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Absolute Calibration of PMTs with Laser light

Christopher Williams

Abstract

We report on the results from calibrating photo-multiplier tubes (PMTs) absolutely. Ob-taining the quantum efficiency measurements of PMTs to better than 10% is very difficult,but this level of accuracy is necessary to make an absolute measurement of cosmic ray airshower fluorescence yield. As a calibration light source we use photons from a 337.1 nm

nitrogen laser passed through an integrating sphere and pinhole collimator. This gives a lowenough energy pulse to measure the single photoelectron spectrum for the PMT with sameaccuracy as the calibrated energy probes.

1. Introduction

The nitrogen fluorescence spectrum, as well as pressure, temperature, and energy de-pendence have been measured accurately[1],[2],[3]. Combining these measurements with anincrease in our understanding of atmospheric effects, and the ability to monitor for theseeffects, the systematic errors in the absolute measurement of cosmic ray fluorescence yield

have become considerably more important in measuring cosmic ray energies. Because boththe Pierre Auger Observatory [4] and Telescope Array [5] experiments use this method asa primary detection technique, a push is now being made to take more accurate measure-ments of the absolute fluorescence yield for cosmic rays, thus lowering the systematic errorson energy reconstruction.

As systematic errors dominate the absolute yield measurements as well, developmentof new methods of detector calibration have become necessary to provide a cross-checkon measured yields. Currently, experiments are using Rayleigh scattered laser light as acalibration method [6],[7],[8]. Rayleigh scattered light is a good source of calibrated lightbecause as will be shown the yield depends on few values which introduce added systematic

errors and these values are easily controlled.In conjunction with the AirFly experiment, we set out to build a calibration set-up that

can be used in situ during measurements. This will help to eliminate as many systematics aspossible because the calibrated light source will share those systematics with the fluorescenceyield measurement. This calibration method is described in [9].

2. Yield Predictions

As a first attempt, we designed and built a set-up to use Rayleigh scattered light fromthe laser pulse in a manner similar to other experiments, passing the laser beam parallel to

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the detection surface. In order to use Rayleigh scattered light as a calibrated light source thenumber of photons entering the detector must be accurately predicted from the measured

energy of the lasers pulsed beam. The general Rayleigh scattering yield, Y, is given by thefollowing,

Y = Nphoton4Ns (1)

In this equation the number of photons in the lasers pulse, Nphoton, can be calculatedby measuring the pulse energy with the a NIST calibrated energy probe. These probes andtheir systematic error are described in the following section 3.1.2. The number density ofmolecules in the scattering medium, Ns, is calculated from the pressure and temperatureof the medium assuming an ideal gas. For a final test these values must be continuouslymonitored to lower systematic error, but will initially be measured at the beginning and end

of the test. The geometric acceptance factor, , calculated using a monte carlo integrationtechnique described as follows in 2.1. The final term, 4, is the total cross section forRayleigh scattering given by,

4 =243(n2s 1)

2

4Ns(n22 + 2)2FK (2)

This prescription is taken from Bucholtz and follows his notation [10]. The refractiveindex of the scattering medium, ns, wavelength of scattering light, , and as above num-ber density of the scattering medium, Ns. The King Correction Factor, FK, accounts forcomposition mixtures in the medium. For dry air FK = 1.053 [10].

2.1. Calculation of Geometric Acceptance

The geometric acceptance factor, , accounts for the number of photons entering a de-tector. This factor can be represented as the integral over the beams total path length, S,and the total angular phase space, for a given detector acceptance function A(l ,,),

=

S

4

A(l ,,)dld. (3)

The integral in Eq. 3 becomes very complicated because any circular aperture, suchas that found on the probes and the entrance to the integrating sphere, leads to elliptic

integrals. It is much simpler to perform this integral through a simple ray tracing montecarlo. For this monte carlo a large number of rays, 109, are generated randomly along thepath of the laser which is in the field of view of the detector. These rays are also generatedfollowing the angular distribution for Rayleigh scattering, 1 + cos2 . Once these rays aregenerated they are traced to the detector face and is given by the fraction of rays thatenter multiplied with the path length, S.

A visualization of this calculation is shown for the NIST calibrated silicon photo-detectorin Fig. 1. This factor, , has a unique value for any given set-up and must be calculatedindividually for each.

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50

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Figure 1: Graphical representation of monte carlo simulation for Rayleigh scattering showing 100 rays.Green square is representation of Si-probe, and red cylinder is shielding around probe.

2.2. Direct Source Calibration

During the final stages of design our laser malfunctioned and needed to be serviced.

Upon return we found it difficult to reproduce earlier results from the Rayleigh scatteringset-up. This led us to believe there were unaccounted for systematic effects from eitherthe laser or the set-up. Due to the in situ nature of our calibration, an easily reproduciblemeasurement is necessary because the experimental set-up must be mobile. An alternativeroute for calibration was then pursued. By using an integrating sphere in combination witha pinhole collimator to directly attenuate the laser beam, we have been able to lower thelaser pulse energy to a level low enough to calibrate for single photoelectrons. This designhas the added benefit that the calibration set-up is very simple and no longer sensitive toenvironmental effects such as temperature and air pressure. Also because of the Lambertianreflective nature of the sphere, any polarization present in the beam is removed through

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many reflections creating a uniform light source, thus eliminating another systematic effect.Further, a third source of systematic error is removed because the aperture of the detector

no longer needs to be calculated through monte carlo methods since light is shone directlyonto the photocathode of the PMT. This leaves only the systematic errors from the energyprobes. Both methods for calibration will be reported on in this paper.

3. Experimental Design

Current design of this experiment includes a large metal trunk with black interior usedas a scatter box. Inside the laser and optical components are placed along with variousmasks and black paper for background control. The contents and interior of the box can beseen mocked up in Fig. 2 and Fig. 3. Where the figures show the Rayleigh scattering set-upand direct source set-up respectively. The components of the test set-up are described inthe remainder of this section.

RjP-465

RjP-735Beam Path

Figure 2: Image showing set-up for Rayleigh scattering measurement. Test components labeled in image.

Initially, measurements of the Rayleigh yield are made directly using the low energysilicon probe described below. This is done as a both a proof a concept for Rayleigh scatteringcalibration measurements and as a study of backgrounds within the scatter box.

3.1. Test Components

The following are major components in this test set-up. Along with these are a numberstandard optical components such as precision pinholes and stepped density attenuators.

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Figure 3: Image showing set-up for direct source calibration. Test components labeled in image.

Also a second PMT, used for triggering off of backscattered light, is placed alongside the

laser as seen in Fig. 3. This trigger PMT was required because the RF noise produced bythe lasers trigger outputs overwhelmed the PMT signal. A small aluminum shield was builtto cover the outputs and the problem was resolved.

3.1.1. Laser

This calibration system uses a nitrogen gas (N2) discharge laser from Spectra-Physics,model VSL-337ND-S. Using a charged nitrogen cartridge the laser emits light at 337.1nmwith a spectral width of 0.1nm. This narrow bandwidth around the 337nm fluorescenceline makes it ideally suited for use as a light source for in situ calibration during absolutefluorescence measurements. The laser output is unpolarized. A polarized beam would

provide an additional systematic in the calculation of Rayleigh scattered light. Maximumquoted pulse energy for this laser is 300J. Attenuation has been implemented down to picoJoule levels with little effect to the beam stability. This allows for a very large range in testenergies and much flexibility in the test set-up.

The Spectra-Physics laser exhibits extremely good stability. Fig. 4 shows the measuredbeam energy with no attenuation. The pulse-to-pulse stability for this test is measuredwith a standard deviation of 2%. This is very good and falls below the claimed maximumdeviation of 4% pulse-to-pulse. When the beam is highly attenuated as in Fig. 5, themeasured pulse-to-pulse standard deviation is 3%. This still falls within the quoted rangefor the laser, and also suggests that very little polarization is being added to the beam by

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Beam Energy

Figure 4: Histogram of laser pulse energy with beam unattenuated and halo removed with large metal ring.

optical components. It should be noted that these deviations represent statistical errorswhich have little effect. The test is performed over a large number of measurements and thestatistical error in the measured value of beam energy drops off as one over the square rootof the number of events.

3.1.2. Energy Probes

Two energy probes from Laser Probe Inc. are used in the current test set-up. Thefirst is a high energy pyroelectric probe RjP-735. The 735 uses a 1.0cm2 detector with anenergy range from 1J to 30J. This probe is calibrated to a a maximum of 5% error inaverage power and a 1% linearity for a given energy range. The low energy probed used isan RjP-465. This probe uses a 1.0cm2 silicon photo-diode, with a pulse acceptance rate up

to 500Hz. The energy range for the 465 is 250nJ to 500fJ. This probe also has a calibratedmaximum error of 5% and 1% linearity for any given energy range.

With the use of these probes it is possible to accurately measure the attenuation of theintegrating sphere used for calibration as well as the energy of a given pulse during thecalibration process. It is also shown in 4 that these two probes can be used in combinationto directly measure the Rayleigh scattered laser light.

3.1.3. Integrating Sphere

An integrating sphere is used in the test set up for a number of reasons. Primarily, thesphere provides attenuation to achieve the desired single photon level at the PMT while still

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Figure 5: Histogram of laser pulse energy with beam heavily attenuated by a 1mm pinhole mask andreflective stepped density filters.

maintaining a beam with enough energy to accurately measure using the RjP-465 probe.The sphere and 3mm pinhole collimator in combination provide a small controlled spot sizeto direct onto the surface of the PMT, or into the test system as will be the case for insitu calibration. Lastly, the spheres diffuse internal scattering surface removed all arrivaldirectionality of the light providing for a spatially uniform source.

For the calibration test a six inch integrating sphere from Sphere Optics is used which isdesigned to be a Lambertian surface in the UV, reflecting light proportional to cos . Testof the sphere and pinhole collimator efficiency was performed using the laser in conjunctionwith the two energy probes. For the given detector geometry used with the PMT, the systemwas found to provide an attenuation of 1.82 107.

3.1.4. PMT

For this calibration test two Hamamatsu H7195P PMTs are used. This PMT has aspectral range of 300nm to 600nm making it suitable for tests involving UV fluorescence.The H7195P has a typical gain of 107 and a quoted efficiency of 26.1% and 24.7% for PMT1 and PMT 2 respectively. While this PMT is chosen purposely to make measurements ofnitrogen fluorescence at 337nm at a beam test, in practice any PMT could be calibrated insitu with this method given a suitable light source. This makes this calibration method veryversatile for any absolute measurements where systematics depend heavily on the testingenvironment set-up.

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4. Measurement of Rayleigh Scattered light

Initial Rayleigh yield measurements were made using the low energy silicon probe. Testwere performed with the probe at a fixed location varying beam energy. Tests were alsomade using an unattenuated beam and varying probe distance relative to the beam. First,the background inside the box was measured and was compared with the electronic noisemeasured by triggering the probe with the beam off. As is seen in Fig. 6, the scattered lightinside the box falls below the a level measurable by the RjP-465 probe.

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NomalizedCou

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Probe Triggered No Beam, Electronic NoiseProbe Triggered, Facing Opposite Beam

Background Energy

Figure 6: Histogram of measured background energy. Red squares show the electronic noise of the probebeing triggered externally with the laser off. Black triangles represent probe oriented away from transversebeam. Probe is triggered by laser pulse, a large beam mask in place to cut the outer halo from the beam.Each pulse has an average energy of 133J.

The Rayleigh measurements made during this process were observed to be stable. Fig.7 shows a typical measurement made at 7.62cm from the beam with an average pulse en-ergy of 133J. The resulting histogram of measured Rayleigh yield energies shows a wellbehaved, normally distributed range of energies with a relative error ofE/E= 4.3%. Thisis comparable to the error in beam energy and below the probe calibration error of 5%.This implies the probes calibration error dominates the measurement of the mean Rayleighenergy for a large number of pulses.

Fig. 8 shows Rayleigh yield measurements performed at 7.62 cm from beam line usingdiffering attenuation, both before and after the servicing of the laser. Only three energymeasurements were possible pre-servicing due to limited attenuation options. By the time

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Rayleigh Scattering at 7.62cm

Figure 7: Rayleigh scattering measured directly at a distance of 7.62cm from beamline. Laser is unattenuatedwith an average pulse energy of 133J.

the laser was returned new attenuators had been acquired. The red line is the Rayleigh yieldprediction for this distance from monte carlo. The pressure and temperature variations effectthe predicted yield at a level of less than 1%. The early data agrees well with the prediction,the error bars corresponding to the 5% error from the detector calibration. The lowest energypoint is in a range below the NIST calibration of the probe and the minimal deviation forthis point should not be consider notable.

Fig. 9 shows the Rayleigh yield measurements for a fixed average pulse energy of 133J.Measurements are taken at various distances and the error bars once again correspond tothe 5% error from probe calibration. As in Fig. 8 the red lines correspond to monte carloprediction at each distance. Because the monte carlo must be performed for each distance

measurement, the prediction can only be presented as a piecewise function. In Fig. 9 thepiecewise monte carlo prediction is plotted with arbitrary width at each distance. Onceagain the measurement of Rayleigh yield appears to match predicted values well at the 5%level.

The post-servicing measurements are shown with 5% error bars as well. For these mea-surements the previous set-up had to be fully deconstructed to remove the laser and wasreassembled upon its return. As is shown the new measurements do no agree with the predic-tion at the 5% level. This is most likely due to a systematic error that has not been accountedfor or possible polarization in the lasers beam that was not there pre-servicing. Finding

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J]Laser Beam Energy [40 60 80 100 120 140

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Energy[fJ]

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Rayleigh Energy D=7.62cm

Figure 8: Points represent measured Rayleigh scattered light at various beam attenuations. Square pointsare early measurements before the laser was serviced, triangle points are measurements made after servicing.Error bars are 5% error from detector uncertainty. Red line is monte carlo prediction for Rayleigh yield.

this systematic was not pursued because the new method using the integrating sphere asan attenuator has fewer systematics and is not affected by polarization. Measurements ofRayleigh yield as a function of distance were not taken post-servicing.

5. Calibration of PMTs

Because of the large systematic discrepancies found in the Rayleigh scattering set-upupon return of the laser from servicing, the calibration of the PMTs was pursued using adirect light source. The laser pulse was heavily attenuated, down to 1.65pJ. It was then

passed into the integrating sphere which passed the light through a collimator with 3mmpinholes directly onto the face of the PMT. This set-up is seen in Fig. 3. The trigger PMTwas used to provide a logic gate for the PMT undergoing calibration. This ensured that allcounted photons would be in coincidence with the laser pulse. Given the pulse energy andthe attenuation of 1.82 107 from the sphere and collimator the expected rate of photonson the face of the PMT is 0.5 photons/pulse. Given that the PMT efficiency is expected tobe of order 25% this low rate will ensure that only the single photoelectron peak is observed.Assuming poisson statistics, the probability of getting two photons in a single pulse fallingon the face of the PMT is .038 when combined with the PMT efficiency the rate of twophotoelectrons is less than 1%.

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]

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ayleigh

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Rayleigh Energy D=[7.62cm,15.24cm]

Figure 9: Points represent measured Rayleigh scattered light at various distances form beam. Laser has anaverage energy per pulse of 133J. Error bars are 5% error from detector uncertainty. Red lines are montecarlo prediction for each distance (arbitrary length).

Fig. 10 show the photoelectron spectrums of the two PMTs. The tall peak is the noisepedestal, and the adjacent peak is the single photoelectron peak. By setting a discriminatorthreshold above the noise pedestal, the number of counts in the single photoelectron peak

is given and the fraction of total counts is then found. Dividing this number by the numberof photoelectrons expected gives the PMTs efficiency. PMT 1 is found to have an efficiencyof 18.1% and PMT 2 an efficiency of 17.7%. Both of these measurements are accurate toa maximum uncertainty of 8.7% due to the systematic error of 5% from the beam energymeasurement during calibration and a systematic error of 7.1% from using both energyprobes to calibrate the sphere/collimator efficiency.

There is a discrepancy between this measurement and the Hamamatsu measurement.This is accounted for by collection efficiency (fraction of photoelectrons reaching the firstdynode) of the PMT. Our measurements are made by putting in a place a discriminator levelfor which we count PMTs. The Hamamatsu measurement is made at the photocathode by

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subtracting the noise pedestal, this accounts for a factor of 80%, which raises the efficienciesof the PMTs to 22.6% and 22.1% respectively. Our measurement takes into account real

world counting effects and other systematics and is not in disagreement with the Hamamatsumeasurement.

6. Conclusion

We measure accurately the energy of our laser using a high-sensitivity probe. This lightis then passed through and integrating sphere and collimator to attenuate the pulse energyto the single photoelectron level. This light is then used to measure the single photoelectronspectrum of PMTs and calculate their efficiency to better than 10%. This light source hasthe advantage that it is environment independent, and insensitive to polarization of the

beam.We have also measured the Rayleigh scattering of our laser beam directly using the samehigh sensitivity probes as a proof of concept for calibration. The Rayleigh scattering crosssection, a well known value, can then be used to calculate the number of photons arrivingat a PMT for given geometry. We have found this system of calibration is dominated bymany more systematic effects and is therefore less desirable to use for a mobile light sourceto perform in situ calibrations.

The current set-up will be used for in situ calibration during test beam measurementsof air fluorescence. By calibrating the fluorescence test set-up to a level better than 10%we will be able to eliminate any systematic effects and we expect to obtain an absolutemeasurement of air fluorescence yield to better than 10%.

References

[1] M. Ave, et al. for the AirFly collaboration. Nuc. Inst. Meth. A 597, (2008), 41-45[2] M. Ave, et al. for the AirFly collaboration. Nuc. Inst. Meth. A 597, (2008), 46-49[3] M. Ave, et al. for the AirFly collaboration. Nuc. Inst. Meth. A 597, (2008), 50-54[4] www.auger.org[5] www.telescopearray.org[6] R. Abassi, et al. Nuc. Inst. Meth. A 597, (2008), 32-36[7] J. Rosado, et al. Nuc. Inst. Meth. A 597, (2008), 32-36[8] T. Waldenmaier, et al. Astroparticle Physics 29, (2008), 205-222[9] M. Ave, et al. for the AirFly collaboration. Nuc. Inst. Meth. A 597, (2008), 50-54

[10] A. Bucholtz, Appl. Opt. Vol. 34, (1995), 2765-2773

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htempEntries 17571

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Figure 10: Single photoelectron spectrum for PMT 1 and PMT 2. Sold red line shows the cut to removepedestal.

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