LITERATURE CITED
(15) "CRC Handbook of Chemistry & Physics", 534 ed., 1972-73, p 6-95. (16) H. J. issaq and W. L. Zieiinski, Anal. Chem., 48, 787 (1976).
(1) T. T. Woodson, Rev. Sci. Instrum., IO, 308 (1939). (2) A. Walsh, Spectrochim. Acta, 7, 108 (1955). (3) Perkin-Elmer, Norwalk, Conn., "Analytical Methods for Atomic Absorption Spectrophotometry", 1973. (4) H. Brandenberger and H. Bader, Helv. Chim. Acta, 50, 1409 (1967). (5) H.Brandenberger and H. Bader, At. Absorpt. Newsl., 7, 53 (1968). (6) W. R . Hatch and W. L. Ott, Anal. Chem., 40, 2085 (1968). (7) J. F. Alder, A. J. Samuel, and T. S.West, submitted for publication in Anal. Chim. Acta. (8) R. D. Ediger, At. Absorpt. Newsl., 14, 127 (1975). (9) H. J. issaq and W. L. Zielinski, Anal. Chem., 46, 1436 (1974). (10) J. W. Owens and E. S.Giadney, Anal. Chem., 48, 787 (1976). (11) E. 8. Sandell, "Colorimetric Determination of Metals", Interscience, New York, 1959, p 625. (12) Description and Operating Instructions, HGA 74, Bodenseewerk PerkinElmer & Co., GmbH, Uberlingen, 1975. (13) D. M. Hingle, G. F. Kirkbright, and T. S. West, Analyst(London), 92, 759 (1967). (14) R. F. Browner, R. M. Dagnail, and T. S.West, Talanta, 18, 75 (1969).
Exchange of Comments:
J. F. Alder* David A. Hickman' Department of Chemistry Imperial College of Science & Technology London, SW7 2AY England Department of Chemistry, Brookhaven N a t i o n a l Laboratory, Upton, N.Y. 11973.
RECEIVEDfor review August 6,1976. Accepted October 28, 1976. We are grateful to the Home Office Central Research Establishment, Aldermaston, for the provision of a research bursary (DAH); during the period of this work one of the authors (JFA) was the holder of an IC1 Fellowship.
Signal Flicker Noise and Noise Power Spectra
Sir: I have read the recent article by Talmi et al. ( I ) with great interest. Clearly this type of characterization of spectrometric sources is useful and necessary to make logical judgments about instrumental design and optimization of instrumental variables. However, I feel that some statements made about the data may be misleading and require clarification. On page 326, the authors state that "[The Poisson statistical] . . .behavior of PMTs is a direct result of their quantum efficiency being less than one. Thus in uv-visiblespectrometric studies, in which the P M T is operated in the dc mode (not saturated and not as a photon counter) the signal to noise ratio (S/N) is proportional to the square root of the signal regardless of whether the detector or the spectrometric source is the dominant noise source". The first sentence is not totally true because even if the quantum efficiency was one, the output would follow Poisson statistics if the input photon flux was Poisson. Because the guantum efficiency is less than one, the mean anodic photoelectron pulse rate is less than the photon rate incident on the photocathode. However, the Poisson nature of the incident flux is still retained, which has been proved mathematically by Fried ( 2 ) . Even if we consider a hypothetical noiseless photon flux (photons equally spaced with respect to time), the number of anodic pulses per unit time with a quantum efficiency less than one would follow a binominal distribution. The binomial distribution would approach the Poission distribution only if the quantum efficiency was very small. Of course, one must also consider the effect on current measurements of the statistical nature of secondary emission which follows a Polya statistics ( 3 ) . The basic idea expressed in the second quoted sentence in reference 1and used in other places in the paper is incorrect in certain situations. Noise from the spectrometric source (i.e., noise related to the magnitude of the analytical signal) can be divided into two types ( 4 ) :Signal shot noise and signal flicker noise. Signal shot noise is proportional to the square root of the signal and its noise spectrum is flat. Signal flicker noise is directly proportional to the signal. Its noise power spectrum may be white, exhibit l/f character, or exhibit higher magnitude at specific frequencies. Because of the difference in the dependence of the noise magnitude on signal level, signal shot noise will be dominant under low light level situations, whereas signal flicker noise will be dominant under high light
level situations. Since often signal flicker noise exhibits l/f character, it is likely to be more significant when measurements are made at frequencies of 1Hz or lower. It is felt that the importance of signal flicker noise (noise not proportional to the square root of the signal) has been underestimated in reference 1 since its significance in common spectrometric measurements has clearly been demonstrated in the literature (5-8). We have observed significant signal flicker noise in typical molecular absorption (91, molecular fluorescence, flame atomic absorption (IO), and flame atomic emission measurements. From a practical point of view, it is vital to realize that signal flicker noise exists. If measurements were always limited by signal shot noise so that the S/N was proportional to the square root of the signal, then the S/N could always be improved by changing instrumental variables to increase the magnitude of the signal. However, at higher light levels, the signal flicker limit is reached and the S/N is independent of the signal. The authors use their data to show that the signal shot noise limit applies in certain situations. In Figure 3, the slope of 0.5 in the log-log plot of noise vs. photocurrent indicates that these experiments are signal shot noise limited and Poisson statistics apply. However, other data in the paper show that signal flicker noise is present in addition to signal shot noise. Since for most measurements, the same PMT and bias voltage (Le., photomultiplier gain) were employed, the relative standard deviation (Le., the relative rms noise) at a given photoanodic current should be the same from experiment to experiment if only signal shot noise was important. Clearly from the data (e.g., Tables 111-V) this is not the case. In Figure 3, the noise from the dc arc is an order of magnitude larger than for other sources at the same photoanodic current or light level, and on page 329, the noise level for the argon microwave plasma was noted to be twice as high as for primary sources at signal levels of 5 X loT8A. The S/N is proportional to the square root of the signal in Figure 3 because measurements were made under low light level conditions where the S/N is not greater than one hundred. At higher levels, where signal flicker noise becomes more important, the slope in Figure 3 would decrease and approach a constant value, as has been experimentally verified (11). On pages 331-333 in reference 1,comments are made about the lack of signal flicker noise of l/f noise in many of the sources. The data presented do not necessarily indicate that
ANALYTICAL CHEMISTRY, VOL. 49, NO. 2, FEBRUARY 1977
339
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)
340
(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-wA 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
