these types of noise would not be important for these sources under certain conditions of usage. The data were taken under relatively low light level conditions where the source flicker noise component will be small compared to the signal shot noise component. Hence a source cannot be stated to be categorically “white” even though under certain experimental conditions, a white noise power spectrum is recorded. Also one cannot necessarily use the photoanodic current to indicate that two experiments were run at the same incident light level since photoanodic current varies with photomultiplier current gain. More correctly, the photocathodic current determines the S/N ( 4 ) .The highest photoanodic current used A which corresponds to a photoin reference 1was 5 x A (with the specified gain of lo5). cathodic current of 5 X Belyaev’s measurements (12) were made a t the same photoanodic current; however, the PMT gain may have been different which means the absolute light levels could be different (assuming about equal P M T quantum efficiencies). We have measured the following photocathodic currents with commercial instruments under normal operating conditions: 10-12-10-11 A (Varian AA-6 spectrophotometer with different elements, AA mode (13)),3 X 10-lo A (Heath UVvisible spectrometer, 4-nm bandpass (9)), 8 X lowloA (Turner 330 spectrometer (13)),2 X A (Spectronic 20 Spectrometer (13)), 5 X 10-’2 A (Varian AA-6 spectrometer, emission mode, 5 ppm Na), 1 X A (ARL plasma emission spectrometer, 1 ppm Mn). Clearly the absolute light levels used with common instruments under typical conditions are often one to over four orders of magnitude higher than measured in reference l. For our measurements specified above, even with primary light sources as the tungsten lamp, signal flicker noise was usually dominant. Note also that the noise for a tungsten lamp (Table 111) at a photoanodic current of 5 X 1O-SA is specified to be 2 X A HZ-~’~. The theoretical shot noise is equal to ( 1 4 ) (2eAf (1 a ) mi) where e = charge of electron, Af = noise equivalent bandpass, CY = secondary emission factor, m = photomultiplier gain, and i = photoanodic current. If we assume typical or given values (Af = I Hz, CY = 0.275, m = lo5,and i = 5 X A Hz-ll2. A), the theoretical shot noise is 4.5 X In Figure 15, the authors note that noise power spectra features become less distinct at smaller currents which they attribute t o dark current noise. This could also be due to the decrease in the relative contribution of signal flicker noise as the signal is decreased. Note in the figure that the change in the noise level at low frequencies when decreasing from a A is essentially prophotocurrent of 5 X 10-8 A to 1 X portional to the signal and not the square root of the signal. The typical value of dark current noise for this type of PMT A Hz-~/*. at the specified voltage is about In summary a noise power spectrum depends upon the magnitude of the signal measured, and the presence or nonpresence of flicker noise and l / f components or other spectral features depends on the signal magnitude. Noise power spectra are most useful if they are taken under the conditions that would normally be used in an analytical situation because the fraction of the total noise due to signal shot noise or signal flicker noise varies greatly with measurement conditions (e.g., slit width, light collection efficiency, electronic bandpass). In general, signal shot noise (or amplifier or dark current noise) will dominant a t low light levels. However, for larger photon signals used in many instruments signal flicker noise and often I / f features are much more likely to dominate. The S/N a t which flicker noise becomes dominant depends on the source and varies from about 100 t o 10,000 ( 1 4 ) .
+
LITERATURE CITED (1) Y Talml, R Crosmun, and N M Larson, Anal Chem, 48, 326 (1976) (2) D L Fried, Appl Opt, 4, 79 (1965)
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(3) Photomultiplier Manual, Technical Series PT-61, RCA, Harrison, N.J., 1970. (4) J. D. Ingle, Jr., and S. R. Crouch, Anal. Chem., 44, 785 (1972). (5) N. Marinkovic and T. J. Vickers, Anal. Chem., 42, 1613 (1970). (6) J. D. Wlnefordner and T. J. Vlckers, Anal. Chem., 36, 1939 (1964). (7) J. C. Cetorelll and J. D.Winefordner, Talanta, 14, 705 (1967). (8) P. A. St. John, P. A. McCarthy, and J. D. Wlnefordner, Anal. Chem., 38, 1828 (1966). (9) L. P. Rothman, S. R. Crouch, and J. D.Ingle, Jr., Anal. Chem., 47, 1226 (1975). (10) N. W. Bower and J. D. Ingle, Jr., Anal. Chem., 48, 686 (1976). (11) J.D. Inge, Jr.. AnalChem., 47, 1217(1975), (12) Y. I. Belyaev, L. M. Ivantsov, A. V. Karyakin, P. H.Phi, and V. V. Shemet, J. Anal. Chem. USSR, 23,655 (1968). (13) N. W. Bower and J. D.Ingle, Jr., Anal. Chem., submitted. (14) J. D.Ingle, Jr., Anal. Chim. Acta., in press.
J. D. Ingle, Jr. Department of Chemistry Oregon State University Corvallis, Ore. 97331
RECEIVEDfor review May 10, 1976. Accepted November 1, 1976.
Sir: Ingle expressed his concern about various statements and conclusions argued in our recent publication ( I ) . It is the intent of this communication to answer his criticism. Throughout the paper the author complains about our disregard for signal flicker noise. We would like to reassure him, that indeed we have a great deal of respect for that “beast”, except that our experimental evidences indicate that very often it is insignificant. Nevertheless, to comply with the author’s rather obsessive conviction in the absolute dominance of flicker noise, we would like to state here the “Universal Flicker Noise Law”: All spectrometric sources are flicker-noise limited at very high signal levels, very low frequencies, and when all other dominant noise sources are eliminated. The author questions the validity of our experiments by suggesting that they were not carried out “under normal conditions of usage”. He presents an entire array of “typical” photocathode current values utilized in various systems. From these values he concludes that “Clearly the absolute light levels used with common instruments under typical conditions are often one to over four orders of magnitude higher than measured in reference I”. While only about 25% of our measurements were made a t a signal-to-noise ratio (SNR) near 100, we do not feel that they were atypical. Fully half of our measurements were made at anode currents that were within a factor of 1000 of the maximum allowable average anodic current for the type of P M T used and were within approximately an order of magnitude of the I-FA average current recommended ( 2 ) by the manufacturer for maximum stability. The author, however, did not provide any pertinent information concerning the detector gain used in each of the systems described by him. For instance, if one considers the “typical” photocathodic current value of 2 X IOhs A (Spectronic 20 spectrometer using a phototube) and applies to it the gain level used in most of our experiments (lo5),an exceptionally high value, 2 X A, will be derived for the photoanodic current of that system. We therefore dispute the author’s rigid definition of “typical” photocathodic currents. Current values so deduced without a thorough consideration of all other experimental parameters (not the least of which is the gain of the detection system) can be very misleading and a t best should be regarded as very qualitative. A case in point is the gas chromatographic-microwave emission spectrometric (GC-MES) system ( 3 ) that has been used routinely in the determination of CH3HgCl in biological samples. The response of the detector
ANALYTICAL CHEMISTRY, VOL. 49, NO. 2, FEBRUARY 1977
was linear over more than four orders of magnitude, 3 x 1O-I1 to 3 X A (anodic currents), corresponding to a concentration range (benzene solutions) of 0.005-50 ppm. Does the author suggest that these routine analyses have been performed under atypical conditions? Molecular fluorescence can serve as another example. We recorded the noise spectrum of a Xenon lamp (a 150-W lamp used in an Aminco-Bowman spectrofluorometer, without a magnetic stabilizer). The source had a perfectly “white” noise spectrum with a “shot noise limited” behavior. In fact, the fluorescence (emission) spectra obtained for quinine sulfate (in 0.1 N &Sod) at the concentration range of 0.01-100 ppb (undoubtedly, a rather typical range) also produced similar noise spectra. Furthermore, an optical multichannel TV detector (a Princeton Applied Research Corporation 1205D Silicon Intensified Target Detector) placed at the focal plane of the emission spectrometer of the same MF fluorometer has shown the exact same “shot” noise-limited behavior. SNR increased as the square root of the number of accumulations (proportional to exposure time). Yet, we are quite aware of the fact that aging Xenon arcs often suffer from substantial flicker noise, mainly l/f noise, due to the wandering of the arc. Contrary to the author, we see much less use in noise behavior studies of analytical systems that operate at very high SNR levels, e.g., lo4. Noise studies are most valuable mainly a t low SNR levels where optimization of the signal extraction process may become detrimental to the experimental outcome. The first comment of Dr. Ingle concerning the effect of quantum efficiency, QE, on the SNR is merely nit-picking. Truly, the author may be correct in suggesting that the definition, “Poisson Statistics” should not be used in our statement, because in certain cases (high $E values) a binominal distribution, rather than Poisson statistics, will describe the probability that a certain number of photoelectrons will be emitted. Nevertheless, we stick to our original statement, that only when the QE of a photocathode, q , is less than unity will the SNR always behave as SNR 0: ./is,where N is the number of photons striking the photocathode, Table I. However, we concede that because of our overzealous attempt to emphasize the inherent differences between infrared and UV-visible detectors, we neglected to mention the case of l/f noise dominance. The statement of p. 326, line 13 ( I ) should therefore read “Thus, in UV-visible spectrometric studies, in which the PMT is operated in the dc mode (not saturated and not as a photon counter) and when the contribution from signal-proportional features is negligible, the SNR is proportional to the square root of the signal regardless of whether the detector or the spectrometric source is the dominant noise source”. Figure 2 ( I ) seems to generate some real fascination for the author. However, contrary to his interpretation of this figure, it indeed proves the capability of our experimental setup to detect flicker noise when it really exists. Both the caption and the text of this figure refer to the “Poisson” nature of the
Table I. Signal-to-Noise Ratio Calculations Based on Photocathode Quantum Efficiency
Nature of photon flux
Quantum efficiency, q
1. Ideal (non-
V
