Photon counting for spectrophotometry

IN8 T R UMENTAT IO N

Advisory Panel Jonathan W. A m y Richard A. Durst G. Phillip Hicks

Donald R. Johnson Charles E. Klopfenstein Marvin Margoshes

Harry L. Pardue Howard J. Sloane Ralph E. Thiers

Photon Counting for Spectrophotometry HOWARD V. MALMSTADT, MICHAEL L. FRANKLIN,] and GARY HORLICK2 School

of Chemical Sciences, University of Illinois, Urbana, IL 61801

Advantages over other light-measurement systems provided by the photon-counting - method include direct digital processing of the inherently discrete spectral information, decrease of effective “dark current,” improvement of signal-to-noise ratio, sensitivity t o very low light levels, accurate long-term signal integration, improved precision of analytical results for a given measurement time, and less sensitivity t o voltage and temperature changes tens of thousands of T research and ofroutine sgectrophotomHE: QUALITY

eters depends directly on the operating characteristics of photomultiplier ( P l I ) tubes and their associated electronic readout, and power supply circuits. The various types of instruments in which P l I tubes are utilized indicate something about their importance. The PlI tube is now foiind in essentially all of the commonly iised molecular uvvisible absorption, fluorescence. phosphorescence, reflectance, laser-Raman, atomic ahsorption. atomic emission, and atomic fluorescence spectrometers and a150 in specialized rapid scan, submicrosecond time-resolved, T-jump. chromatogram scanning. multichannel sparksource direct readers, densitometers, and other types of instruments ( 1 ) . I n nearly all instruments it, has been standard practice to measure the output signal of the P l I tube by using analog techniques. That is, the tube is operated under conditions and with measuring circuits eo that an output, current or voltage is obtained whose m’agnitude is directly proport.iona1 to the radiant power incident, on the photocathode. This has proved to be a generally acceptable modr. of operation. Prcsent address, Medical School, Uniy s i t v of Colorado. Denver, CO 80210. - Present address. Dr2nartmmt of Chemistry. L-nivcrsity of ‘Alberta, Edmonton 7 . =1LT,Canada.

However, it has become increasing11 apparent that in some spectrophotometers the output signal of the PA1 tube can be ndvantageously measured by using direct digital techniques I n the digital mode the PA1 tube and associated circuitry provide discrete electron piilses so that the number of counted pulses is directly proportional to the number of photons incident on the photocathode This approach is commonlv called “photon counting ” Compared to other Iight-measurement PT stems, the apparent advantages ( 2 ) provided directly or indirectly b y the photon-counting method are direct digital procewng of the inherently discrete qpectral information, decrease of effectir e “dark current improvement of signal-to-noise ratio, sensitiwtv to very low light levels accurate longterm signal integration, improved precision of anal>tical results for a g n e n measurement time, and less sensitivitl t o 1 oltaqe and temperature changes The basic and practical characteristics are presented to illustrate that photon counting can be made xidell applicable for man\- types of spectrophotometry including absorption, fluorescence, emission and scattering methods &o, some of the difficultieq are considered Even in those caqes where the PA1 tube is used as an analog detector the photon-counting concepts can be uscd for the analvsi. of its performance, :ind these can be xer] useful 3”

several applications of photon count,ing will be illustrated, including considerations for high-precision spectrophotometry.

PM TUBE AS DIGITAL OR ANALOG TRANSDUCER

The intensity of a light signal falling on the PlI tube is directly dependent on the rate at which photons arrive a t the photocathode ( P h ) This rate fluctuates as a result of radiation noise (photon noise) inherent in the incoming light, and the fluctuation is, in general, random ( 3 ) . When photons of a specific wavelength arrive at the photocathode, they eject photoelectrons with an efficiency that depends on the quantum efficiency, Qx, of the photocathode surface (4, 5 ) The photoelectrons from the cathode are attracted to the first dynode by electrostatic focusing Honever, not all of the photoelectrons reach the first dynode and this collection efficiencv, f, ih typically about 75% There is a high probabilitv that each photoelectron that reaches the first dynode will elect several secondary electrons (51 The transfer efficiency, g, of electron bursts between djnodes is almost so that the number of anode pulses is nearly equal to the number of photoelectrons reaching the first dynode, assuming negligible dark pulses The number of electrons in each anode pulse depends greatly on the PI1 voltage, but the number is typically 105 t o 107 electrons per pulse Even a t constant PI1 T oltage, the statistical nature of secondary emission from the dvnodes introduces an amplitude fluctuation of the anode pulses If it is assumed that there is negligihle pileup of anode pulses, i e , nearly all anode pulses are resolved, then the number of anode pulses per second, N , , can be written

N , = g.fQxPi, (1) The counting of the anode pulses, which are directly related to the num-

ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, J U L Y 1972

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ber of photons incident on the cathode, provides the measurement technique appropriately called “photon counting.” Although the output at the anode of the P1I tube is inherently a series of pulses. the output signal can be expressed as an average rate of flow of electrons per second or current, as summarized in Equation 2 .

coulombs (electron)

coulonibs =

7(2)

For example, if the number of anode pulses’sec, So equaIs lo6, and the a\ erage electrons/anode pulse, G, equals lo6, then

N,Ge

1.6

x

10-’A

(3) However, this is an average current, and it is apparent from Equation 2 that the output current fluctuates as -Vc and G fluctuate That is, the random-time behaxior of the anode pulses ab a result of the incident radiation, and t h e amplitude distribution caused bv secondarv electron emission cause the so-called “shot noise” on the P1I analog signal By use of suitable electronic filters the fluctuations are averaged or integrated so that the alerage current can be observed Because an average current can he related to the number of pulses in unit time, it is f(A) =

64 A

=

frequently convenient to determine the noise component of an analog P1I signal by utilizing count statistics. PHOTON -COUNTI NG SYSTEMS

The required equipment used to implement phot.on counting in spectrophotometry is illustrated in Figure 1. The photomultiplier tube is enclosed in a compartment that) must, be perfectly light tight, and it. is powered by n regulated high-voltage ( H Y ) poxver supply. The output signal current pulses are coupled through a resistivecapacitive load or pulse transformer into a pulse amplifier. A11 pulses ivithin a preset discriminator voltage range are counted by the digital counter during an accurate preset time interval. The total count per integration period is read from the digital counter or printer. I n analog readout iq often made available to provide graphic monitoring. -4 digital-to-analog convert‘er converts the photon count; to a de voltage which is sent, to a chart recorder, Each of the blocks of Figure 1 is briefly considered so as to summarize the important characteristics. Photomultiplier Tube and Power Supply. Incoming photons eject pho-

toelectrons with a n efficiency that, depends on the quantum efficiency of the photocathode surface. Thii efficiency dependent on 1%-avelengt h: on8e characteristic is chosen that resu1t.s in high efficiency for the n-avelength of interest. ST’hen the P1I

ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972

is part of a spectrophotometer, the spectral characteristics of the source and monocliromator must also be t,aken into account. The overall response characteristics are determined by the convolution of the spectral response of the detector with the spectral out,put of the source and optical system. The gain, frequency response, and dark-count characteristics of the P l I tube are very important and are discussed in the next major section. The required operating voltages betn-een P1I tube electrodes are provided ’ across by connecting a chain of re sistors R stable HT’ power supply. The voltage drops across the resistors provide the voltage increments between suecessive electrodes ( 6 ) . The applied voltages influence the pulse-height distribution, but as the applied voltage is increased, a value is reached where changes in P11 voltage cause relatively little change in pulse height. Pulse Amplifier. A low-noise amplifier is required for photon counting because any noise induced by the amplifier increases the background count rate vhen the discriminator is set at a low level. The input of the amplifier should offer a minimum of shunt eapacitance to reduce pulse degradation. and great care milat be used in connecting from the anode of the PhI to the pulse-amplifier input ( 2 ) . .In ac-coupled amplifier is usually employed because it eliminates the de drift from the P1f. -41~0,reducing the

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low-frequency cutoff of the amplifier reduces a considerable amount of noise. Bandwidths from 10 KHz to 100 MHz are used in photon counting to reject the low-frequency noise but still provide adequate pulse fidelity. The gain from the pulse amplifier must be st.able so that the pulse-height shift, does not change the number of photon counts getting through the discriminator. Sharing the gain requirement between the P11 and the amplifier requires that the amplifier voltage gain be about 100-1000 for use ivith most P1I tubes. At high-count, rates the amplifier duty cycle becomes large, and a baseline shift owing to ac coupling results. This changes the number of pulses getting through the pulse-height discriminator. I t is often necessary to use a de level restorer to pro.iide a zero reference line. -1simple diode clamp circuit can be employed with good results in some cases at count rates not exceeding 100 KHz. Other methods can be used to reduce. the base-line shift with . increasing count rate. siich as the Robinson clamp, bipolar pulses. base-line shift compensation at the discriminator, or a de amplifier s!-stem. I n many instances using n fast ac amplifier and keeping the duty cycle low result in accept,able base-line shift n-ithout dc restoration. Pulse-Height

Discriminator.

A

pulse-height discriminator useful for photon counting must be stable and sensitive to small voltages so that, small signal pulses can be effectively counted; tlie frequency response must’ be high so that the upper count, rate is not limited at. this stage. Tunnel diode discriminators are available which operate at 50-mT: sensitivity and at greater than 100 NHz. Pulse-Pileup (Coincidence) Egects. Two effects are possible owing to pulse pileiip at a fixed discriminator level. Two pulses which should each be counted can pile up so that only one count, is recorded. 9 net, loss of one count results. Tu-o smaller pulses can pile up and sum t o produce a pulse large enough to be counted Tvhen neither pulse should have been counted: thus, n net excess of one count is recorded. The discriminator level determines the relative importance of these two effecta on the recorded count. At low discriminator levels v-lien a large fraction of the theoretical count is recorded, the major effect is the loss of pulses owing to pileup. Discsiminator-Lezlel Setting. Because of the count.ing statistics. the standard deviation of a measurement is determined by the square root of the number of counts. This means the more counts recorded for a given mea66A

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surement time, the bett.er the precision will be. The pulse-height discriminator level should, therefore, be set) to accept the largest fraction of the theoretical signal counts possible without. picking up a large amount of background pulses. By setting the discriminator level t o accept the largest, number of signal counts in a given observation time, both utilization of the frequency response of t.he system and less susceptibility to drift are realized. If the discriminator level is set so that only a small fraction of the theoretical count rate is admitted, a small drift, in discrimination level causes a large change in count rate because the signal count rate changes rapidly with discriminator voltage in this region. Digital Counter. Fortunatel:-, many new types of counters operate at rates of greater than 100 1 I H z so that this part of tlie system should not limit overall frequency response. Since the standard deviation is equal to the reciprocal of the square root of the number of events counted, the number of readout digits having significance can be estimated. Therefore, it is not necessary to provide readout of the total recorded events, but it is rather the scaled-down counts that are significant. Accurate Preset Timer. Crystal clocks provide precision and accuracy better than 1 part in 106 for a wide range of time bases from 1 p e e to 10 see or more. Integration times in photon-counting applications usually range from 0.1 to 10 sec or the duration of a specific event. Digital-to-Analog Converter. The same pulses from the output of the pulse-height discriminator which are counted can be fed simultaneously to a digital-to-analog con\-erter. This circuit shapes each input pulse so that each output pulse becomes equally weighted. The equally weighted pulses are then smoothed to provide a dc voltage out,put. A conventional diode pump circuit can be used after simple R C differentiation (6) to produce tlie analog output for locating trends in the counting data, such as peak-signal location during scanning. Chart Recorder. After the pulses are con\-erted t o a de voltage, the accuracy of the analog readout is determined by the reading accuracy and by the observation time. This integration time is determined by the time constant of tlie filter in the digital-to-analog converter. Chart recorders are iisually accurate to 0.5% of full scale ivith a reading error of about 02q. The 5ipnal pulse-height fluctuation has been removed, but the random-time clistribiition is still present. in the signal. I n many analog photometric meaairements. the major portion of the un-


wanted fluctuation results from the reading error and not from the fundamental “shot noise limit.” of the signal. S o t e that with digital readout of all the pulses, the reading error is eliminated, and wide dynamic mnge is available. Commercial Systems. Several companies offer instrumentation packages or modules rvhich can be used for photon counting a t rates in excess of 1 1IHz. Three of these systems are mentioned along with their specifications and special features. Solid %ate Radiations, Inc. (SSRI) offers a pulse-amplifier-discriminator combination with gain of 2400 and bandn-idth from 10 KHz to 100 NHz. The pulse-pair resolution specification is 10 nsec. -4 shielded P1I housing is also available along with de power supplie. for the P1I and amplifier. There is a separate module for each unit listed:

P l I housing and dynode chain P1I and amplifier power supplies Pulse amplifier Digital computing counter -1pprosimate total cost, $4700 The digital counter has several modes of operat.ion useful in photon counting. There are two separate registers so both the background and signal counts can be stored separately. Both background and signal counts can be integrated for equal preset periods in the synchronous mode. The background register can be subtracted from t.he signal register in still another mode of operation (7‘). Elscint Instruments manufactures a tem with PA1 and preamplifier power supplies, counter, and amplifier in one instrument, package. This system has upper and lower level discriminators; thus, an energy window can be set to eliminate large as well as small pulses. I n the synchronous mode the background pulses are subtracted from the signal plus background by an up-down counter. However, it is often desirable to knmv both the background and the signal rate for error analysis, not simply the difference. -4 novel feature is the utilization of the upper discriminator level to correct, for first-order pileup effects. Pulses esceeding the lower discriminator level are counted normally. ivhereas pulses esceeding the upper discriminator le\-el arc counted t,wice. This corrects for the c n e where two pulses add together to give a single pulse of tivice the amplitiide. The total amplification of the preamp and the amplifier is 300 with a puke-pair resolution of 12 niec. The modiiles necessary for photon counting are the following (8):

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67A

Low-level counter spectrometer

PlI housing Fast preamplifier -4pproximate total cost, S3300 Ortec offers n SI11 bin system which can be used for photon counting. The amplifier has a gam of 200 with a 4-nsec rise time. The signal 1s fed to a 100-MHz discriminator and on to a dual counter timer Both background and signal plus background counts can be stored The SI11 bin system offers some flexibility since it uses standardized plug-in modules -4dditional modules can be plugged in to provide a teletype data logging system. The basic modules necessary for photon counting are as follows (9) : SI11 bin and power supply HT-power supply PlI base Amplifier Dual counter timer with crystal time base Alpprowmatetotal cost, S3200 BASIC CONSIDERATIONS I N UTILIZING PHOTON COUNTING

’

The possibility of measuring low-intensity light with improred signal-tonoise ratio was one of the original reasons for interest, in photon counting and remains a major basic consideration for any discussion of the topic (10-16). Other basic considerations nhich influence the applicability of photon counting and vhich are considered in this section are dynamicrange or frequency-response considerations. dark count, and pulse-height distribution. Signal-to-Noise Ratio. The signalto-noise ratio of a photon-counting measurement may be considered from the point of view of counting statistics. The fundamental noise in a photontem is the fluctuation in the signal coiint as determined by the statistics of the photon arrival at the photocathode. I n general, the arrival of photons at the photocathode is random: thus, the probability of fluctuations about the rate of arriral is determined by taking the square root of the number of counts ( 1 7 ) . For the specific case of a Gaussian distribution, the reciprocal of the square root of the number of counts is equal to the standard deviation. On this basis the “signal-to noise ratio’’ for a single measurement can be estimated by dividing the count by the square root of the count, Many photon-counting measurements are made in situations such that unwanted background pulses are present. In these cases the background count must be subtracted from Ihe measured 68A

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background plus signal count. This makes the signal-to-noise ratio expression more complicated (10-13). The fluctuation in the signal count (noise) is calculated b y using the standard equation for the counting statistics of n difference. This equation can take the form:

F , = (R, 4- 2 Rg)li2T1” (4) where F , is the fluctuation in the signal count, R, is the signal count rate, RB is the background count rate, and T is the counting time. I n this case it is assumed that the counting time is the sime for the measurement of the background count and the signal plus background count. The signal is R,T; thus, the signal-to-noise ratio can be expressed as:

s_ -N

Rsl12Tl12 (1 2 RB/R,)”2

+

(5)

Equation 5 has tm-o limiting forms. If the background rate is small with respect to the signal count rate, the equation reduces to Rs1/2T1/2,the square root of total signal count. Thus, for a total count of 106 the signal-to-noise ratio is 1000. If the background count rate is large with respect to the signal count rate, Equation 5 becomes the following :

For n signal count rate of 2 cps and a background count rate of 100 cps, a signal-to-noise ratio of 4.5 can be achieved in 1000 see. The stability of most, photon-counting y s t e m s allows siich long coiinting times. The relative rates of the signal and background counts (and. hence. the signal-to-noise ratio) can, to some estent, be controlled by adjusting the pulse-height discriminator. Thus, it is important to consider briefly the prilse-height distributions of both background (dark) and signal pulses. Pulse-Height Distribution of Pulses. Current pulses which have been caused by incident photons and. hence, have undergone the full amplification of the P1I tube have a pulse-height distribution closely approsimated by a Poisson distribution ( 4 . 1 9 - Z I ) . The integral pulse-height spectra for s i p nal and dark pulses for n 1P28 photomiiltiplier tube are shown in Figiire ?. I n this case all counts above a certain diwiminator level were coiinted. S o t e that the pulse-height spectrum for tlip dark-current piilees i. not the same as that for the signal pulses. I t contains n larger number of smaller pulses than XI-onld be predicted on the basis of a Poisson distribiition. This can be es-


Figure 2. Integral pulse-height spectra of signal and dark pulses (2)

plained if the pulse components of the dark current are examined. Figure 2 should be considered specific to this tube. The specific shape can differ for different photomultiplier tubes and even for the same t.ube under different esperimental conditions (different dynode voltages) magnetic defocusing) . Dark Current. There are a number of soiirces of dark currents in a photomultiplier. Some of the more common soiirces are discussed by Lallemand ( 2 2 ) . Among these are thermionic emission. cold-field emission, radioactivity, arid ohmic leakage. The first three are pulsed in natiire. The pulses from thermionic emision and cold-field emission often originate don-n tlie dynode chain and, hence, do not undergo full amplification in the tube. These pulses give rise to the large: number of smaller pulses in the pulseheight spectrum of the dark current. I n addition, a dramatic increase in the count, rate at low discriminator levels is evident in the dark-current, pulseheight spectrum (Figure 2 ) . These pulses arise from stray electrical noise and amplifier-induced noise. Pulses originating from cosmic rays and radioactive potassium ( p particle emission) in the glass envelope of tlie tube shoiild result in a slightly elevated le\-el of higher pulses in t.he dark current than woiild be expected on the basis of a Poisson distribution. hiit these are generally negligible for practical spectrophotometry. Therefore, an upper dis-

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ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JUL" 1972

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Photon counting for spectrophotometry

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