an investigation ofphotomultiplier background

technical reprint R/P

075

an investigation of photomultiplier background

A G Wright, Electron Tubes Limited,Bury Street, Ruislip, Middlesex HA4 7TA, UK

technical reprint R/P075

abstractThe inter-relationship between dark current, darkcount rate and photomultiplier gain is explained,using the results obtained from measurements on arelatively large sample of photomultipliers. Theabsolute manner in which the known sources ofbackground contribute to the dark count and darkcurrent parameters is examined. Practical recom-mendations, based on tube measurements, aregiven which help provide optimum performance forDC detection and photon-counting applications.

1 introduction

The ultimate detectivity that can be achieved withphotomultipliers is determined by two considera-tions. The first of these is a theoretical argumentand is a direct consequence of the statistical natureof both optical radiation and the secondary emis-sion process which provides the high gain unique tophotomultipliers. Key papers by Oliver and Pike(1968), Young (1969) and Robben (1971) give thetheoretical justification in favour of photon countingas the preferred method for measuring low lightfluxes. The second factor is a practical one whichconcerns the nature of the photomultiplier back-ground. The term background refers to the anodesignal measured when the tube is in complete dark-ness. The dark current is the appropriate parameterwhere DC or narrow-band detection is under con-sideration, whereas, for the pulse-counting tech-nique, the pulse height spectrum together with theintegral rate of dark counts is relevant.

The basic processes contributing to backgroundwere already well known some twenty years agofrom the studies of Baicker (1960), Sharpe andStanley (1062), Young (1966, 1969) and Krall(1967). Detailed studies on particular photomultipli-er types have been reported by Barton et al (1964),Gadsden (1965), Oliver and Pike (1968) andCoates (1971, 1972). These studies, by providing abetter understanding of the sources of background,have undoubtedly led to the manufacture of betterphotomultipliers. Two aspects of background per-

formance, of direct relevance in the use of photo-multipliers, have been noted by the more criticalusers of photomultipliers, although not fullyexplored in the scientific literature. The first con-cerns the observation that the dark current seldomvaries linearly with overall gain: a relative improve-ment or deterioration with increasing gain may beobserved. Secondly, there is poor correlationbetween the dark current and dark count parame-ters measured in the same tube. This is particularlyevident when a set of photomultipliers is graded inaccordance with either dark current or dark counts the two groups of data do not always agree.

If it is assumed that dark current is solely derivedfrom the emission of single electrons from the pho-tocathode, then the anode current Ι and the totaldark count Ν s-1 would be related as follows:

Ι=Νe ...(1)

where e is the electronic charge is the meanmultiplier gain obtained from the single=electrondistribution measured with the photocathode illumi-nated with single photons (Wright 1981). Assumingfurther that Ν is independent of gain, then followingSharpe and Stanley (1962) we may use equation(1) to check on the departure from ideal perform-ance by noting that Ι/, the effective cathodecurrent, should remain constant as is varied.However, it is known from the references alreadyquoted that

(i) dark counts vary with applied voltage;(ii) the dark count is not solely derived from the

emission of single electrons at the cathode;(iii) the anode current Ι′ comprises a pulsed

component iq from the electron multiplication process and a direct current Ι′ from leakage within the photomultiplier.

It is shown that individual tube behaviour canalways be explained in terms of these three consid-erations, in particular the inter-relationship betweendark current, the dark count rate and the photomul-tiplier gain. With the exception of Barton et al(1964) and Sharpe and Stanley (1962), most inves-tigations have been confined to the measurementof samples containing between one and three tubesonly. Photomultipliers exhibit a wide variation in thenature and quality of their performance and it istherefore unwise to generalize on the basis of avery small sample. Results of measurements onthirty-two photomultipliers of various types arereported in this work for the purpose of providing amore reliable description of the range of tubebehaviour.

In order to quantify the contributions from the con-stituents of the photomultiplier background, it wasfound convenient to subdivide the spectrum intofour regions as describe in section 3. Three photo-multipliers were selected for detailed measurement,including the effects of cooling on the backgroundspectrum. This provided further information on thesources themselves, but more importantly, led to abetter understanding of the practical limits attain-able in low light level detection. The final section,by providing a better understanding of tube selec-tion criteria, helps categorise photomultipliers suit-able for photon counting and for DC detection.Practical guidance and means of optimizing theperformance of a given photomultiplier concludethis study.

2 experimental apparatus and procedure

The term dark count has meaning only when lowerand upper acceptance thresholds have been speci-fied. Threshold levels are ideally measured incoulombs when referring to pulses but otherderived quantities, such as peak voltage or current,may be appropriate depending on the details of theinstrumentation. In this work there was consider-able advantage in using scale with units in photo-electrons equivalent by referring to the photocath-ode, results may be expressed independently ofmultiplier gain, g. Certain type of photomultipliersprovide a peaked output pulse height distributionunder single photon excitation, in which case, thepeak is taken as one photoelectron equivalent.Photomultipliers with a venetian blind multiplier, forexample, do not in general resolve a single electronpeak and for tubes of this type is is necessary tobase the scale on the man multiplier gain .Fractional and multi-electron pulses arise as a con-sequence of the statistical nature of g. Small pulsesare also produced, for example, when the point ofinitiation is a dynode; multi-electron pulses are gen-erated by ion bombardment of the cathode (Bartonet al 1964, Morton 1967, Coates 1973 a, b).

Measurements of pulse height spectra were madewith a charge-sensitive multichannel analyzer(Tracor Northern TN 1705). The instrument was cal-ibrated in terms of picocoulombs per channel, asdescribed in a previous paper (Wright 1981). Thecontribution to the dark current from the pulses inthe spectrum may be assessed from the followingrelationship

iq = n(q)q dq ...(2)

where n(q) is the number of pulses per second with

charge between q and q + dq. The calibration accu-racy of the analyzer allows the conversion in (2) tobe made with an uncertainty of about 5%. The mul-tichannel analyzer was also used to measure themultiplier gain of each photomultiplier. This is notstraightforward, but it has been shown that themean multiplier gain, , can be measured withan accuracy of about 10% (Wright 1981). The multi-channel analyzer incorporates a preamplifier ofvariable gain with a maximum sensitivity of 0.025pC per channel. Increasing the preamplifier gain toprovide more than this sensitivity led to an unac-ceptable level of noise and hence dead-time. Thelowest gain at which N could be measured was,therefore, restricted to 5 x 106. The range of theanalyzer was such that photomultiplier gains up to108 could be measured directly. Having measuredthe gain at a particular operating voltage, anextended gain-voltage calibration was thenobtained using a single-photon source of fixedintensity and a Keithley Picoammeter (type 160B).The intensity of the light source as adjusted to givean anode current of ~1 µA at a voltage for which was already known. The measured variation ofcurrent at a function of EHT about this voltage wstaken to be directly proportional to the variation ingain.

Measurements were made on thirty-two photomulti-pliers incorporating various types of multiplyingstructures and photocathodes. The details of thetubes tested are given in the table 1. The apparatuswas arranged so that the photomultiplier outputcould be connected to either the multichannel ana-lyzer or to a picoammeter by a simple switchingarrangement. All photomultipliers were tested in alinear voltage divider chain, decoupled on the lastthree stages and with the cathode at high negativevoltage. A more stable configuration is undoubtedlythat with the cathode at earth potential, but theneed to measure dark current favoured the use ofnegative high voltage. As a precaution against highvariable dark counts, every tube was externally cov-ered with a conductive coating of aqadag and main-tained at cathode potential. External leakage effectswere kept ot a minimum by ensuring that each tubebase and socket were scrupulously clean prior tomeasurements. Cleaning with alcohol followed bydistilled water ws adopted for this purpose.

The photomultipliers under test were stored andmeasured in a temperature controlled dark box (20± 1°C) and always allowed at least two weeks darkadaption. Ideally a tube should be run continuouslyuntil such time as the dark current stabilizes andonly then should measurements be taken. The peri-od required depends on the individual tube and canvary from a few hours to many weeks. In most

∫∞

0

instances, only an hour was allowed after applica-tion of the high voltage. While this is admittedly notideal, it was adopted as a practical expedientbecause of the number to be tested.

A preliminary experiment was carried out to checkthe degree to which photomultipliers follow idealbehaviour stated in equation 1). The points linkedby straight line segments, shown in figure 1, referto the same photomultiplier operated within the gainrange 5 x 106 to 109. An ideal tube is representedby a single point lying on the straight line of theslope e. The coding symbols refer to the lowestgain at which each tube was operation (5 x 106)with the arrow indicating the path taken withincreasing gain. There is no common pattern: forsome tubes the arrow points towards ideal behav-iour with increasing gain whilst in other the reverseis true. The 9798 type photomultiplier conformsbest to ideal performance because the low workfunction of the S20 photocathode provides copiousthermionic emission at room temperature, and fortubes of this type the assumptions implicit in equa-tion 1) are not unreasonable. For the majority oftubes, however, equation 1) is a gross oversimplifi-cation of real photomultiplier behaviour.

figure 1 the equivalent cathode current, I, measured overa range of multiplier gains from 5 x 106 to 109. Data pointslinked by straight line segments refer to the same photomultipli-er. N is the integral number of background pulses of amplitudebetween 0.2 and 10 photoelectrons equivalent. The method ofgain assignment is described in section 2. ∆, 9798; !,9811; x, 9813; +, 9814; !, 9954.

table 1summary of the photomultipliers tested

Type Number Tested Cathode Type Diameter (in) Multiplier Stages V(k-d1)

9814 8 Bialkali 2 LF 12 3009813 5 Bialkali 2 LF 14 300 9811 4 S11 2 LF 12 3009954 6 RbCs 2 LF 12 3009798 4 S20 1 BG11 1509635 5 Bialkali 2 VB13 150

LF, linear focus; BG, box and grid; VB, venetian blind

3 sources of background

Pulse height distributions were recorded for twelvephotomultipliers, a representative selection of whichare shown in figure 2. For convenience, four pulseheight regions have been defined: A

figure 4 the effect of cooling ($, T = +25°C; !, T = -25°C) on the background for the photomultipliers; (a), 9814 6777; (b), 981312123; (c), 9813Q 4284. The spectrum in (a) shows little change on cooling because the background in this photomultiplier iserived largely from the presence of 40K in the window material. (b) is an example of a tube made from low-background glass; theintegral counts decrease from 50 s-1 to 20 s-1 upon cooling. (c) is representative of an exceptional quartz photomultiplier with darkcounts of ~10 s-1 at 25°C reducing to ~1.5 s-1 at -25°C.

figure 3 pulse heigh distributions for a 9814 6777 operated at three gain settings: ", = 6 x 106; +, = 5 x 107; #, = 2.8 x 108. (a) Backgound distribution at 20°C exhibiting an increase in region aA, b and c with gain. (b) Single photon exci-tation. The relative proportion of counts in C, compared with the single electron peak, is two orders of magnitude less than in thecorresponding bacground spectra. Note the absence of region D in (b).

Electron Tubes, Gencom Inc.) operated at tempera-ture of +25°C and -25°C. The background spectrain figure 4 show that the spectral content in regionsA and B, decreases substantially upon cooling infigures 4b and c but considerably less so in 4a - aresult of the 40K contribution which is temperatureindependent. Again referring to regions A and B, thereduction in count rate with temperature if figures4b and c is characteristic of thermionic emission,although Young (1969) has suggested that thereare possibly other temperature-dependent sourceswhich contribute.

The spectrum in region D is independent of temper-ature in all three photomultipliers. These very largepulses are a direct consequence of the passage ofrelativistic cosmic rays (mainly muons and elec-trons) through the photomultiplier window (at a rateof about 15 min-1 for a 51 mm diameter tube). Thisaspect of photomultiplier background has been cov-ered in detail by Young (1966). It is interesting tonote that the photomultiplier with a quartz window(figure 4c) gives a peaked response at 80 photo-electrons whereas those with glass faceplates onlyexhibit a shoulder in region D. This can beexplained in terms of the superior transmission ofquartz for the uv-rich Cerenkov emission.

4 relationship between dark currentand dark counts

In order to explain why most of the experimentalpoints in figure 1 generally lie above the line repre-senting ideal behaviour, the spectral content of thedark counts must be taken into account. A term rep-resenting the contribution from leakage currentsflowing into the anode, due to the applied biasingvoltages on the dynodes, must be including. If I'represents this components, including any othersource in the photomultiplier, responsible for a DCcontribution, then

I=iq+I'

I = n(q)q dq + I' ...(3)

Figure 2 illustrates the wide variation in the back-ground spectra from one tube to another and helpsto explain how the multi-electron pulses can makea significant contribution to iq. Plotting n(q)q dqagainst q shows the extend to which regions A, B,C and D contribute to the dark current.

The leakage component I′ may be estimated withreasonable accuracy in the following way. Shortingthe cathode d1 and d2 together, while maintainingthe same voltage distribution on the remaining dyn-

odes, reduced the contribution from iq to negligibleproportions. This was checked by noting that thepulse height distribution measured under theseconditions consisted of very few pulses. The meas-ured dark current is taken to the be same as I' inequation (3). This is of course an underestimatebecause the photomultiplier operating conditionshave been altered and any signal-induced leakagedue to the cathode emission is also removed.However, there is no other obvious way of deducingI'.

The contribution from the dark pulses, taken fromfigure 5a, are shown in 5c (circles). Adding tothese, the measured I' (squares), gives the fullcurve. The agreement between the observed totaldark current (small dots), and that predicted (fullcurve) is remarkably good when allowance is madefor the uncertainty in the charge calibration of themultichannel analyzer and the assumption inherentin deducing I'. The same procedure has beenadopted in arriving at the results in figure 5d wheretheory and experiment again agree rather well. Asmentioned earlier, pulse height distribution (andhence iq) could not be measure for g < 5 x 106.Values of iq deduced from an extrapolated curvewere therefore assumed in the low-gain region offigure 5c and d. The results shown in figure 5e andf indicated that N approaches an asymptotic valueas g → 0 and so the extrapolation is not unreason-able.

I/ has been plotted against in figures 5eand f for the same two photomultipliers. Referringto serial number 6777 we see that I/ is essen-tially constant over a wide range of gain extendingfrom 106 to 5 x 107. The other curve in figure 5e,showing the dark count rate increase with appliedvoltage, accounts very nicely for the upward devia-tion of I/ for serial number 6777 at the highergains. Departure from ideal behaviour is alsoapparent for g < 106. The dark current is leakagedominated in this region and virtually independentof the dark count rate. In contrast serial number12123 is leakage dominated for all g < 108 and onlyapproached ideal performance when g > 108.

The complete set of thirty-two phototubes of six dif-ferent types, were measured with the resultsobtained in figures 6a-f. The majority of curves areconsistent with a typical behaviour pattern: a curvewith a broad minimum lying between = 5 x 106and 107. The exceptions are worthy of note.

(i) serial number 6680 (figure 6a) is an exampleof a tube with exceptionally high leakage, account-ing for the major component of dark current up tog~107. Although very poor with regard to dark cur-rent, the dark counts at 65 s-1 for this tube werevoltage independent up to g = 7 x 107.

(ii) serial number 11086 (figure 6a) has a low leak-age current component. The dark counts for thistube vary from 100 at g=107 to 440 s-1 at

∫∞

ο

figure 5 illustrating the absolute contributions made by regions A, B, C and D to the dark current: (a), (c), (e), 9814 6777; (b), (d),(f), 9813 12123. the photomultiplier in (a) is characterised by a significant contribution from region C, while that in (b) has a lowerproportion of large pulses. The contribution to the dark current, derived from dark counts, is given by the asymptotic value of thefunction e ∫οq n(q)q dq. iq values so derived are used in (c) and (d) (circles) which illustrate how the measured dark current canbe accounted for in terms of iq and I. The measured dark currents can be expressed as equivalent cathode currents, I/, as infigures (e) and (f); an ideal tubes is one for which I/ = constant. The variation of count rate, N, with gain is also shown in (e)and (f).

figure 6 equivalent cathode currents plotted agains multiplier gain for the set of photomultipliers tested: (a), 9814; (b) 9813; (c)9811; (d) 9954; (e) 9798 and (f), 9635. The serial numbers of tubes referred to in the text are indicated on the curves.

g =3 x 108 which explains the turn-up in the curveat high gain.(iii) the curve representing serial number 6675remains flat between 107 < g < 3 x 108. This isbecause the dark counts do not increase with gain.

(iv) an example of a photomultiplier suffering fromexcessive light generation is that of serial number105418. Light feedback sets in at g > 108.

The variation of darks with for the tubesreferred to in (i)-(iv) are shown in figure 7.

Comparing the results in figures 6a and b we notethat three of the tubes with 14 stages of gain oper-ate satisfactorily up to g ~109. The limiting gain forthe 9814s is typically 3 x 108 and beyond this gain,light feedback sets in.

The best tube in figure 6b has I/(min )= 10-17whereas the corresponding figure for the 9814s is 2 x 10-17. The minimum values attained by the S11and S20 tubes (9811) and (9798) (6c and e) lie inthe range I/ = 10-16 to 3 x 10-15. This isbecause the background counts are an order ofmagnitude higher than those for the bialkali photo-multipliers.

The 9635 venetian blind tubes behave in a similarway to the 9813 photomultipliers. Three of the sam-ples attain very low values of I/ at the minimumand all perform satisfactory at high gain.

figure 7 the variation of dark counts with gain for a set ofselected tubes. The steep rise in count rate exhibited by105418 is symptomatic of light feedback

All the photomultipliers in figure 7 show anincrease in background counts with gain, particular-ly at gains in excess of 108. We have no means ofdetermining whether this occurs as a consequenceof the higher voltages applied to the tube orwhether the increase in counts relates to the signalcurrent density in the tube, which naturally variesproportionally with g. It seems reasonable toassume that the counts continue to decrease slowlyas g is reduced below 5 x 106, perhaps approach-ing the true thermionic emission rate from the cath-

ode as → 0. Taking an asymptotic value of100s-1 as representative of a good bialkali tube(see figure 7), which is an equivalent cathode cur-rent of 1.6 x 10-17 A, we note from figures 6a andb that even for the best tubes I/ tends to be anorder of magnitude higher than this value at g = 105for example. Furthermore, I/ is varying some-thing like 1/½ as g 0. If it is assumed that I' ispurely due to ohmic leakage, then I' would be pro-portional to V and since g∝V10 in the region ofinterest, I'/ will vary as -0.9. Two tubes thatperform poorly at low gain, serial numbers 6680and 12123 from figures 6a and 5f respectively,both vary as -0.8, supporting the view that thesetwo tubes suffer from having an ohmic leakage pathsomewhere in the dynode stack. The majority oftubes vary approximately as -0.5 in the region of = 105 and ohmic leakage alone clearly cannotaccount for this magnitude of dark current.

Serial number 12123 is an interesting example of aphotomultiplier that improved with continuous oper-ation. Because of the high leakage current, thistube was left with the voltage applied for two daysand then remeasured with the results shown in fig-ure 6b. Comparing I/ value at = 105 in fig-ures 5f and 6b we note an improvement of twoorders of magnitude in the leakage. Similar treat-ment applied to number 6680 did not result in thesame degree of improvement and it seems plausi-ble to attribute the behaviour of these tubes to theexistence of a low resistance leakage path whichcleared itself in the one tube but not in the other.The fact that photomultipliers tend to improve aftera continuous period of operation is well known tomost users.

5 conclusions and implications for lowlight level measurements

This work shows that the suitability of a particulartube for low light level applications is best ascer-tained by a measurement at the intended operatinggain. In fact, there is an optimum gain, for which aphotomultiplier will provide the best signal to back-ground ration (S/B). A tube which performs well atlow gain will not necessarily do so at a higher gainand vice versa. The dark current does not correlatewell with the dark count rate except under high gaincondiditions where the DC component is usually anegligible proportion of the total dark current.Examination of the set of curve in figure 6 allowsthe following generalization to be made. The S/Bratio for DC detection is a minimum within therange 3 x 106 < (g) < 108 for the most of the photo-multipliers tested. The curves of figure 6 suggest asimple but effective way of setting up a commercialdetector system which includes ad DC amplifier ofvariable gain. The total gain in the system is theproduct of the multiplier gain and the amplifier gainand the experimentalist can choose the relativecontributions from each. The optimum gain assign-ment is readily arrived at by plotting a family of

I/ curves for various combinations of amplifierand photomultiplier gain. In fact it is sufficient forthis purpose to plot I/(relative gain) since a knowl-edge of the actual gain is not required to optimizeS/B - it is only the overall voltage at which the mini-mum of the curve is attained that is important.Relative gain can be measured as described in Section 2 by using a steady light source and vary-ing the applied voltage.

Similar considerations apply in setting up a photoncounting system. The curves of figure 7 indicatethat the lower the photomultiplier gain, the betterthe dark counts. Photon counting systems are sen-sitive to electrical interference and it is thereforeunwise to derive too high a proportion of the overallgain from the amplifier. The optimum gain assign-ment in this case is obtained by plotting a family ofcurves of dark counts against system gain. A pho-ton counting system can be further optimized bycareful selection of the upper and lower thresholdlevels which determine the actual rate of measuredsignal and background. Figures 2, 3 and 4 suggestthat the lower acceptance level for pulse countingshould be set at ~0.3 and the upper at ~3 photo-electrons equivalent to eliminate the majority ofsmall and large amplitude pulses in the backgroundwhile sacrificing very little counting efficiency withrespect to signal. This manner of S/B optimizationis of course not possible in DC detection where allcontributions to the dark current have to be accept-ed. We note from figure 5a that small amplitudepulses barely contribute whereas those from C andD can account for 20-30% of I. For an exceptionalphotomultiplier, such as as the 9813Q 4282, thecontribution from C and D exceeds that from A andB. Cooling this photomultiplier to -25°C reduces therate from A + B to less than 1s-1 while C + Dremains constant at about 1s-1; the dark current isnow almost entirely derived from large amplitudepulses. It is not difficult to appreciate how a sourceof large amplitude but relatively infrequent pulseswill lead to a dark current with high variance. Thismanifest itself most noticeably as 'kicking noise' inchart recordings of low level dark current.

The purpose of this study has been to gain anunderstanding of the constituents of the dark cur-rent in a photomultiplier. A simple model assuminga pulse like component and a DC component issufficient to account for the magnitude of the darkcurrent and its dependence on tube gain. This workalso underlines the arguments in favour of photoncounting for low level applications by showing forexample how selected cooled photomultipliers canexhibit an effective cathode dark current of lessthan one electron per second. This is achievablewith quartz windowed photomultipliers only; forthose in low background glass the figure is about10 s-1 whereas those in glass envelopes have ahigh 40K content give rise to at least 40 counts s-1.These figures apply to counting window correspon-ding to region B; considerable S/B advantage isalways sacrificed by following the common expedi-

ent of using only a single detection threshold.

Finally, the notion that a particular photomultipliertype can be categorised in terms of quoted typicalbackground performance figure seems spurious.The wide variation in the results of figure 6 aretaken in support of this view. In addition, it shouldbe noted that the photomultipliers examined in thiswork had undergone the standard factory screeningprior to measurement. Those with excessive darkand leakage currents had thus already been elimi-nated. It is undoubtedly more meaningful for photo-multiplier manufacturers to classify tubes as 'goodfor low background counting' or 'suitable for lowcurrent measurements' or both.

references

Allen J S 1952, Los Alamos Report LA 1459

Baicker J A 1960 Dark current in photomultipliersIEEE Trans Nucl. Sci NS-7 74-80

Barton J C, Barnaby C F and Jasani B M 1964 Aninvestigation of noise in venetian blind photomulti-pliers J. Sci Instrum. 41 599-604

Coates P B 1971 Noise sources in the C31000Dphotomultiplier J. Phys. E: Sci. Instrum. 4 201-7

Coates P B 1972 Photomultiplier noise statistics J.Phys. D: Appl. Phys. 5 915-30

Coates P B 1973a The origins of afterpulses inphotomultipliers J. Phys. 6 1159-66

Coates P B 1973b A theory of afterpulse formation Iphotomultipliers and the prepulse height distributionJ. Phys. D: Appl. Phys 6 -1862-9

Gadsden M 1965 Some statistical properties ofpulses from photomultipliers Appl. Opt. 4 1446-52

Jerde K L, Peterson LE and Stein W 1967 Effectsof high energy radiations on noise pulses from pho-tomultiplier tubes Rev. Sci. Instrum. 38 1387-94

Krall H R 1967 Extraneous light emission from pho-tomultipliers IEE Trans. Nucl. Sci. NS-14 455-9

Morton G A, Smith H M and Wasserman R 1967Afterpulses in photomultipliers IEEE Trans. Nucl.Sci. NS-14 433-8

Oliver C J and Pike E R 1968 Measurement of lowlight flux by photon counting J. Phys. D: Appl. Phys.1 1459-68

Oliver C J and Pike E R 1970 The edge effect inelectron multiplier statistics J. Phys. D: Appl. Phys 3L73-5

Robben F 1971 Noise in the measurement of lightwith photomultipliers Appl. Opt. 10 776-96

Sharpe J and Stanley V A 1962 Photomultipliers fortritium counting Tritium in the physical and biologi-cal sciences (Vienna: IAEA vol. 1 pp 211-29)

Wright A G 1981 Determination of the multipliergain of a photomultiplier J. Phys. E: Sci. Instrum.14 851-5

Young A T 1966 Cosmic ray induced dark current inphotomultipliers Rev. Sci. Instrum. 37 1472-80

Young A T 1969 Photometric error analysis IX:Optimum use of photomultipliers Appl. Opt. 8 2431-47

acknowledgementReproduced by kind permission of the Institute ofPhysics from Journal of Physics E; ScientificInstruments 16 300-7

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