from dc emission within the spectrometer bandpass, so the spectral bandpass of the signal is still the width of the atomic line. Flame background fluorescence or scatter cannot be easily distinguished from atomic fluorescence except by spectral (rather than electronic) discrimination (or by time resolution).
When these are appreciable or when signals are not modulated, as in atomic emission, the signal spectral bandpass and the noise spectral bandpass are both determined by the spectrometer slit width. An interesting consequence results when the signal and background are considered as separate noise sources. Consider a modulated atomic line with a white light dc background measured by a conventional dispersive spectrometer. The detected radiation originating from both the analyte and the background may carry noise ( Z ) , photon (shot) noise which is proportional to the square root of the light flux, and other noises ( l / f noise, flicker noise, etc.) which are directly proportional to the light flux. If the modulation frequency is properly chosen, the limiting noise will be shot noise on the signal for small values of the slit width. Because the signal measured from narrow line sources is proportional to the slit width, and because the shot noise is proportional to the square root of the signal (and the square root of the slit width), a plot of the log S/N vs. log (slit width) will have a slope of 0.5. However, the intensity of the white light background increases with the square of the slit width. Shot noise from the background must be increasing linearly with the slit width. A point must be reached where the background shot noise exceeds the signal shot noise and then dominates the total noise. When this occurs, the S/N has reached a constant value, and the slope of the logflog plot above becomes zero. Alternatively, proportional signal carried noise may become dominant. This also gives a slope of zero. Further increases in the slit width will not increase the S/N but, when background carried proportional noise ultimately becomes dominant, the S/N will decrease and the slope will be -1. This behavior is shown in Figure 1. The S/N for a spectrometric dispersive system can be treated in a more exact manner ( 2 )by writing
where Rs is the count rate of the signal light component (as-
I
/Slops
I
Present address, Procter &Gamble Co., Miami Valley Laboratories,
P.O. Box 39175, Cincinnati, Ohio 45247.
0.5
LOG(Slit Width1
Figure 1. Behavior of log (SIN) vs. log (slit width) for the measurement of a line vs. a continuum background ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
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2.oc
I .75
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0
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325
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375
LOG ( s l i t w i d t h , U m )
Figure 2. Family of curves of log (SIN) vs. log (slit width) for constant signal and varying background Evaluated for to = 1 s, Rs = 1000 s-’, and RB = 300 S-’ (a), 1000 s-‘ (b),3000 s-‘ (c),and 10,000 s-l (@ (Rsand RB given for W = 100 pm) and CB = 0.01
2.00
I .75
1.50
1.25
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1.00
a
0.75
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s
0.50
0.25
0 100
125
150
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200 LOG
(Silt
225
250
275
300
325
350
375
Wldth.Mm)
Figure 3. Family of curves of log (SIN) vs. log (slit width) for constant background and varying signal Evaluated for to = 1 s, RB = 1000 s-’, and RS = 100 s-l (a),300 s-’ (b),1000 s-’ (c),3000 s-l (d)(Rs and RB given for W = 100 pm) and EB = 0.01
suming photon counting is used), R g is the count rate of the background light component, t o is the total analysis time, and [s and (B are the proportionality constants for the signals and background, respectively, which relate the observed proportional noises to the light flux carriers; detector and electronic noises are neglected in this treatment because they are generally negligible compared to the other noises. The total noise is the quadratic sum of the independent (rms) noises. Thus, 120
ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
the first two terms in the denominator are squares of shot noises for the signal and background and the last two terms are the squares of the proportional noises. Equation 1 can be evaluated as a function of slit width by letting RsT = KsW and RBT = KgW2,where K s and K B are proportionality constants for the signal and background light count rates, respectively, and W is the spectrometer slit width. Arbitrary choices of Rs, Rg, and T a r e then made for a value
2.00
I .75
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0.25
0
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LOG [ s l i t width,um)
Figure 4. Family of curves of log (S/N)vs. log (slit width) for constant signal and background but varying Eo Evaluated for
to = 1 s, RS = 1000 s-',
and RB = 1000 s-l (Rs and RB given for W = 100 pm), and
200
= 0.01 (a),0.003 (b),0.001 (c),and 0.000 (4
-
150 -
I
15
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I
2s
30
050
-
LOG ( d i t width,arn)
Figure 5. Log (SIN)vs. log (slit width) for flame atomic emission 0L
(a)30 fig/ml Mg and (b)10 pg/ml Mg aspirated. The solid lines are from Equation 2
of W to assign values to K s and Kg. Equation 1 can then be written as
After choices are made for and t ~Equation , 2 for S/N may be evaluated as a function of W . This was done for a variety of situations, and the resulting plots of log S/N vs. log W are given in Figures 2,3, and 4. Figure 2 shows a family of curves for constant signal and varying background. Figure 3 is the same but for constant background and varying signal. Figure 4 shows the effect of changing FB for constant signal and background.
EXPERIMENTAL The S/N for Mg flame atomic emission and fluorescence (excited by a chopped CW xenon arc lamp) were measured as a function of
' I50
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LOG (slit w\dth.Hml
Figure 6. Log (S/N) vs. log (slit width) for flame atomic fluorescence of 0.1 pg/ml Mg excited with a modulated (50 Hz) continuum source. The solid line is from Equation 2 spectrometer slit width and are plotted in Figures 5 and 6. The experimental details are given in Tables I and 11. The S/N for atomic emission was obtained (for each slit width) digitally from a photon counter (S/N = the mean number of signal counts obtained in a series of 2-s integration periods divided by the standard deviation), while the S/N for atomic fluorescence was estimated from strip-chart recordings of a lock-in amplifier output (photon counting was not used) taking the rms noise as Ys of the observed peak-to-peak noise. Slit widths smaller than 32 pm were not used because the signal decreased faster than the expected behavior as the slit was reduced to lower values. This may have been avoided if curved slits were employed rather than the straight slits which were used. Mg was chosen because it has a single atomic line which appears a t a wavelength (285.2 nm) where the separated air/C?Hr flame background is reasonably flat (Le., continuum-like) and thus does not violate the assumptions given for Equation 2.
ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
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Table I. Experimental Components of Atomic Flame (Emission and Fluorescence) Spectrometric System Component
Model No.
Company address
Monochromator
218
Photomultiplier
EM1 62568
GCA/McPherson, Acton, Mass. 01720 Gencom Div., Plainview, N.Y. 11803 Princeton Applied Research, Princeton, N.J. Perkin-Elmer Corp., Norwalk, Conn. Laboratory constructed
Photomultiplier housing Burner
1151
290-0110
Capillary burner head (Emission measurements only) Aniplifier/discriminator
1120
Digital synchronous computer
1110
(Fluorescence measurements only) Lock-in amplifier
220
Princeton Applied Research, Princeton, N.J. Princeton Applied Research, Princeton, N.J.
Rotary light chopper Xenon arc lamp
R300-1
Power supply
1505-71
Recorder
Princeton Applied Research, Princeton, N.J. Laboratory constructed Eimac Div., Varian, San Carlos, Calif. Eimac Div., Varian, San Carlos, Calif. Sargent-Welch, Anaheim, Calif.
XKR
Table 11. Experimental Conditions of Atomic Flame (Emission and Fluorescence) Spectrometer Monochromator Slit height Slit widths Wavelength Flame Air/CzHz (Ar separated) Emission Measurements Only Signal integration time Fluorescence Measurements Only Lamp power Chopping frequency Time constant
RESULTS AND DISCUSSION Figure 5 shows plots for two different Mg concentrations (10 and 30 pg/ml) resulting from flame emission. The solid lines shown were derived from Equation 2. Notice the similarity to the theoretical curves in Figure 3. The absence of a plateau indicates that flame background shot noise (or analyte signal proportional noise) is not of great importance here. Therefore, in brighter emission sources (such as dc arcs and induction coupled plasmas), background shot noise will probably never be of importance in emission measurements. Figure 6 shows the behavior of S/Nin flame atomic fluorescence of 0.1 pg/ml Mg. The broad plateau in this case is due to flame background shot noise limitation. This behavior, as compared to the atomic emission curves, is due to the reduction of EB which is accomplished by signal modulation, and to the reduction in the background proportional noise relative to background shot noise resulting from a decreased observation time (Le., a 300-ms time constant for fluorescence compared to a 2-s integration period for emission). If an interferometric or multiplexed technique is considered 122
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600 groove/mm grating blazed at 300 nm, straight slits 10 mm 32,56,100,178,316,563,1000,1780pm 285.2 nm
Air 9.7 l./min CgH? 1.5 l./min A i 16.5 l./min 2s
150 W 50 Hz 300 ms
for a measurement which is limited by noise carried on the spectral background, and if this technique offers a geometric throughput increase for the signal equal to J as compared to a dispersive spectrometer, from shot noise arguments alone there will be no improvement in the S/N obtained if the spectral bandpass for the noise (i.e., the background) is increased more than the factor J 2 as compared to the conventional technique, for the measurement of a single spectral component. Furthermore, the probability of the S/N limitation by background carried proportional noise also increases with the throughput, and this may lead to S/N degradation even if the bandpass is increased by a factor less than P.Thus, the only true throughput advantage is derived from an increase in the solid angle of collection rather than from an increase in the bandpass, even if the signal spectral resolution remains the same. If the spectral bandpass of the signal is determined by non-optical means (as above, i.e., demodulation of a modulated line), then the slit of the conventional dispersive spectrometer may be opened, without loss of signal selectivity or purity, to any width providing an improvement in S/N. When the usual slit width restriction (for maintaining signal purity)
is thus eliminated, a potential throughput advantage of an interferometric or multiplexed instrument for the same measurement may not exist. Finally, the optimum (maximum) S/Nfor the measurement of a modulated atomic line (e.g., Figure 6) occurs if proportional signal carried noise is limiting; however, this can only occur for relatively large signals. For smaller signals, i.e., a t or near the detection limit, the best S/N ratio will result when background shot noise limitation occurs. If the spectrometer disperser (grating or prism) is substituted for one with larger dispersion, the background will be reduced while the signal remains constant. Thus, the resulting S/N ratio will be higher at the same slit setting after such a substitution. Furthermore, the limiting noise may revert back to signal carried shot noise, in which case more improvement could be realized by further opening the slits until background carried shot noise is dominant again. Thus, for atomic fluorescence excited with a line source, the optimum single channel spectrometer should have
the greatest dispersion possible (as allowed by the wavelength of the line being measured, Le., with the use of a grating with groove spacing just greater than half the wavelength of the line) and a slit width wide enough to achieve background shot noise limitation. With a multichannel spectrometer, an increase in dispersion to achieve a S/Ngain will result in a simultaneous decrease in the monitored spectral region, assuming the use of image detector.
LITERATURE CITED ( 1 ) T. L. Chester and J. D. Winefordner, Spectrochim. Acfa, Part 6, 31, 21 (1 976). (2) J. D. Winefordner, R. Avni, T. L. Chester, J. J. Fitzgerald. L. P. Hart, D. J. Johnson, and F. W. Plankey, Specfrochin?.Acfa, Part B, 31, 1 (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.
Determination of Hydrogen Sulfide, Carbonyl Sulfide, Carbon Disulfide, and Sulfur Dioxide in Gases and Hydrocarbon Streams by Gas Chromatography/Flame Photometric Detection C. David Pearson* and W. J. Hines Phillips Petroleum Company, Research and Development, Bartlesville, Okla. 74004
The application of a gas chromatograph/flame photometric technique to the separation and measurement of four compounds, H2S, COS, CS2, and SO2 in inert gases and hydrocarbon streams, is described. Three columns were necessary to achieve separation of the sulfur compounds from each other and from interferences. These procedures are appllcable up to the 50-ppm level. Higher levels are measured after dilution. The lower detection limits in mol ppm are: COS and CS2,0.2; SO2, 0.4; and H2S, 0.8. The standard deviation for H2Sat 6.70 mol ppm level is 0.23 and for COS at 3.97 mol ppm is 0.06. Although not measured, CS2 is expected to behave like COS and SO2 like H2S. The accuracy of the blends prepared by means of permeation tubes is estimated to be 3 % of the amount present.
The determination of trace sulfur compounds is a difficult problem and the analysis of the four compounds which are the subject of this report is no exception. Chemical methods of analysis are in use for carbon disulfide (CSz), sulfur dioxide (SO?),and hydrogen sulfide (H2S); the first two are limited to liquids. Carbonyl sulfide can be analyzed chemically down to 10 ppm and by gas chromatography down to 0.1%. The development of the flame photometric detector (FPD) ( 1 , 2 ) in conjunction with gas chromatography (GC) has allowed the determination of these four compounds a t levels down to 0.5 mol ppm. Below this level special techniques and apparatus have made possible the detection of selected compounds as low as 10 ppb ( 3 , 4 ) . This report describes the experimental work carried out in developing analytical techniques for the determination of H2S, COS, SO.,, and CS2 in gases and refinery streams. A previous publication described the modifications to the gas chromatograph and the detector (5).Our system will detect down to
0.2 mol ppm of COS and CS2,0.4 mol ppm of SO2 and 0.8 mol ppm of H2S. This is satisfactory for the uses that have been encountered to date. The stainless steel GC columns described in this report are more robust than the glass or Teflon columns used by others for measurement of sulfur compounds at sub-ppm levels ( 3 , 6 ) .Calibration of the GC/FPD is by permeation tube blends which provide a stream of known composition ( 4 , 6, 7). The hydrocarbon portion of a sample frequently extinguishes the flame in the FPD causing a loss of sensitivity and necessitating recalibration. Reversal of the fuel gas inputs, as recently described (8), eliminates this problem and gives satisfactory operation despite a reduction in response by a factor of two or three. In addition, for quantitative analysis it is essential that the sulfur compounds be separated from the hydrocarbons. When hydrocarbon replaces hydrogen in the flame, the excitation energy-and hence the signal-is reduced. Separation has been accomplished of the four sulfur compounds from each other and from hydrocarbons in the list of samples below. Three GC columns are used. Each specific sulfur compound requires a separate calibration. The determination of these four sulfur compounds in natural gas, nitrogen, hydrogen, stack gases, shale oil off-gases, coal liquefaction off-gases, propane, butanes, ethylene, propane/propylene, butenes, Claus unit tail gases, butadiene, light ends of gasoline, and gases given off polymers when heated is described herein.
EXPERIMENTAL Apparatus. A Tracor Model 550 gas chromatograph equipped with dual electrometers and a flame photometric detector, Tracor Analytical Instruments, Austin, Texas, were used in this work. Samples were admitted t o the GC from 1- or 5-cm3 glass sampling loops through a 6-port rotary gas sampling valve, Perkin-Elmer Corp., ANALYTICAL CHEMISTRY, VOL. 49, NO. 1, JANUARY 1977
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