min, and add 1 cc of a 10-lM F e S 0 4 solution. After 5 min more of nitrogen bubbling, measure at 304 mp the Fe(II1) ions formed in the reaction of Fe(I1) with the remaining Ce(1V) ions and the S20e2-ions present in the sample. After correction for the Ce4+ Fe2f reaction, this measurement gives the peroxydisulfate concentration in the sample. Measure the total oxidizing power in another 5-cc aliquot by adding 1 cc of a 10-IM F e S 0 4 solution. There is no need for N2 bubbling. The peroxymonosulfuric acid concentration is obtained by difference between the T.O.P. and the sum [H202] [H&05]. In the more acidic solutions, [HZS04] 5M, it is con-
+
+
venient to dilute the sample with water to minimize the hydrolysis of the peroxyacids (avoid an overheating of the solution). ACKNOWLEDGMENT
We are indebted to L. Santos for his advice concerning some valuable preliminary experiments and to M. Coimbra whose skillful technical assistance and understanding of the problems involved in the experimental side of this study have greatly contributed to the achievement of this work. RECEIVED for review March 4, 1968.
Accepted May 21, 1968
A Precision Photometer Using Milliwatt Light Sources and Photon Counting Edward H. Piepmeier, Donald E. Braun,' and Roxie R. Rhodes Department of Chemistry, Oregon State University, Corvallis, Ore. 97331
A precision photometer with digital readout has been built using milliwatt light sources and a pulsedetection system that counts single photoelectron events. The system can be used over more than two orders of magnitude of radiant power before pulse overlap becomes significant. Because the detection system primarily depends upon counting photoelectron pulses rather than upon pulse amplitudes or their integrals, neither the voltage applied to the photomultiplier nor the pulse amplifier gain need be highly stable to achieve precise results. Two colorimetric systems were studied and the results shown to agree with Beer's law.
THEADVANTAGES of a photometer that uses a pulse detection system with digital readout have been discussed by Ross (1). He originally introduced the pulse counting concept in precision photometric analysis by using a radioisotopic light source and a pulse height discrimination detection system. His particular technique takes advantage of the negative exponential distribution of pulse heights observed when the multiphoton pulses from a beta-activated scintillator are detected by a photomultiplier tube. An important characteristic of this system is the very stable light source. However, because the system depends upon distinguishing pulse heights, precise results require that the photomultiplier dynode multiplication system, amplifier, discriminators, and counting intervals be stable. Although common light sources are usually thought of as emitting energy continuously, they are sources of discrete photons. When light from these sources is measured with a detector such as a photomultiplier, the photons are converted to current pulses which may not be completely resolved in time from each other. Usually these pulses are smoothed to what appears to be a continuous or continuously varying signal and recorded by a readout device such as a meter or servo recorder. However, the number of photons per unit time reaching the detector can be decreased to a point where they are resolved from each other. This can be done by del Present address, Department of Chemistry, Pacific College, Fresno, Calif. 93702
(1)
H.H. Ross, ANAL.CHEM., 38,414 (1966).
creasing the intensity of the light source, by isolating a wavelength region of interest with a filter or monochromator, and by stopping down the optical aperture of the light beam. If the photon pulses are also resolvable from the noise pulses so that the noise can be subtracted from the total counting rate to give the photon counting rate, or if the noise is sufficiently low, then a practical detection system can result by counting pulses. This type of system, ideally depending only upon pulse counting rate, and being independent of pulse height, has a number of important advantages over the system used by Ross, or the more common techniques which provide a smoothed current or voltage proportional to the radiant power falling upon a detector. For instance, if individual photons of a chosen wavelength were counted, the counting rate rather than the integral of the pulse heights would be a direct measure of the radiant power reaching the detector, and would be relatively independent of variations that might occur in pulse heights. Therefore, a highly stable detection system would not require that the pulse amplifiers, pulse-height discriminators, and power supplies be highly stable. The stability of the detection system would be primarily dependent upon the stability of the counting time intervals. The stability of a photon counting detection system that used a photomultiplier as the detector would also be dependent upon the stability of the quantum efficiency of the photocathode (2) and the collection efficiency of the dynodes, which can be made to be only a moderate function of the applied voltage (3). Engstrom and Weaver (3) have discussed the ability of a photomultiplier to provide pulse counting rates that are relatively independent of the applied photomultiplier voltage. The stability of a single beam photometer that uses a photon pulse detection system would be primarily dependent upon the stability of the light source, the stability of the efficiency of the optical system, and the stability of the counting time intervals. The research presented here shows in detail how a low power tungsten bulb or hollow cathode tube can be used (2) J. R. Prescott and P. S. Takhar, IRE Trans. Nucl. Sei., NS-9, 36 (1962). (3) R. W. Engstrom and J. L. Weaver, Nucleonics, 17 (2), 70 (1959). VOL 40, NO. 1 1 , SEPTEMBER 1968
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with a photomultiplier pulse detection system to count single photelectron events over several orders of magnitude of radiant power. The resulting digital readout photometer retains the essential advantages of the Ross system while having unique additional advantages of its own. EXPERIMENTAL
Light Sources. A neon-filled calcium hollow-cathode light source (Westinghouse No. 22610) was powered by a Heath EUW-15 regulated power supply in series with five IOOK 1/2-wattmetal-film ballast resistors having temperature coefficients of less than 100 ppm/"C. To keep the intensity to a minimum the source was run at 0.55 mA, corresponding to a power dissipation by the light source of 5 5 milliwatts. A 421-mp interference filter having an 11-mp bandpass together with a broad band filter that nominally cut off above 400 mp isolated a narrow band of neon lines between 331 and 360 mp, A 14-mA, 10-volt tungsten bulb (No. 1869) was operated at 11 mA and 7 volts by using a 1K metal-film resistor in series with the 18-volt regulated supply used t o power the amplifier. The tungsten bulb operating at 7 0 z of rated voltage has a life expectancy according to the manufacturer of over 10 years, making its lifetime comparable t o that of the radioisotopic light source used by Ross ( I ) . The same optical filters mentioned above were used and isolated a spectral band which peaked near 390 mp. Sample-Detector Unit. A housing was fabricated from two 3-inch X 4-inch X 5-inch aluminum utility boxes to hold the filters, the tungsten light source, a sample cell consisting of a 14-mm i.d. test tube with water jacket, a n HTVR212 photomultiplier tube, a shutter, and a transistor linear pulse amplifier. Accommodation was also made for a standard 1-cm spectrophotometer sample cell. The inside of the unit was sprayed black and great care was used t o make all joints light-tight because of the very low light levels used. The tungsten light source was located about 2 cm behind the sample cell, which was about 2 cm from the photomultiplier. A shutter was located in front of the photomultiplier. When the hollow cathode source was used, the tungsten light source was removed and a 6-mm by 0.1-mm slit was located in the wall of the unit on the optical axis t o reduce the radiant power. The hollow cathode tube was located outside the unit. A black cloth was draped around the unit t o eliminate room light. Detection System. The dynode voltage divider consisted of 470K resistors stiffened with 0.1- and 0.01-pF capacitors. The relatively small average anode currents allowed the use of the large value of resistance to minimize power consumption. This is highly desirable for a unit that could eventually become portable. The anode pulses of the photomultiplier were capacitively coupled t o a three-stage amplifier built with circuits similar to those suggested by Emmer (4). The schematic of the complete system is available from the authors upon request. The gain of the amplifier system is 1600. The observed rise time of a typical pulse is less than 0.05 psec. The fall timecan be controlled independently of the rise time and was in this case less than 0.3 psec. An integrated circuit, pA-710 differential comparator with a 40-nsec response time, was used as a pulse height discriminator to eliminate pulses with heights lower than a preselected value. A IO-turn potentiometer provided a precise voltage level control to vary the discrimination level. The voltage transfer characteristic of this unit provides a discrimination resolution of better than 2 mV. The discriminator was calibrated with a pulse generator and was found to be linear within the 1 accuracy of the calibrating unit. Performance did not deteriorate for pulses as short as 100-nsec duration. Following the comparator, a monostable multivibrator built -~
(4) T.L.Emmer, IRE Trcrrzs. Nitel. Sei., NS-8, 140 (1961). 1668
ANALYTICAL CHEMISTRY
from a pL-914 dual NOR gate gave each pulse a I-psec duration. This was necessary to eliminate regeneration pulses (3) and cable ringing for very large pulses. Two decade counting units similar t o one described by Math (5) using inexpensive pL-923 and pL-914 integrated circuits followed the monostable multivibrator t o divide the pulse frequency by exactly 10 or 100 so that the readout would not overspill on the face of the 5-decade readout counter when high counting rates were used. The counting unit also increased the maximum counting rate of the readout counter from 100 kHz to 10 MHz. A crystal-controlled Hewlett-Packard Model 521C counter with a Model 562A digital recorder was used for readout. The total counts per unit time obtained with the single discriminator are proportional t o the integral of the pulseheight distribution curve between the limits of the discrimination level and infinity. The pulse height distribution curves were calculated from the integral data by taking the differences between the total counts observed during 10-sec intervals (or multiples thereof) for two adjacent pulse height levels 0.125 V apart, and plotting this value at the average of the two pulse heights. This technique compared favorably with data obtained from an ordinary single channel analyzer using a 0.05-V window t o obtain the pulse height distribution data directly. RESULTS AND DISCUSSION
Before the photometer could be used to obtain transmittance measurements, it was first necessary to ensure that the photometer was counting pulses that were only due to singlephoton events. Assume for instance a hypothetical case in which the light source emitted only 2-photon pulses. Assume also that the photocathode efficiency was one, so that single photon pulses were observed, and that the observed pulse height was proportional to the number of photons in a pulse of light. If now a sample solution with a transmittance of 0.75 were placed between the light source and the detector, 2 5 x of the photons would be absorbed. The particular photons to be absorbed would be selected in some random fashion so that some of the 2-photon pulses would be completely absorbed, some would pass through the solution unattenuated, and other pulses would lose one photon, retain the other, and still be counted. Because some of the absorbed photons allow single-photon pulses to reach the detector to be counted, fewer than 25 of the original photons cause a loss of counts. The counting rate is therefore decreased by something less than 25z and is not a direct measure of the total number of photons per unit time reaching the detector. In an extreme case where each absorbed photon resulted in a single-photon pulse, there would be no loss in pulses and n o change in counting rate would occur even though 25 of the original photons were absorbed. On the other hand, in the case where each pulse is originally due to only one photon, the loss of each photon results in the loss of a pulse and thence loss of a count. In this case the counting rate is directly proportional to the photon rate, and can be used directly to obtain transmittance values. Notice in the latter case that a change in photon rate does not change the distribution of the pulse heights, for all pulses have heights equivalent to one photon. However, in the 2-photon pulse case when an absorber is present, the distribution of pulse heights changes from one where all the pulses have heights equivalent to two photons to a distribution having pulses with heights equivalent to one photon as well as pulses with heights equivalent to two photons. Therefore, by studying the pulse height distribution curve, one can de-
z
(5) I. Math, Electrorfics, 40 (7), 99 (1967).
PULSE
HEIGHT, VOLTS
Figure 1. Pulse height distribution curves at constant photomultiplier voltage of 750 V A. B. C, E.
Hollow cathode source Tungsten bulb source D. Hollow cathode source with absorber present Dark counting rate
termine whether or not the pulses are due to single photon o r multiphoton events. To obtain pulse height distribution curves, and for the photometric measurements, each light source was adjusted until the counting rate was such that there was negligible overlapping of the successive pulses from the amplifier as observed with a Tektronix 555 oscilloscope. Such counting rates were on the order of 50,000 counts per second or less. The dark counting rate was on the order of 1 % of the total counting rate. Pulse height distribution curves for both light sources are shown in Figure 1. The curves are similar in shape but not identical. The minor variations are attributed to the fact that the hollow cathode illuminated a 1-mm slit region in the center of the photocathode, whereas the tungsten bulb illuminated most of the photocathode. Similar changes in shapes of the curves resulted when various regions of the photocathode were optically masked. The shape of the curve is therefore to some extent dependent upon the region of the photocathode that is illuminated. This effect has been studied in more detail by Prescott and Takhar (2). Because of the statistical nature of the multiplication processes occurring within a photomultiplier (2), anode pulses that are due to single photoelectron events have a wide range of pulse heights, such as those shown in Figure 1. When pulse height distribution curves are plotted with a logarithmic ordinate as in Figure 1, a downward shift of the curve along the ordinate occurs without a change in shape when the frequency or probability of occurrence of pulses of each
height is decreased by the same factor. A downward shift of this type would occur, for instance, if an absorber were placed in the path of a beam of single-photon pulses assuming a constant quantum efficiency. On the other hand, a horizontal shift or change in shape of the curve with or without a vertical shift indicates a significant change in the distribution of the pulse heights and therefore a change in the statistics of the processes causing the distribution. As indicated in the hypothetical example above, placing a n absorber in the path of multiphoton pulses causes this type of change. A case where more than one photoelectron reaches the first dynode during each pulse has been studied by Prescott and Takhar ( 2 ) , who derived a statistical model for their observed distribution curves. Their model was based on a light source that emitted many photons during each pulse, the number of photons per pulse being Poisson distributed. Their model also assumed binomial transfer of the photons to produce photoelectrons that reach the first dynode, and a negative exponential electron multiplication process. For pulses caused by an average of more than two photoelectrons reaching the first dynode their distribution curves were peaked, and were similar to those in Figure 1. When they inserted light absorbers or changed the intensity of the source, their curves changed shape and shifted along the absissa, because the average number of photoelectrons per pulse was changed. Figure 1 shows how our photomultiplier anode pulse height distribution curves shift only vertically with no significant change in shape when a light absorber is placed between the light source and the photomultiplier. Turning the light source down in intensity gives the same result. This vertical shift with little change in shape of the curve was observed over two orders of magnitude of radiant power. This suggests that not more than one photoelectron reaches the first dynode during each observed pulse and that the distribution of pulse heights observed at the anode is controlled by the multiplication processes occurring within the photomultiplier, rather than by multiphoton emissions from the light source. The fact that our curves peak for a single photoelectron per pulse reaching the first dynode and that corresponding curves of Prescott and Takhar (2) are amodal can be reconciled by assuming that the multiplication processes of the two tubes are different. The effect of the voltage applied to the photomultiplier dynode chain on the pulse height distribution curve shape was also studied. Increasing the voltage caused the dynode chain multiplication factor t o increase and the peak of the distribution curve shifts to higher pulse heights and is lowered. This further indicates that the shape of the curve is caused by the electron multiplication processes rather than by the characteristics of the light sources. Considering the results of Prescott and Takhar (2) and the fact that when the photon rate is changed in our system the shape of the curves does not change and the peak does not shift along the abscissa, it can be concluded that the average number of photoelectrons per pulse does not change with photon rate, and that therefore the counting rate is proportional to photon rate. Further support for this conclusion is obtained from the following results. The acidic dichromate system was chosen because of its absorption peak near 350 mp and because it was found to be sufficiently stable. Figure 2 is a plot of absorbance cs. concentration of chromium in an acidic dichromate solution using both light sources. Absorbance, A , was calculated by A
=
log
YO
-
rc
VOL. 40, NO. 11, SEPTEMBER 1968
1669
4
0*4 I
1
I
I
I
1
I
4a0
3
w *
0 2
a m a
2 m 4 1
0 0 CHROMIUM, pg/rnl
Figure 2. Calibration curves for chromium
1
I
IO PPM I2
I
20
30
IN KI
Figure 3. Calibration curve for tri-iodide with hollow cathode source
A . Using hollow cathode source B. Using tungsten bulb source
where ro is the total counts per unit time for the blank and rc is the total counts per unit time for each sample solution. Both were corrected for dark counting rate. The counting interval was 10 seconds. The runs were made in the round cell with an effective path length of 1.40 cm. The hollow cathode source with filters provided a series of lines between 331 and 360 mp in the region of the absorptivity peak. The calibration curve was linear up to 50 pg/ml chromium and then curved toward the concentration axis. The curvature took place in a high absorbance region and was most likely due to the presence of stray light that was passed by the filters in wavelength regions of lower absorptivity than that in the region of interest. The tungsten bulb with filters provided a rather broad emission peak that stood on the shoulder of the absorbance peak. The slope of the calibration curve using this light source was therefore less than the hollow cathode calibration curve and was considerably curved as would be expected. Again stray light passed by the filters could also be a significant factor especially because of the broad continuum which must be filtered. The ratio of the initial slopes of the two calibration curves to each other were the same as would be expected from the ratios of the absorbances of the sample measured with a Beckman D B spectrophotometer in the wavelength regions of the light emitted from the three sources. A precise comparison of the absorbance measurements of the photometer with the Beckman DB spectrophotometer was not possible because of the rather broad spectral bandpass of the photometer. The absorbance of a dichromate solution obtained with a 1-cm cell in the photometer with the hollow cathode source corresponded 1670
0
ANALYTICAL CHEMISTRY
to the absorbance at 340 mp obtained with the spectrophotometer. This was within the 331 mp to 360 mp spectral bandpass of the photometer. These results indicate that the counting rate is directly proportional to the photon rate and provide further evidence that the observed pulses are due to single photoelectrons reaching the first dynode. The values of r, for the above runs were 240,800 for the hollow cathode and 89,120 for the tungsten bulb, with a dark count of 1360 for 10-sec counting intervals. Counting rates of up to about 300,000 cps have been used but the resulting overlap of successive pulses caused the slope of the calibration curves to be less than those in Figure 2 and to be highly dependent upon discriminator level. A calibration curve for iodine in 6 % KI is shown in Figure 3. The hollow cathode tube with the above filters was used as the light source. The value of r, was 220,800 with a dark count of 300 for 10-sec counting intervals. The curve is linear up to an absorbance of 1.5 and then deviates from Beer's law in a negative direction as did the dichromate calibration curve. The stability of this photometer over a I-hour period using the hollow cathode 'lamp is of the same magnitude as the expected counting error. For instance, for a series of ten 100-sec runs evenly spaced over 1 hour the calculated standard deviation was 2700 counts or 0.07% of the 4,128,200 counts average of the 10 counting periods. By using the square root of the total to estimate the standard deviation, a counting error of 2032 counts is expected. Because of the long counting times required to obtain sufficient statistical data, no attempt was made to match the 0.005% stability of the Ross system reported in a private communication (6). The tungsten bulb drifted 2.5% over a 2-hour pe( 6 ) H. H. Ross, personal communication, 1968.
,
700
"600
800
900
1000"
W L I E D PHOTOMULTIPLIER VOLTAGE, V
Figure 4. Effects of discriminator level and photomultiplier voltage on the signal and dark counting rates Signal counting rate at 0.1 V Signal counting rate at 0.2 V Signal counting rate at 0.3 V D. Signal counting rate at 0.4 V E. Dark counting rate at 0.1 V F. Dark counting rate at 0.2 V G. Dark counting rate at 0.3 V H. Dark counting rate at 0.4 V A. B. C.
riod. However, the calculated standard deviation of ten 10sec runs over a 5-minute period was only 0.3 %. Ross ( I ) has discussed in detail the counting errors associated with a photometric system such as this one where the pulses occur randomly in time. The primary advantage of this detection system compared to the one used by Ross ( I ) is its minimal dependence on drift in the electronics. This is basically due to the fact that our system must only determine whether or not a pulse is present, whereas the system used by Ross must precisely amplify a pulse and determine whether it is above or below a certain height. The effects of changes in discriminator level and photomultiplier voltage on the signal counting rate for a fixed radiant power level and dark counting rate are shown in Figure 4. As the photomultiplier voltage is increased, a slowly rising plateau is reached where changes in photomultiplier voltage cause only smaller relative changes in the observed counting rate. Similar plateaus have been reported and discussed in detail by Engstrom and Weaver (3). At 850 V and a discriminator level of 0.25 V a 1 change in photomultiplier voltage results only in a 0.65% change in counting rate. When the same photomultiplier tube was used in a conventional anode current measuring system (7) a 1 change in photomultiplier voltage caused a 6.8z change in readout at a wavelength of 360 mp. A similarly large change would be expected to occur if this tube were used in a system similar to the one used by Ross ( I ) . At this same operating point a 1% change in discriminator level causes only a 0.15 change in counting rate. If a change in discriminator level is assumed to have approximately the
z
z
(7) H. V. Malrnstadt, R. M. Barnes, and P. A. Rodriguez, J . Chern. Educ., 41, 236 (1964).
same effect as a change in amplifier gain, then it is apparent that the amplifier gain need not be highly stable for precise results to be obtained. As suggested by Engstrom and Weaver (3)the best operating point would be at the starting end of the plateau because the dark counting rate is lowest in that region and increases exponentially with increase in photomultiplier voltage. An additional factor that must be considered for this system is that increasing the discriminator level not only decreases the dark current counting rate, but also causes the start of the plateau to shift to higher photomultiplier voltages, resulting in relatively larger changes in signal counting rate for a given change in photomultiplier voltage. A compromise is of course necessary. For the light levels used in this work the dark counting rate was about 1% of the total counting rate and the choice of operating point was not critical. Two somewhat arbitrarily chosen operating points were selected from the curves in Figure 4: 850 V and 0.25 V for the iodine curve, and 770 V and 0.3 V for the dichromate curve. At 850 V and 0.25 V a 1% change in photomultiplier voltage causes a 7 . 2 z change in dark counting rate and a 1 % change in discriminator level causes a 1.7 change in dark counting rate. The effect of these changes on the total counting rate will depend upon the light level used, but at the higher light levels used in this work would amount only to a few tenths of a per cent change. The stability of a single beam photometer is directly dependent upon the stability of the light source. The highly stable radioisotopic light source used by Ross ( I ) is the primary advantage of his system over ours. Such a light source cannot be used in this system unless multiphoton pulses can be eliminated. Although the hollow cathode source in this instrument was powered by a stable but inefficient power supply, the availability of regulated high voltage power supplies with efficiencies of about 5 0 2 (see for instance the 9589 series made by Transformer Electronics Co., Boulder, Colo.) makes the total power required by the light source system less than 1 W. This is comparable to the power consumption of 900 mW required by the photomultiplier, amplifier, and discriminator system, It would be best to eliminate the influence of variations in light source intensity by using a double-beam system. A stable double-beam photometer could be made by monitoring a reference beam from the light source with a second pulse detection system or by using the same detection system alternately to observe rapidly the reference and sample beams. The pulse counts from the reference beam would be used to control the counting interval for the sample beam. By means of common electronic counting and switching circuits, the reference beam system would allow the sample beam counting system to count pulses until the reference beam system had accumulated a predetermined number of counts. This would eliminate the need for a stable light source and precise counting intervals. The ratio of the beam intensities or the predetermined number of counts accumulated by the reference beam system could be adjusted until the sample beam system read, for instance, 100,000 counts when a sample blank was inserted. The number of counts for the sample beam would then be numerically equal to transmittance and a direct digital readout of transmittance would occur.
z
RECEIVED for review April 5, 1968. Accepted June 6, 1968. This work was supported in part by the National Science Foundation Research Participation for College Teachers Program.
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