Some Comments on the Signal-to-Noise Characteristics of Real Photomultiplier and Photodiode Detection Systems SIR: We have read the recent correspondence by Ingle and Crouch ( I ) with great interest. In this article a comparison was made between the signal-to-noise characteristics of a high gain photomultiplier (PMT) and a photodiode when the overall gain of the total system including the electronic amplifiers is the same. It was concluded that the PMT system possessed a definite signal-to-noise advantage over the photodiode system below about lO-gA photocathode current. This result rests upon the fundamental assumption that both photoelectric devices are internally shot noise limited (see Equations 4 and 5). As a result, the performance of a photodiode system was found to be limited by the thermal noise in the feedback resistor of its amplifier system which is amplified along with the relatively low output current of the photodiode, and overides the shot noise. DISCUSSION
It is necessary to make several comments upon this conclusion in the light of practical experience with these two design approaches in our laboratory. Comments will first be addressed to the short-term noise characteristics of these systems and then to the long-term drift problems which we have encountered. With respect to short-term noise, it is not strictly correct to assume that the PMT is internally shot noise limited. Even in the ideal case, there is thermal noise associated with the resistors in the dynode voltage divider network. The gain of a PMT may be expressed as follows (2), assuming equal dynode voltage drops per stage: G
=
y(kk’Vdm)n
where = the cathode-1st dynode collection efficiency = the dynode transfer efficiency k k‘ and m = empirical constants for a given type of dynode surface and m = 1 n = the number of dynodes = the dynode voltage drop/stage v d G = the PMT gain
Y
Clearly small changes in dynode voltage have a disproportionate effect on the gain of the tube, If these changes are due to resistor noise in the dynode network, at some point the noise from this effect must completely predominate as it is independent of photocathode current. If the dynode resistors were ideal to the extent that the Nyquist formula did actually describe their behavior, these gain variations in the tube would not be particularly important until the PMT was operated into the photon counting range. It has been our experience that this ideal is not true of even the highest quality film type resistors. Given the assumption of AF = 1 Hz., at dc the l/F noise characteristics of typical resistors predominate over the predicted Nyquist behavior of ideal resistors by about three orders of magnitude (3). The experimental result is a decrease in the signal(1) J. D. Ingle and S.R. Crouch, ANAL.CHEM., 43, 1331 (1971). (2) R . E. Santini and H. L. Pardue, ibid.,42,706 (1970). (3) J. J. Brophy, “Basic Electronics for Scientists,” McGraw-Hill, New York, N.Y., 1966, p 271, Fig. 7-33. 1708
to-noise ratio of the PMT by an order of magnitude or more beyond that expected by shot noise alone. The low frequency noise characteristics of a given resistor type are extremely difficult to predict on theoretical grounds. The actual signal-to-noise ratio which is obtained is, therefore, highly dependent upon these components which are external to the PMT itself. The use of wire-wound resistors to avoid the l/Fnoise may produce regenerative behavior in the PMT. The dark current of the PMT was assumed to be small compared with the total anode current by Ingle and Crouch. In Table I, the typical anode dark currents of a number of commonly used PMT’s are summarized. These data are taken from manufacturer’s specification data sheets. The anode dark current for many of these tubes is about lO-9A. However, it will be noted that a number of these tubes exhibit a much larger dark current value. This effect is apparently common for PMT’s which are optimized for response in the red and infrared regions. For these cases, it is necessary to measure signal current after a much larger value of dark current has been nulled. It has been reported that the dark current itself possesses a significant noise component (4). We have observed these instabilities in the dark current even though the PMT was handled in darkness and operated far below the manufacturer’s specified maximum anode current. In these cases the observed noise is independent of the signal current. There exists one mechanism for gain changes in PMT devices which is often overlooked. In the case of tubes constructed with semi-transparent photocathodes, it has been shown (5) that there exist very large changes in the area sensitivity of the PMT from one small spot to another on the photocathode. Any mechanical instabilities which cause the light beam to be shifted on the photocathode will result in uncontrollable gain changes in the device. This effect can result in long- and short-term noise in the amplified signals. The theoretical treatment of the photodiode-operational amplifier combination is straight-forward. In this case we agree that the detector is internally shot noise limited, and 1/F noise is the limiting factor in the amplifier system. A factor which could change this situation is the recent introduction of solid state diode detectors with sensitivities and quantum efficiencies which appear to be substantially better than existing vacuum photodiodes (6). Thus for the same photon input greater output currents may be obtained. In our experience the real problem with PMT devices occurs when an attempt is made to use these tubes in longterm measurement situations. In these cases, the PMT exhibits dc drift and gain changes which are difficult to control, The problem here appears to be that the PMT is a very high gain device which does not possess any known mode for internal feedback stabilization. A PMT-low gain amplifier combination thus represents a system where the primary gain of the system is dependent upon a device where no feedback exists. In the case of the photodiodehigh gain amplifier combination, the electronic amplifier is usually designed with a high degree of feedback in order (4) J. Morrow, Amer. Lab., 3, 11 (1971). (5) 0. Youngbluth, Jr., Appl. Opt.,9,321 (1970). (6) P. H. Wendland, Electronics, 44 ( l l ) , 50 (1970).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
Table I. Anode Dark Current Levels of a Selection of Typical PMT Devices from Various Manufacturers
PMT type 8575 8550 1P-21 1P-28-A 9558-B 6097-s 9637-R XP1015 XP1004 56TUVP R207 7102
Manufacturer RCA RCA
RCA RCA EM1 EM1 EM1 Amperex Amperex Amperex Hamamatsu Hamamatsu
Typical anode dark current, ampere 1 x 6 X 2 x 5 x 2 x 1 x 2 x 1 x 1.5 X 5 x 5 x 5 x
10-0 10-1"
10-9 10-0
10-9 10-0 10-10
10-9
lo-^
10-7 10-6
to maintain constant gain. As a result, the primary gain of the system is dependent upon a device which tends to correct itself for long-term drift and gain errors. CONCLUSION
The results of Ingle and Crouch are a useful treatment. Given their simplifying assumptions, we do not disagree with the conclusions. However, theoretically and experimentally the noise characteristics of the PMT device must depend upon additional variables which were not considered. As a result, in terms of short term noise, the PMT-low gain amplifier combination is probably not as favorable as it would at first appear to be in their treatment. For experiments in which data collection is over prolonged intervals (1 hour or more), the PMT exhibits unavoidable, uncontrollable drifts. This problem is especially severe at low anode currents where the dark current is a significant factor. Experimentally we have found that the most successful PMT applications involve short-term experiments (such as stopped-flow kinetic measurements) where it is possible to make frequent recalibrations of the PMT to a known standard. As better diode detectors appear, the PMT is being
displaced from these applications, even at very low light levels. The one area where the PMT is outstanding is in photon counting applications. Here it is possible to utilize the PMT as a high gain pulse amplifier such that gain stability is not so important a parameter. Finally, in the current range where either a PMT or photodiode could be used, the performance of a given device is subject to a sufficient number of external empirical parameters that theoretical treatments are a rough guide to actual performance. A great deal depends upon the measurement system design and the way in which it is constructed. It is possible, by careful experimental design, to do an adequate job with either detector system such that the detector system itself is not the limiting factor in the experiment. The above discussion is largely with reference to analog dc detector systems. Optically chopped experiments produce two classes of results. Either the photoelectric device becomes a simple null detector for a servo system; or, in the case of a modulated system with a phase detector, the observed signal-to-noise ratio becomes a function of the demodulation circuit (independently of its preceding amplifiers) as well as the photoelectric device. At present we are evaluating the general performance characteristics of a modern solid state photodiode system which is carefully matched to a high gain-low noise amplifier. The results of these studies will be reported in a manner consistent with the above criteria. ACKNOWLEDGMENT
The author would like to acknowledge the assistance of J. W. Amy in preparing this work. R. E. SANTINI
Department of Chemistry Purdue University West Lafayette, Ind. 47907 RECEIVED for review September 30, 1971. Accepted April 19,1972.
Signal-to-Noise Ratio Characteristics of Photomultipliers and Photodiodes An Exchange of Comments SIR: In our previous correspondence ( I ) we were concerned with comparing the inherent signal-to-noise ratio (S/N) characteristics of photomultiplier tubes and vacuum photodiodes. Thus our comparison considered only fundamental noise (shot noise and Johnson noise), which cannot be eliminated, and did not consider excess noise (amplifierreadout noise, source flicker noise, photomultiplier flicker noise, etc.), which is the result of imperfect instrumentation. The purpose of our correspondence was to show that when only fundamental noise is considered, the photodiode-high gain amplifier combination can provide higher S/N's at high light levels, while the photomultiplier with internal amplification can show higher S/N characteristics at lower light levels.
An approximate criterion was derived to indicate the crossover point. While we agee with Santini's comment that our correspondence applied to an idealized system, we feel that our conclusions are valid even in the presence of excess noise. In a recent paper (2) all the major noise sources in a spectrometric system were discussed. A S/N comparison of the two transducers based on the results of the above paper ( 3 )reveals that the basic criterion which established the crossover point is only slightly changed (within a factor of 5) in most cases. Thus, a more rigorous S/N comparison will not be presented here because the development is long and tedious and hence unjustified, since the simpler treatment already presented ( I )
(1) J. D. Ingle, Jr., and S. R. Crouch, ANAL.CHEM.,43, 1331 (1971).
(2) Ibid.,44, 785 (1972). (3) J. D. Ingle, Jr., Ph.D. Thesis, Michigan State University, East Lansing, Mich., 1971.
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