ANALYTICAL CHEMISTRY, VOL. 51, NO. 12, OCTOBER 1979
2001
Optimization of Parameters in Photon Counting Experiments T. M. Niemczyk," D. G. Ettinger,' and S. G. Barnhart' Department of Chemistty, University of New Mexico, Albuquerque, New Mexico 8713 1
The effects of photomultiplier voltage, discriminator setting, and temperature on the signal-to-noise ratio in a photon counting experiment have been measured for several photomultiplier types. The photomultiplierstested were an RCA 1P28A, an RCA 4832, an RCA 1P21, and a Hamamatsu R406. The results Indicate that photon counting experiments should be performed at the hlghest possible photomultlpller voltage. The data also show that the increase in the signal-to-ndse ratio realized when the photomultiplier is cooled is very dependent on the photomultiplier type.
A photomultiplier (PMT) is often used as the photon flux to electronic signal transducer in a system designed to measure optical signals. The resultant electronic signal can be processed by any one of several techniques, but photon counting has been shown both theoretically and experimentally to be superior to other techniques when the light levels are low (1-6). The inherent advantages of photon counting are many. The signal is processed in a discrete manner reducing the number of domain conversions (7), which leaves the information in a form directly compatible with computer processing. The processing of the signal by digital circuitry makes photon counting detection less susceptible to long term drift and l / f noise which often limit analog techniques. Photon counting circuits also include the circuitry necessary to discriminate against P M T dark current originating down the dynode chain, and because the output is in digital form the reading error inherent to analog systems is virtually eliminated. The overall result is that at low light levels photon counting yields a higher signal/noise ratio (SNR) when compared to other techniques. The SNR of an experiment often determines the extent to which information can be extracted from the experimental data. Thus when a low level signal is to be measured, the technique that realizes the highest SNR is the method of choice. Also, it is important that the optimum experimental conditions are chosen so the best possible SNR is obtained from the actual experiment. This is certainly the case when photon counting is used to measure a weak optical signal. Nakamura and Schwarz (6) discuss the selection of optimum parameters in a photon counting experiment. They present three methods of determining the optimum discriminator setting and conclude that actually measuring the SNR as a function of discriminator setting is the best method. They also discuss the selection of the proper P M T voltage and conclude that a low voltage is the optimum. I t is stated in their paper, without experimental justification, that increasing the voltage increases the dark current level and randomness faster than the gain. Many experimenters have shared the feelings of Nakamura and Schwarz and thus have always performed their measurements using low or moderate P M T voltages. In a very recent study (8),Darland et al. use the results of pulse height distribution and linearity measurements to select the best operating parameters. Their results indicate that Current address: University of Toronto, Lash Miller Chemical Laboratories, 80 St. George Street, Toronto, Ontario, Canada M5S 1Al.
Current address: Department of Chemistry, University of Wisconsin, Madison, Wis. 53706 0003-2700/79/035 1-2001$01.OO/O
although the dark count rate increases with voltage, the excess noise in the dark count measurement can be reduced by operating a t high voltages. They also point out that there is an optimum discriminator setting but the optimum choice depends on trade-offs among stability, sensitivity, and dynamic range. In this paper, we present the results of actually measuring the SNR as a function of the P M T voltage and the discriminator level setting. Thus, the optimum settings of the P M T voltage and discriminator can be easily determined. In addition the effects of cooling the P M T are reported. I t is well documented (6, 9-13) that the dark current of a P M T is reduced by cooling, and this is an often used technique to increase the SNR when weak signals are measured. The specific results obtained are indicative of the types of PMTs actually studied, but the method of optimization presented and the general conclusions made on the basis of the data obtained are applicable to any photon counting system.
INSTRUMENTAL The computer controlled photon counting apparatus used in the experiments presented here has been previously described (14). The PMT housing was, however, replaced with a Pacific Photometric Instruments Model 3461 thermoelect rically cooled housing powered by a Pacific Photometric Instruments Model 33 power supply. The PMT housing was modified by the manufacturer to include an iron-constantan thermocouple which was used to monitor the temperature of the PMT. Four different PMT types were used in these studies, an RCA 4832, an RCA 1P28, an RCA 1P21, and a Hamamatsu R406. Three different RCA 1P28s were tested. One was a new 1P28A and the results obtained from this tube are reported here. The results from the two lP28s were essentially identical to those from the 1P28A, but the 1P28A was more sensitive. Two RCA 4832 PMTs were tested and the results from these were essentially identical. None of the PMTs were specially selected, but at least one example of each type was new when the testing began. All of the PMTs were kept from exposure to bright light, even when changing the PMT. Once the PMT was installed in the housing, it was kept in the dark overnight with voltage applied in order to let the background settle. When any measurements were made at temperatures below room temperature the PMT was given 2 h or longer to equilibrate. The light sources used in these experiments were Westinghouse hollow cathode lamps. The power supply for the hollow cathode lamps was a GCA-McPherson Model EU-703-70 constant current supply. All the lamps used were operated at low currents, 3-5 mA, and allowed to stabilize for 30 min before any measurements were made. The light intensity was adjusted so that the signal count rate was approximately equal to the room temperature dark count rate. Neutral density filters and slit width adjustments were used to vary the light intensity. At the low count rates used in these measurements, pulse overlap is certain to be negligible. Count periods were necessarily long, approximately 5G100 s, in order that a sufficiently large number of counts was obtained. Each data point represents an average of ten measurements of each of the signal plus background and the background made in a synchronous fashion. In all cases, the relative standard deviation in the SNR measurements was less than 1%. The PAR Model 1120 amplifier/discriminator used in these experiments is mounted so that the connection between the PMT and the amplifier input can be kept short, in this case about 2 in. The output of the amplifier/discriminator is connected to the computer controlled counter previously described (14). The Model 1120 amplifier/discriminator has no facilities for mea0 1979 American
Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 12, OCTOBER 1979
surement of the actual discriminator level, thus the discriminator is set by adjusting a 20-turn pot, and all discriminator level settings are reported 85 turns of the screw from the zero setting. The zero setting corresponds to a discriminator coefficient of one.
RESULTS AND DISCUSSION
0 3 0
Signal-to-Noise Ratio. In order to calculate the SNR in a photon counting experiment, two measurements must be made: the combined signal and dark current pulse rate and the dark current pulse rate alone. The SNR is thus the number of signal counts divided by the square root of the sum of the variances of the two measurements and is given in Equation 1
S
F7
RtT - RdT = (S?+ Sd2)1/2
st
s d 2 = RdT and Rt and S,2 are given by R, = R, Rd
+ s? = sa2+ s d 2
(2)
(3)
(4) (5)
Substituting these expressions into Equation 1and rearranging gives
which is the equation used to calculate the SNR used in this discussion. A more detailed expression for the SNR of a photon counting experiment which takes the discriminator coefficient setting into account has been derived by Ingle and Crouch (17) and is shown in Equation 7
S
5a W
m
9
20
I
-I
a 2 s2 rJY
'0
(1)
where R, = total average arrival rate of pulses a t the anode, s-l. R , d - average dark current pulse rate, s-'; T = measurement = variance in the total pulse rate; and s d 2 = time, s; variance in the dark current pulse rate. For visible and ultraviolet radiation the photoelectron pulses arrive randomly a t the P M T anode and follow Poisson statistics (15). The major source of dark current is thermionic emission. The arrival of pulses at the anode due to thermionic emission have also been shown to follow Poisson statistics (6, 13, 16). Other sources of dark current, such as cold field emission, Cerenkov photons, glass fluorescence, cosmic rays, etc., do not necessarily follow Poisson statistics (6,12,13, 16). Since these other sources are small, it will be assumed that the arrival of all dark current pulses fqllow Poisson statistics, thus, s d 2 and the signal pulse rate variance, S:, can be readily calculated. Thus
Ss2= R,T
I P28A RDOM TEMPERATURE
(AR,T)1/2
where R d = average rate of arrival of anode pulses due to thermal emission at the cathode, s-l; Rnd = average rate of arrival of anode pulses due to dark current sources other than cathodic thermal emission, s-l; A = discriminator coefficient for signal pulses and dark current pulses due to thermal emission at the cathode; Ad = discriminator coefficient for dark current pulses from sources other than thermal emission a t the cathode. Equation 7 is very useful in the interpretation of the data presented here. 1P28 Photomultiplier. The SNR for an RCA 1P28A was determined as a function of the voltage across the P M T and the discriminator level setting and plotted in Figure 1. These
I O
P M
DISCRIMINATOR SETTING
L
(Arb Units)
Figure 1. Signal-to-noise ratios determined for the RCA 1P28A PMT
at room temperature and various voltages data were obtained with the P M T at room temperature, the
AI 309.27-nm line and the light source level such that the signal count rate was about equal to the dark count rate. The room temperature dark count rate measured at a P M T voltage of 1000 V and the optimum discriminator level setting was approximately 290 s-l. Note that for any P M T voltage, the SNR remains relatively constant as the discriminator coefficient is raised, then shows a maximum at intermediate levels, and then rapidly falls to zero with further increase. This behavior can be interpreted by looking at Equation 7. If the nonthermal noise is made up of a significant fraction of small pulses from down the dynode chain, then the ratio of &/A decreases as the discriminator level is increased. After a point, further increases in the discriminator level lead to decreased SNR since the SNR is proportional to All2 when Ad/A is small or a constant. Perhaps the most important feature of Figure 1 is that the SNR increases with the P M T voltage. The plots of SNR vs. discriminator setting for each voltage are very similar in shape, but the ultimate SNR increases with increased voltage. Measurements of the dark current show a steady increase with voltage until a maximum voltage was reached after which the P M T showed completely erratic behavior. For the 1P28A tested, this maximum was 1300 V. The other two 1P28s showed slightly higher maximum voltages, but in general the maximum useful voltage corresponded fairly well to the manufacturer's recommended maximum. Figure 2 represents the data obtained when the same experiment was repeated with the PMT temperature at -23.0 f 1.0 "C. As expected Rd decreases with decreasing temperatures, but the sensitivity of the P M T also decreased. Changes in cathode sensitivity with temperature are well known, and PMTs with CsSb photocathodes, e.g., the 1P28, show decreased sensitivity with decreasing temperature (6, 9,18,19). The ultimate SNR obtained at -23.0 "C was within a factor of two of that obtained at room temperature. The change in SNR with temperature is shown in Figure 3 where the SNR was measured using the optimum discriminator level setting and a high PMT voltage (loo0V). It has been pointed out that nonthermal dark current sources show higher variances than predicted by Poisson statistics. The lack of significant increase in the SNR a t low temperatures might be partly due to the nonthermal dark current becoming significant as the thermal dark current is reduced. Identical tests were run on two different RCA 1P28 PMTs. These two PMTs were somewhat less sensitive than the 1P28A as expected, but all three PMTs showed similar room temperature dark count rates. The SNRs measured for the three
ANALYTICAL CHEMISTRY, VOL. 51, NO. 12, OCTOBER 1979 4832 ROOM TEMPERATURE
IP28A -23 ' C
I
,
,
,
2003
,
0
,
.
,
I
1
5
I IO
DISCRIMINATOR SETTING
u
_
L
15
DISCRIMINATOR SETTING
A r b drits)
Signal-to-noise ratios determined for the RCA 1P28A PMT at -23 O C and various voltages Figure 2.
IAfb
Unit;)
Signal-to-noise ratios determined for the RCA 4832 PMT at room temperature and various voltages Figure 4.
0 50I-
2 w 40 % f 30 0 I-
/--/"Z/
I
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a
z
z07
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20
IO
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TEMPERATURE PC)
Temperature dependence of the signal-to-noiseratios of the RCA 1P28A and the RCA 1P21 PMTs Figure 3.
1P28s under identical conditions qhowed some differences, but the trends depicted by the SNR plots are exactly the same as shown in the figures presented here. Results obtained at other wavelengths, the Ca 422.67-nm and the La 550.13-nm lines, were identical to those obtained at the A1309.27-nm line. Other Photomultipliers. The other varieties of PMTs evaluated were ari RCA 4832, an RCA 1P21 and a Hamamatsu R406. The data obtained for the RCA 1P21 were essentially the same as those obtained for the 1P28s, and the SNR as a function of temperature for this P M T is shown in Figure 3. The data in Figure 3 were obtained at the Ca 422.6'7-nm line and the P M T voltage a t 1000 V. The similarity of the 1P21 to the 1P28 is to be expected since these PMTq are nearly identical. Two examples of an RCA 4832 were tested and although these tubes showed slight differences in sensitivity and dark count rate, the results obtained for the two PMTs were very similar. The SNR determined as a function of the P M T voltage and discriminator level setting are shown in Figure 4. These data were obtained at the Ne 640.22-nm line, the P M T a t room temperature, and the signal count rate about equal to the dark count rate. The room temperature H d for this P M T a t 1200 V and the optimum discriminator setting was about 160 counts per second. An equivalent plot obtained at -23.0 "C appears very similar. Figure 5 shows the temperature dependence of the SNR obtained for the RCA 4832 PMT. These data were obtained using the Ne 640.22-nm line, a measurement time of 50 s, the P M T voltage at 1200 V, and the optimum discriminator level setting. The increase in SNR with cooling for this P M T was approximately a factor of 4. When this P M T was compared to the 1P28A, it produced a better SNR in all spectral regions
20
IO
0
-10
-20
-30
TEMPERATURE PCl
Temperature dependence of the signal-to-noise ratios of the RCA 4823 and the Hamamatsu 13406 PMTs. The SNRs of the R406 were multiplied by a factor of 2 before plotting Figure 5.
tested. This was especially true for longer wavelengths and for operation at cold temperatures. The reasons for the better performance are the lower dark current and the fact that the sensitivity did not appear to be altered greatly with temperature. The fourth type of P M T tested was a Hamamatsu R406. A plot of the SNR as a function of the discriminator setting and P M T voltage shows all the same features and trends shown by the other PMTs except the SNR produced under similar conditions was much smaller. The sensitivity of this P M T is very low and Rd a t room temperature is very large. A t the optimum discriminator setting and a P M T voltage of 1000 V Rdwas approximately 18500 s-l. The high dark count rate is due to the low work function of the S-1 photocathode. The SNR as a function of temperature for the R406 P M T is shown in Figure 5 . These data were obtained using the Ne 640.22-nm line, a measurement time of 100 s, the PMT voltage at 1200 V, and the optimum discriminator level setting. The SNRs were multiplied by a factor of 2 before plotting. The increase in SNR, with cooling, for this P M T was a factor of 4.
CONCLUSIONS We have presented a straightforward method for the determination of optimum system parameters in a photon counting experiment. The data presented here suggest that each experiment may require different optimum operating conditions. The conditions under which the data contained
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 12, OCTOBER 1979
in this paper were obtained were very low light levels, for those are the conditions for which photon counting has the most advantages. We performed identical experiments using much higher light levels and found the trends in the data to be the same as in the data presented here. The relative changes in the SNR were, however, smaller due to the much higher SNR to begin with. The specific PMTs tested here may not be optimum for use as photon counting detectors (16), but they are very commonly used PMTs. However, the data presented do seem to be generally representative of all P M T types. Each P M T tested showed optimum performance when used with a high operating voltage. Although each investigator should determine the best conditions for his experiments, it is safe to assume that operation of the P M T used a t or near the highest safe voltage will produce the best results. The effects of temperature on the SNR produced seem to be very much dependent on the specific PMT type used. This is in a large part due to relative changes in the cathode sensitivity with temperature. For a given PMT these changes can be wavelength dependent, especially when close to the long wavelength cutoff for the P M T (20). In general the increase in SNR obtained when the P M T is cooled is small, and may not be worth the additional expense, especially if the measurement system is very stable and long count times can be used. Also, there is a lower temperature limit after
which additional cooling no longer results in any increase in the SNR. For the PMTs tested here, only the R406 would have benefitted significantly from temperatures lower than the -23 "C reached by the thermoelectrically cooled P M T housing used here.
LITERATURE CITED Ingle, J. D.. Jr.; Crouch, S. R . Anal. Cbem. 1972, 44, 785-94. Murphy, M. K.; Clyburn. S.A.; Veilbn, C. Anal. Chem. 1973, 45,1468-73. Tull, R . G. Appl. Opt. 1968. 7 , 2023-29. Jones, R.; Oliver, C. J.; Pike, E. R. Appl. Opt. 1971, 10, 1673-80. Amoss, J.; Davidson, F. Appl. Opt. 1972, 7 1 , 1793-1800. Nakamura, J. K.; Schwarz, S. E. App. Opt. 1968, 7 , 1073-78. Enke, C. G. Anal. Cbem. 1971, 43(1), 69A-80A. Darland, E. J.; Leroi, G. E.; Enke, C. G. Anal. Cbem. 1979, 51, 240-45. Young, A. T. App. Opt. 1963, 2, 51-60. Morton, G. A. Appl. Opt. 1988, 7 , 1-10, Oliver, C. G.; Pike, E. R . J . Pbys. D . 1968, 1 , 1459-68. Gadsden, M. App. Opt. 1965, 4 , 1446-52. Rodman, J. P.; Smith, H. J. App. Opt. 1963, 2, 181-86. Niemczyk, T. M.; Ettinger, D. G. ADD/. Spectrosc. 1978, 32, 450-53. Fried, D. L. Appl. Opt. 1965, 4, 79-80: Footd, R.; Jones, R.; Oliver, C. J.; Pike, E. R. Appl. Opt. 1969, 8 , 1975-89. Ingle, J. D., Jr.; Crouch, S. R . Anal. Cbem. 1972, 44, 777-84. Ozolins, A.; Lineberger. W. C.; Niles, F. E. Rev. Sci. Instrum. 1968, 39, 1039-43. Boileau, A. R.; Miller, F. D. Appl. Opt. 1967, 6 , 1179-82. Martin, H. "Electro-Optical Systems Design" 1976, 8, 16-20
RECEIVED for review April 23, 1979. Accepted July 26, 1979. The authors are pleased to acknowledge the support of the University of New Mexico Research Allocations Committee.
Trace Element Characterization of the NBS Urban Particulate Matter Standard Reference Material by Instrumental Neutron Activation Analysis Robert R. Greenberg Center for Analytical Chemistry, National Bureau of Standards, Washington, D.C. 20234
The Urban Particulate Matter, SRM 1648, recently prepared by the National Bureau of Standards, with partial support from the Environmental Protection Agency, has been analyzed by instrumental neutron activation analysis (INAA) for 32 elements. Special attention has been given to reducing and evaluating the analytical errors. SRM 1632, Trace Elements in Coal, was also analyzed and the results were compared with literature and NBS certified values.
Well characterized reference materials have proved to be useful aids in verifying the accuracy of analytical procedures. Many analytical techniques suffer from problems due to chemical blank, interferences, losses during sample dissolution, incomplete sample dissolution, etc. Additional confidence in an analysis can be obtained if, by using the same procedures, the correct concentrations are found in a similar reference material. Among the most useful of the reference materials have been the National Bureau of Standards Standard Reference Materials (SRMs), because of the high degree of accuracy usually associated with the NBS certified concentrations. For an element to be certified, its concentration is usually determined by two or more independent analytical This article not subject to U S Copyright
techniques, or by a definitive method ( 1 ) . The National Bureau of Standards cannot certify the concentration of every element in an SRM. However, the utility of many SRMs could be greatly increased if the concentration of additional elements were known. Perhaps one of the most widely referenced, recent papers in the field of analytical chemistry has been one by Ondov et al. ( 2 ) in which the concentrations of approximately 40 elements were determined in SRMs 1632 and 1633 (Trace Elements in Coal and Trace Elements in Coal Fly Ash). Another area in which knowledge of the concentrations of a large number of elements is particularly important is the study of atmospheric particulate matter. Attempts to resolve urban aerosols into their component sources frequently require that the concentrations of many elements be determined (3, 4).
The National Bureau of Standards, with partial support from the U.S. Environmental Protection Agency, has recently prepared an Urban Particulate Matter SRM from natural urban atmospheric particulate material which was collected in the St. Louis (Mo.) region. This SRM should be very useful to the many researchers analyzing atmospheric particulate material, or other material of a similar nature. The concentrations of nine elements have been certified by NBS. T o
Published 1979 by the American Chemical Society
