ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A
journal homepage: www.elsevier.com/locate/nima

Calibration and characterization of the IceCube photomultiplier tube
R. Abbasi z, Y. Abdou t, T. Abu-Zayyad af, J. Adams o, J.A. Aguilar z, M. Ahlers ae, K. Andeen z, J. Auffenberg al,
X. Bai ad, M. Baker z, S.W. Barwick v, R. Bay g, J.L. Bazo Alba am, K. Beattie h, J.J. Beatty q,r, S. Bechet l,
J.K. Becker j, K.-H. Becker al, M.L. Benabderrahmane am, J. Berdermann am, P. Berghaus z, D. Berley p,
E. Bernardini am, D. Bertrand l, D.Z. Besson x, M. Bissok a, E. Blaufuss p, D.J. Boersma a, C. Bohm ag,
O. Botner aj, L. Bradley ai, J. Braun z, S. Buitink h, M. Carson t, D. Chirkin z, B. Christy p, J. Clem ad, S. Cohen w,
C. Colnard u, D.F. Cowen ai,ah, M.V. D’Agostino g, M. Danninger ag, C. De Clercq m , L. Demirörs w,
O. Depaepe m, F. Descamps t, P. Desiati z, G. de Vries-Uiterweerd t, T. DeYoung ai, J.C. Dı́az-Vélez z,
J. Dreyer s,j, J.P. Dumm z, M.R. Duvoort ak, R. Ehrlich p, J. Eisch z, R.W. Ellsworth p, O. Engdegård aj,
S. Euler a, P.A. Evenson ad, O. Fadiran d, A.R. Fazely f, T. Feusels t, K. Filimonov g, C. Finley ag,
M.M. Foerster ai, B.D. Fox ai, A. Franckowiak i, R. Franke am, T.K. Gaisser ad, J. Gallagher y, R. Ganugapati z,
M. Geisler a, L. Gerhardt h,g, L. Gladstone z, A. Goldschmidt h, J.A. Goodman p, D. Grant ai, T. Griesel ab,
A. Groß o,u, S. Grullon z, R.M. Gunasingha f, M. Gurtner al, C. Ha ai, A. Hallgren aj, F. Halzen z, K. Han o,
K. Hanson z, Y. Hasegawa n, J. Haugen z, K. Helbing al, P. Herquet ac, S. Hickford o, G.C. Hill z,
K.D. Hoffman p, A. Homeier i, K. Hoshina z, D. Hubert m, W. Huelsnitz p, J.-P. Hülß a, P.O. Hulth ag,
K. Hultqvist ag, S. Hussain ad, R.L. Imlay f, M. Inaba n, A. Ishihara n, J. Jacobsen z, G.S. Japaridze d,H. Johansson ag, J.M. Joseph h, K.-H. Kampert al, A. Kappes z,1, T. Karg al, A. Karle z, J.L. Kelley z,
N. Kemming i, P. Kenny x, J. Kiryluk h,g, F. Kislat am, N. Kitamura z, S.R. Klein h,g, S. Knops a, G. Kohnen ac,
H. Kolanoski i, L. Köpke ab, D.J. Koskinen ai, M. Kowalski k, T. Kowarik ab, M. Krasberg z, T. Krings a,
G. Kroll ab, K. Kuehn q, T. Kuwabara ad, M. Labare l, S. Lafebre ai, K. Laihem a, H. Landsman z, R. Lauer am,
A. Laundrie z, R. Lehmann i, D. Lennarz a, J. Lünemann ab, J. Madsen af, P. Majumdar am, R. Maruyama z,
K. Mase n,, H.S. Matis h, M. Matusik al, K. Meagher p, M. Merck z, P. Mészáros ah,ai, T. Meures a,
E. Middell am, N. Milke s, H. Miyamoto n, T. Montaruli z,2, R. Morse z, S.M. Movit ah, R. Nahnhauer am,
J.W. Nam v, U. Naumann al, P. Nießen ad, D.R. Nygren h, S. Odrowski u, A. Olivas p, M. Olivo aj,j, M. Ono n,
S. Panknin i, L. Paul a, C. Pérez de los Heros aj, J. Petrovic l, A. Piegsa ab, D. Pieloth s, A.C. Pohl aj,3,
R. Porrata g, J. Posselt al, P.B. Price g, M. Prikockis ai, G.T. Przybylski h, K. Rawlins c, P. Redl p, E. Resconi u,
W. Rhode s, M. Ribordy w, A. Rizzo m, P. Robl aa, J.P. Rodrigues z, P. Roth p, F. Rothmaier ab, C. Rott q,
C. Roucelle u, D. Rutledge ai, B. Ruzybayev ad, D. Ryckbosch t, H.-G. Sander ab, P. Sandstrom z, S. Sarkar ae,
K. Schatto ab, S. Schlenstedt am, T. Schmidt p, D. Schneider z, A. Schukraft a, A. Schultes al, O. Schulz u,
M. Schunck a, D. Seckel ad, B. Semburg al, S.H. Seo ag, Y. Sestayo u, S. Seunarine o, A. Silvestri v, A. Slipak ai,
G.M. Spiczak af, C. Spiering am, M. Stamatikos q,4, T. Stanev ad, G. Stephens ai, T. Stezelberger h,R.G. Stokstad h, S. Stoyanov ad, E.A. Strahler m, T. Straszheim p, G.W. Sullivan p, Q. Swillens l, I. Taboada e,
A. Tamburro af, O. Tarasova am, A. Tepe e, S. Ter-Antonyan f, C. Terranova w, S. Tilav ad, P.A. Toale ai,
D. Tosi am, D. Turčan p, N. van Eijndhoven m, J. Vandenbroucke g, A. Van Overloop t, J. van Santen i,
B. Voigt am, D. Wahl aa, C. Walck ag, T. Waldenmaier i, M. Wallraff a, M. Walter am, C. Wendt z,,S. Westerhoff z, N. Whitehorn z, K. Wiebe ab, C.H. Wiebusch a, G. Wikström ag, D.R. Williams b,
R. Wischnewski am, H. Wissing p, K. Woschnagg g, C. Xu ad , X.W. Xu f, G. Yodh v, S. Yoshida n,, P. Zarzhitsky b
aIII. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USAc
Department of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USAd
CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USAe
School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USAf
Department of Physics, Southern University, Baton Rouge, LA 70813, USAg
Department of Physics, University of California, Berkeley, CA 94720, USAb0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.nima.2010.03.102

ARTICLE IN PRESS
140

R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152hLawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germanyj
Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, GermanykPhysikalisches Institut, Universität Bonn, Nussallee 12, D-53115 Bonn, GermanylUniversité Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, BelgiummVrije Universiteit Brussel, Dienst ELEM, B-1050 Brussels, Belgiumn
Department of Physics, Chiba University, Chiba 263-8522, Japano
Department of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealandp
Department of Physics, University of Maryland, College Park, MD 20742, USAq
Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH 43210, USAr
Department of Astronomy, Ohio State University, Columbus, OH 43210, USAs
Department of Physics, TU Dortmund University, D-44221 Dortmund, Germanyt
Department of Subatomic and Radiation Physics, University of Gent, B-9000 Gent, BelgiumuMax-Planck-Institut für Kernphysik, D-69177 Heidelberg, Germanyv
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USAw
Laboratory for High Energy Physics, École Polytechnique Fédérale, CH-1015 Lausanne, Switzerlandx
Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USAyDepartment of Astronomy, University of Wisconsin, Madison, WI 53706, USAz
Department of Physics, University of Wisconsin, Madison, WI 53706, USAaaPhysical Sciences Laboratory, University of Wisconsin, Madison, WI 53706, USAab
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germanyac
Université de Mons, 7000 Mons, Belgiumad
Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USAae
Department of Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UKaf
Department of Physics, University of Wisconsin, River Falls, WI 54022, USAag
Oskar Klein Centre and Department of Physics, Stockholm University, SE-10691 Stockholm, SwedenahDepartment of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USAai
Department of Physics, Pennsylvania State University, University Park, PA 16802, USAaj
Department of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
ak
Department of Physics and Astronomy, Utrecht University/SRON, NL-3584 CC Utrecht, The NetherlandsalDepartment of Physics, University of Wuppertal, D-42119 Wuppertal, Germanyam
DESY, D-15735 Zeuthen, Germanyia r t i c l e in f o

a b s t r a c t

Article history:
Received 4 March 2010
Accepted 6 March 2010
Available online 18 March 2010

Over 5000 PMTs are being deployed at the South Pole to compose the IceCube neutrino observatory.
Many are placed deep in the ice to detect Cherenkov light emitted by the products of high-energy
neutrino interactions, and others are frozen into tanks on the surface to detect particles fromatmospheric cosmic ray showers. IceCube is using the 10-in. diameter R7081-02 made by Hamamatsu
Photonics. This paper describes the laboratory characterization and calibration of these PMTs before
deployment. PMTs were illuminated with pulses ranging from single photons to saturation level.
Parameterizations are given for the single photoelectron charge spectrum and the saturation behavior.
Time resolution, late pulses and afterpulses are characterized. Because the PMTs are relatively large, thecathode sensitivity uniformity was measured. The absolute photon detection efﬁciency was calibratedusing Rayleigh-scattered photons from a nitrogen laser. Measured characteristics are discussed in thecontext of their relevance to IceCube event reconstruction and simulation efforts.
& 2010 Elsevier B.V. All rights reserved.

Keywords:
PMT
Neutrino
Cosmic rays
Ice
Cherenkov

1. Introduction
IceCube [1,2] is a kilometer-scale high energy neutrino
telescope currently under construction at the geographic South
Pole. A primary goal is to detect high energy neutrinos fromastrophysical sources, helping to elucidate the mechanisms for
production of high energy cosmic rays [3].

 Corresponding authors. Tel.: + 608 890 0577.

E-mail addresses: mase@hepburn.s.chiba-u.ac.jp (K. Mase),chris.wendt@icecube.wisc.edu, chwendt@icecube.wisc.edu (C. Wendt),syoshida@hepburn.s.chiba-u.ac.jp (S. Yoshida).

1
Afﬁliated with Universität Erlangen-Nürnberg, Physikalisches Institut,
D-91058 Erlangen, Germany.
2
On leave of absence from Universita di Bari and Sezione INFN, Dipartimento
di Fisica, I-70126 Bari, Italy.
3Afﬁliated with School of Pure and Applied Natural Sciences, Kalmar
University, S-39182 Kalmar, Sweden.
4
NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA.

IceCube uses the 2800 m thick glacial ice sheet as a Cherenkov
radiator for charged particles, for example those created when cosmic
neutrinos collide with subatomic particles in the ice or nearby rock.
Neutrino interactions can create high energy muons, electrons or tau
particles, which must be distinguished from downgoing backgroundmuons based on the pattern of light emitted. The Cherenkov lightfrom these particles is detected by an embedded array of Digital
Optical Modules (DOMs), each of which incorporates a 10 in. diameter
R7081-02 photomultiplier tube (PMT) made by Hamamatsu Photonics. The DOMs transmit time-stamped digitized PMT signal waveforms to computers at the surface.
The ﬁnished array will consist of 4800 DOMs at depths of1450–2450 m, deployed at 17 m intervals along 80 vertical cables,
which in turn are arranged in a triangular lattice with a horizontal
spacing of approximately 125 m. An additional 320 DOMs will befrozen into 1.8 m diameter ice tanks located at the surface to form
the IceTop array, which is designed for detection of cosmic ray air
2
showers. The geometrical cross-sectional area will be  1 km
3
and the volume of ice encompassed will be  1 km . Another 360
DOMs will be deployed in a more compact geometry (‘‘Deep Core’’[4]) using PMTs almost identical to those described here but witha higher efﬁciency photocathode.

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

In this paper we describe measurements characterizing andcalibrating IceCube PMTs, and discuss their relevance to detector
performance and event reconstruction. First we describe thesignals of interest in Section 2. Section 3 brieﬂy describes the
DOMs in which IceCube PMTs are deployed. Section 4 describes
selection and basic features of the PMT, including the darknoise rate. Section 5 presents the design of the HV divider circuit.
Sections 6–9 discuss characteristics of the PMT in the photon
counting regime, starting with single photon waveforms andcharge distributions. Time resolution is studied with a pulsed
laser system. Uniformity of the photon detection response on thephotocathode area is measured by scanning the entire cathodesurface with a UV LED. Absolute efﬁciency calibration of the
IceCube PMTs is carried out using Rayleigh-scattered light from acalibrated laser beam. Sections 10–11 describe response to brightpulses of light, including saturation behavior and afterpulse
characteristics.

2. Characteristics of optical signals in IceCube
We begin by summarizing what the PMTs are supposed todetect, namely the optical signals generated by neutrinos in
IceCube [1,2]. Of particular relevance are the amplitudes andwidths of the pulses, requirements on time resolution, and how
the pulses are used to reconstruct physics events or rejectbackgrounds.
In detection of a high energy nm by IceCube, the neutrino
interaction creates a muon that traverses kilometers of ice andgenerates Cherenkov light along its path. Above 1 TeV, the muon
loses energy stochastically to produce multiple showers of
secondary particles, resulting in an overall light yield proportional
to the muon energy [5,6]. Most light is emitted near the
Cherenkov angle, which is 413 away from the track direction.
The arrival times of detected photons depend on the position ofeach DOM relative to the muon’s path. For close DOMs, mostphotons arrive in a pulse less than 50 ns wide, in which theearliest photons have traveled straight from the muon track
without scattering. Signiﬁcant scattering accumulates along
photon trajectories with a characteristic length scale of about
25 m [7], so light pulses lengthen with distance and reach 1 ms
(FWHM) for DOMs 160 m away from a muon track. Depending on
primary energy and distance from the track, each PMT can see
single photons or pulses ranging up to thousands of photons.
Event reconstruction [1,2,8] builds on principles established
for the predecessor array, AMANDA [9,10]. The observed PMT
waveforms from individual DOMs are correlated and built into
events, which are ﬁtted to physics hypotheses using the
maximum likelihood method. Each ﬁt has access to the complete
pattern of light amplitude and timing seen by the DOMs, andaccounts for the DOMs’ time response and optical sensitivity as
well as time dispersion and optical attenuation introduced by theice. The ﬁt gives the direction and energy of the muon, which inturn characterizes its parent neutrino.
The observed light pattern is also used to distinguish the rare
neutrino events from the large background of muons created incosmic ray air showers, which are 106 times more numerous. For
this the reconstructed direction is key, because neutrinos cancome from any direction, even up from below, but the backgroundmuons are downgoing. A small fraction of background events canbe misreconstructed in direction, thereby appearing to come fromneutrinos, but the pattern of detected light will generally be apoor match compared to expectations for a properly reconstructed track. Misreconstruction can be aggravated by additionalmuons from the same shower or other coincident showers. This
separation between signal and background is accomplished by

141

evaluating relative probabilities on an event-by-event basis, andis aided by good time and amplitude resolution as well as by low
PMT noise rates.
Similar principles apply to other types of high energy neutrino
interaction. Instead of a muon, an electron can be created thatloses its energy in a few-meter-long particle shower [11]; on thescale of IceCube, such a shower appears almost like a point sourceof Cherenkov light. For a sufﬁciently energetic neutrino, the light
can be detected hundreds of meters away, and nearby DOMs cansee enough light to drive their PMTs into the nonlinear saturation
regime. Therefore proper modeling of saturation behavior isneeded for good reconstruction and background rejection.
Design studies [2] for important physics goals have shown that
sufﬁcient reconstruction quality is achieved for a PMT timing
resolution of 5 ns, low-temperature noise rate below 500 Hz, andeffective dynamic range of 200 photoelectrons per 15 ns.
In the case of lower energy (MeV) neutrinos from supernovae,
IceCube cannot resolve individual interactions. Instead, supernovae
would be detected as a momentary increase in the collective photon
counting rate for the whole array, corresponding to a large numberof neutrino interactions within a few seconds. The dark noise rate of
the PMTs is particularly important here, because it dictates thestatistical signiﬁcance of any excess count rate.
IceTop uses DOMs identical to those in the deep ice. Here thesignals arise from muons, electrons and gamma rays in cosmic ray
air showers [12]. These particles deposit energy in the ice tanks
housing the DOMs, resulting in light pulses up to several hundred
nanoseconds long. The arrival times and amplitudes in the surface
array are then used to reconstruct the shower core position,
direction, and energy. An overall timing resolution of 10 ns
provides pointing accuracy of about 11. The PMT pulses range
from single photoelectrons at the periphery of showers to 105
photoelectrons for a 1 EeV shower that strikes within the array. To
achieve the implied dynamic range, each tank contains two DOMs
operating at gains differing by a factor 50.

3. The IceCube optical detector: DOM
The Digital Optical Module is the fundamental element for
both optical detection and data acquisition in IceCube [2,13,14]. It
contains a 10 in. diameter PMT supported by coupling gel, thePMT high voltage generator and divider circuits, an LED ﬂasher
board used for calibration of the array geometry and study of ice
properties, and the DOM mainboard which contains the analog
and digital signal processing electronics [14]. The PMT issurrounded by a mmetal grid to shield it from the terrestrial
magnetic ﬁeld and improve the PMT performance. All systems arehoused within a pressure sphere made of 0.5 in. thick glass,capable of withstanding pressures to 70 MPa. The glass and gel set
the short wavelength cutoff of the DOM at about 350 nm, where
the PMT by itself is still relatively efﬁcient.
Strings of DOMs are deployed into water columns that havebeen melted by a hot-water drill. After refreezing, DOMs are
optically well coupled to the surrounding glacial ice. Signal andpower connections between the DOMs and the surface areprovided by copper twisted-pair wires bundled together to form
the main cables. PMT signals are digitized on the mainboard,
buffered in memory, and sent to the surface upon command of
surface readout processors.

4. PMT selection and dark noise rate
A number of large-area PMTs are commercially available andhave been used successfully to instrument large volumes in otherARTICLE IN PRESS
R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

experiments. IceCube selected the R7081-02 made by Hamamatsu
Photonics, emphasizing the criteria of low dark noise and goodtime and charge resolution for single photons. Some manufacturer’s speciﬁcations are shown in Table 1, and more detailed
measurements are described in the following.
The nominal gain of 107 was chosen to give single photon
pulses around 8 mV, which is well above the digitizer precisionand other electronic noise levels (both  0:1 mV). Aging was not aconcern for gain selection, since at the expected noise rates, thecorresponding total charge delivered by each deep-ice PMT willbe less than 1 C after 20 years (or 100 C for IceTop). Tubes with 10
and 12 stages were evaluated, with the 10 stage options showing
a better peak-to-valley ratio at this gain. Lower gains of 5  106
and 105 were chosen for IceTop PMTs because air shower pulses
generally comprise many photon detections.
The R7081-02 has 10 linear focused dynode stages andachieved the nominal gain of 107 at about 1300 V in our tests
with the recommended divider ratios (observed range 1050–
1600 V for 3744 PMTs). Its 10 in. diameter photocathode iscomposed of the standard bialkali material (Sb–Rb–Cs, Sb–K–Cs)
with a peak quantum efﬁciency of approximately 25% at 390 nm.
With a borosilicate glass envelope, the spectral response [16] is agood match to the spectrum of Cherenkov light after propagation
through ice [7], especially considering the 350 nm cutoff of the
housing.
In response to IceCube requirements, the supplied R7081-02
units were manufactured with a custom low radioactivity glass.
The resulting dark count rate at low temperatures is close to
300 Hz in the 40 to 20 3 C range of greatest interest for IceCube(Fig. 1). The higher room temperature rate can be attributed
mostly to cathode thermionic emission, which is suppressed at
low temperature. The low temperature rate is believed to be
dominated by radioactive decays plus scintillation in the PMT
glass envelope, and shows a rise with decreasing temperaturesimilar to that reported in other studies [17]. The association ofthis rate with decays is supported by time correlations observedon scales up to 1 ms, as can result from delayed particle capture orde-excitation of states created by decays. It is also supported by
the observed effect of taping: for these measurements, the entire
outside surface of the PMT glass was covered in black vinyl tape,pulled tightly against the glass to avoid bubbles. The taping isobserved to reduce the low-temperature noise rate by about half.
The reduction is attributed to absorption of outward going decay
photons, which can otherwise be channeled to the photocathodevia internal reﬂection. The taped result is appropriate for PMTs
installed in IceCube DOMs because they are optically coupled togel (then glass and ice) where the refractive index matches better
than it does for air.
The low dark rate allows IceCube to record all events thatsatisfy simple multiplicity conditions, and is particularly important for observation of any galactic supernova event. Such asupernova could yield about 106 excess photon counts in IceCube
over a few seconds [18]. The single-PMT dark rate, multiplied by
the number of PMTs, contributes a background rate of
1:5  106 Hz, with a similar contribution from decays in the

Table 1
Hamamatsu speciﬁcations for the R7081-02 PMT (typical) [15].
Spectral response
Quantum efﬁciency at 390 nm
Supply voltage for gain 107
Dark rate at 40 3 C
Transit time spread
Peak to valley ratio for single photons
Pulse linearity at 2% deviation

300–650 nm
25%1500 V
500 Hz3.2 ns
2.5
70 mA

Dark count rate (Hz)

142

1000

500

0
–80

–60

–40
–20
Temperature (°C)

020

Fig. 1. Dark count rate versus temperature for a sample IceCube PMT covered withblack tape (see text). Rates were recorded after a settling time of 12 h of dark
operation at gain 107 and discriminator threshold 0.25 times the single
photoelectron peak. An artiﬁcial deadtime circuit rejected additional hits within
6 ms of each count, including about half of all afterpulses (Section 11). The
contribution from cosmic rays (o 5 Hz) has not been subtracted.

DOMs’ glass housing. The excess from a supernova would be
easily observed above this background, even including the detailsof its time structure.
On the other hand, a high energy neutrino event creates opticalpulses distributed over 3 ms, with most information contained
within a time window less than 300 ns wide in each DOM.
Because this window is so short, the low PMT dark rate implies
that only 1% of muons would be accompanied by a relevant noise
count among the 100 DOMs closest to the track, and many ofthese DOMs detect multiple signal photons. Therefore thedegradation of reconstruction and background rejection is verysmall. The dark noise rate has even less effect for IceTop DOMs,
due to higher thresholds and coincidence requirements.

5. High voltage divider circuit
The relative dynode voltage ratios for R7081-02 have been
optimized by Hamamatsu to achieve a maximum collection
efﬁciency while achieving 107 gain between 1050 and 1600 V.
Our high voltage subsystem design fulﬁlls the additional requirements of low power consumption, long-term reliability, andsustained response to very bright pulses lasting up to a
microsecond.
The dynode voltages are provided by a passive resistive divider
with a total resistance of 130 MO (Fig. 2). The rather high total
resistance is chosen to minimize power consumption, which is an
important economic consideration for operations at the South
Pole. A custom, compact, high voltage generator [19] that is both
low power ( o 300 mW) and low noise ( o 1 mV ripple, peak-topeak) is used in conjunction with the passive divider.
Capacitors are placed across the last six dynode intervals andbetween the last dynode and anode. These capacitors help sustain
the PMT output for large pulses of up to 106 photoelectrons (p.e.).
Even for illumination in the PMT saturation region (  200 p:e:=ns,
see Section 10), the transient gain loss after a 1 ms pulse(2  105 p.e.) is observed to be less than 1%. A detailed simulation[20] indicates that such a pulse could arise from a 50 PeV electron
shower 100 m away from the PMT, which would then be faithfullyrecorded. Pulses up to ﬁve times this large (106 p.e.) still result inless than 20% transient gain loss, so while the primary pulse
would be completely saturated, afterpulse amplitude could be
used to estimate the total illumination (Section 11). Finally above

ARTICLE IN PRESS
R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

K

DY1 F2F1 F3DY2

DY3 DY4DY5 DY6DY7 DY8

DY9 DY10

R13
100

R15
100

R14
100

143

P

Front-end
Amplifier
T1

95Ω

R16
100

95
+

R1
52.5M

R2
R3
R4
R5
R6
R7
R8
R9 R10 R11
1.9M 10.5M 15.4M 10.2M 5.1M 3.1M 3.7M 4.6M 6.8M 9.3M

R12
7.5M

Pedestal

–

R17
100K
Ferrite

C1
C2
C3
C4
C5
C6
C7
3.3nF 4.7nF 4.7nF 4.7nF 10nF 10nF 22nF

R18
100K

+

–

PMT High Voltage
Fig. 2. Schematic of the passive HV divider circuit, shown with coupling to the front-end ampliﬁer on the digitizer board.

0
Signal (mV)

2  107 p.e. the gain loss rises rapidly above 50%. For all thesetransient gain losses, recovery occurs within the RC time
constants of order 1 s.
Low-inductance resistors (100 O, R13 through R15) are used todampen ringing that arises from coupling of the larger dynodeﬁlter capacitors with parasitic inductance in the dynode leads andprinted circuit traces. This ringing could otherwise be a nuisancewhen reconstructing a single PMT output waveform as a series ofphoton hits.
The IceCube PMTs are operated with their cathode at ground
potential. Therefore the high voltage anode is AC coupled to the frontend ampliﬁers. For the AC coupling, we use a custom biﬁlar-wound
1:1 toroidal transformer rather than a DC blocking capacitor. High
voltage reliability is achieved in the transformer winding using wirewith insulation rated for over 5 kV DC. The resulting stray capacitancefrom anode to front-end ampliﬁer is only 30 pF, which limits thestored energy which might damage the analog front-end if sparking
should occur in the HV system. In contrast, a coupling capacitor large
enough to meet the signal droop speciﬁcation would be at least 1000
times larger than the stray capacitance of the transformer. The
transformer topology also reduces noise by avoiding noisy highvoltage ceramic signal coupling capacitors and by breaking a groundloop path involving the HV power supply. The ferrite and resistors inseries with the HV supply further reduce coupling of high frequency
noise to the front end input.
The transformer coupling delivers good signal ﬁdelity for singlephotoelectron (SPE) waveforms with risetimes of a few ns, whiletransmitting wide pulses exceeding 1 ms with less than 10% droop
and undershoot. The custom design uses 18 biﬁlar turns on a ferrite(Magnetics Type H) toroid core, providing roughly ﬂat coupling from
8 kHz to over 100 MHz at operating temperatures down to 40 3 C.
The self-resonant frequency is above 150 MHz. The low operation
temperature presented a challenge because the permeability of thetransformer core decreases rapidly with temperature, leading to ashorter droop time constant. Although most DOMs have a time
constant around 15 ms at ambient temperatures near 30 3 C, 1200
DOMs were built using an older transformer design yielding a time
constant around 1:5 ms at 30 3 C. The improved performance of the
new design was achieved with a larger core and more turns, at theexpense of a slightly wider SPE pulse shape (Fig. 3). The two designs
are deployed intermixed.
The droop and undershoot are relevant for the ms long trains ofphoton pulses expected in DOMs over 100 m away from high

–4

–8
0

20
Time (ns)40

Fig. 3. Average of 10,000 SPE waveforms for one PMT at gain 1  107, as seen at
the secondary of the AC coupling transformer. Results for other PMT samples arevery similar. The solid and dashed curves correspond to new and old transformer
designs discussed in Section 5.

energy events, such as 10 TeV electron showers or 500 TeV muontracks. The small remaining effects are corrected by a software
digital ﬁlter as a ﬁrst step in event reconstruction, based on
individual time constants for each DOM. The residual error istypically less than 1% of the pulse amplitude (except for pulses
with peak or undershoot outside the ADC dynamic range, which islimited after 400 ns [14]).
The divider circuit is constructed on a 10 cm-diameter printed
circuit board which is directly solder-mounted to the PMT. Allcomponents (except R13–R16) are through-hole mount type,selected with a voltage derating factor of two or greater (typicallyfour) to ensure long-term reliability. Strict voltage and voltage
gradient rules are applied to the board layout.
Coaxial cables are used for the connections to the high voltage
generator and the front end ampliﬁer on the digitizer board. The
effective load for anode output pulses is 50O (43O for the oldertransformer design), which includes a back-termination resistor
on the primary side of the transformer (R16), the transformer AC
response, and the input impedance of the ampliﬁer.

6. Single photoelectron waveform and charge
The SPE waveform shape and charge probability distribution
are important for event reconstruction. The DOM waveform

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

coincidences of noise pulses such as from thermionic emission at
the dynodes. The check for a noise contribution was done with the
LED light output disabled (but not the synchronization signal thattriggers acquisitions); all counts outside the narrow pedestal
region were greatly suppressed compared to Fig. 4.
The low-charge component has been described in the past for
many PMTs [21], and has been attributed to a sizable probability
for backscattering of the primary photoelectron at the ﬁrst
dynode [22,23], leading to events where only a few secondaries
are produced instead of the usual 10–20.
The shape of the low-charge component is important becauseeven small pulses below the DOM’s trigger threshold will berecorded in events with multiple photoelectrons. Therefore event
reconstruction should account for the entire charge probability
distribution down to zero charge, which we model as a Gaussianplus an exponential term [21]:
"
#


Pe
q
1
ðqq0 Þ2
þ ð1Pe Þ pﬃﬃﬃﬃﬃﬃ
:
ð1Þ
exp 
exp 
f ðqÞ ¼
qt
qt
2s2q
2psq
Here Pe is the fraction of events in the low-charge exponential
part, q0 is the charge at the SPE peak which deﬁnes the PMT gain,
sq is the width of the Gaussian ﬁt around the SPE peak, and qt isthe decay constant in the exponential component. Fig. 4 showsthat this is a good model for the shape of the charge histogram
away from the pedestal.
Fig. 5 shows results of ﬁtting equation (1) for a large sample of
PMTs at different gains above 5  107, excluding the very low
charge region q o 0:15q0 and the very high charge region morethan 2s past the peak. The value of qt =q0 is substantiallydegenerate with Pe for describing observed spectra in the ﬁtted
range, so it has been ﬁxed at the representative value of 0.20. The
scaled quantities sq =q0 , qt =q0 , and Pe are found not to varystrongly with the PMT gain. The very small pulses with q o0:15q0
were omitted to avoid confusion with the tail of the pedestal
distribution; results were the same if the low-charge cut was
moved to 0.25q0. The charge resolution sq =q0 has been separately
studied for gains between 107 and 108 and again no signiﬁcantvariations were seen.
Fig. 5 also shows the spread in parameters from PMT to PMT.
The distribution in each parameter is approximately Gaussian,

0.4
Pe

digitizers are triggered when the signal reaches about 0.25 times
the typical SPE peak amplitude, after which the PMT output
waveform is digitized for up to 6:4 ms. The detection efﬁciency forsingle photons depends directly on the fraction of the SPE charge
distribution above trigger threshold. For high energy neutrino
events, many waveforms show contributions from multiple
photons, all of which could provide useful information during
event reconstruction. The overall light yield provides an estimateof the neutrino energy, and the space and time distribution oflight helps to reconstruct direction and reject backgrounds. The
time distribution of photons can be extracted from each PMT
waveform if the response to single photons is well understood.
The response to each photon is approximately given by theaverage SPE waveform, scaled randomly according to thecomplete charge probability distribution.
In order to mimic the ambient temperature in the ice, PMTs
were placed in a freezer box at 32 3 C and illuminated by diffusedlight from a 375 nm UV LED. The light was generated in 10 ns
pulses with intensity of about 0.1 photons per shot (  0:02
photoelectrons per shot), dim enough to initiate only SPE signals.
Fig. 3 shows the average SPE waveform, measured at theoutput of the AC coupling transformer with a digital storage
oscilloscope (LeCroy LT374, 500 MHz bandwidth, 0.5 ns samples).
Here the 95 O input impedance of the DOM’s front end ampliﬁer
was replaced by the series combination of a 50 O resistor and theoscilloscope input.
Individual waveforms have different amplitudes but theirshapes are similar to within a few percent. The waveform isdominated by a peak of Gaussian shape (s ¼ 3:2 ns) which
accounts for 83% of the area. A tail on the late side of the peakaccounts for the remaining area and exhibits a small amount ofringing. About 90% of the charge is collected before 10 ns after the
peak. A substantial part of the observed pulse width is attributed
to the damping resistors and the coupling transformer (Section 5).
To study the total charge in SPE events, a computer-controlled
integrating ADC module (LeCroy 2249A) was used to integrate
charge in a 70 ns window, triggered by the synchronization signalof the LED pulse generator. Fig. 4 shows a typical charge
histogram, which exhibits a clear SPE peak to the right of thepedestal peak. The Gaussian part of the SPE peak corresponds to acharge resolution of approximately 30%.
The non-Gaussian component rising below 0.3 times the SPE
charge in Fig. 4 has been studied to verify that such small pulses
actually reﬂect in-time detection of photons, and not accidental

Data

106

0.2

Model
Model (Scaled)
0Gaussian Fit

104

0

5

0

5

10

15

10

15

Pedestal Fit
103
0.4

102
σq / q0

Counts per bin

105

101

0.2

0

10

0

5

10
Charge (pC)

15

20
0
7

Fig. 4. Typical pedestal-subtracted SPE charge histogram at gain 5  10 ,including pedestal peak. Fits refer to Eq. (1), with the constraint qt =q0 ¼ 0:2. The
remaining parameters are optimized to ﬁt this histogram for the curve labeled‘‘Model’’, while ‘‘Model (Scaled)’’ optimizes only the scale parameter q0 while
holding sq =q0 and Pe at values that describe the average of 120 PMTs.

Gain / 107
Fig. 5. Scaled parameters from Eq. (1) as a function of PMT gain. The error bars
show the 1s spread in parameters obtained for a sampling of 115 PMTs.

ARTICLE IN PRESS
R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

with the width shown by the error bars. The spread is substantial,
but is not expected to have a large effect on data analysis, so the
IceCube PMTs do not need to be parameterized individually.
Instead, an average model is currently used in event simulation
and reconstruction, without modeling the spread. The similarity
among PMTs can also be gauged from Fig. 4, where data from one
PMT is compared with a model curve scaled from the average ﬁtresults for 120 PMTs.
The above measurements were performed with diffuse lightand represent an average over the photocathode surface. In a
separate measurement at gain 107, substantial differences wereobserved as a function of position; for example, the peak-to-valley
ratio decreased to near unity close to the edge of the photocathode, compounding the effects of gain variation (Section 8).

7. Time resolution
The timing of recorded SPE waveforms, relative to the photon
arrival time, was studied at 40 3 C using fast pulses (FWHM 50 ps)
from a Hamamatsu PLP-10 diode laser. Pulses were opticallyattenuated and diffused over the PMT face, yielding an average of0.04 photoelectrons per shot. The wavelength was 405 nm.
Each PMT was set for gain 107 based on its SPE charge
spectrum. Hits greater than 0.4 times the SPE charge wererecorded using the DOM digitization and readout electronics.
Synchronization pulses from the laser were also digitized toindicate the true photon arrival times to within a ﬁxed offset. Hittimes were deﬁned as the points where each waveform reached
50% of its maximum, resulting in the time resolution histogram ofFig. 6.
The main peak of the time histogram has width equivalent to a
Gaussian of s ¼ 2:0 ns, although the rising and falling edges of thepeak ﬁt better to half-Gaussians with s ¼ 1:2 and 2.7 ns,
respectively. Some of the width can be attributed to simultaneous
illumination of the entire photocathode in our tests. Whenilluminated at the center only, the width decreased to 1.5 ns;
conversely, the outer 3 cm of the photocathode exhibited
additional delay of about 3 ns and additional broadening. The
data acquisition system contributed a time smearing of less than
0.6 ns, which has not been subtracted.

105

Counts / ns

104
103
102
101
100
–50

0

50

100

150

Hit time (ns)Fig. 6. Typical distribution of SPE hit times for an IceCube PMT, when illuminatedby narrow pulses from a diode laser. Counts are shown for 1 ns time bins,
referenced to a laser synchronization pulse. A small fraction of late pulses (dashedline) are due to laser afterglow plus the random background count rate; hit
fractions described in the text are corrected accordingly. The random backgroundalso explains the counts before the synchronization pulse.

145

About 4% of hits are found in a shoulder (25–65 ns) andsecondary peak at 71 ns, and 0.2% make up a corresponding
tertiary structure (85–160 ns). The delayed hits are believed toarise when an electron trajectory is scattered back from the ﬁrst
dynode towards the photocathode, where it turns around andthen eventually arrives back at the ﬁrst dynode to initiate thepulse [23–25].
Because of strong photon scattering in the ice, the dispersion of
hit times by the PMT at the 2 ns scale is not a limiting factor forreconstruction in IceCube; likewise for the tail at late times.
Considering the spacing between DOMs, photons must typicallytravel tens of meters before detection, which is comparable to thescattering length of around 25 m [7]. A detailed simulation ofphoton scattering [26] showed that at 10 m distance, about 40% of
photons are delayed by more than 5 ns, and 10% of photons aredelayed between 20 and 80 ns. This is larger than the corresponding effects from the PMT itself. On the other hand, DOMs close to ahigh energy track can be expected to detect at least one photonwith negligible delay, and then the very small 1.2 ns dispersion on
the early side of the time resolution peak may be relevant whenreconstructing arrival time of the earliest photon or the pulse risetime.
The time resolution study also reveals DOM-to-DOM differences in the nominal delay of SPE waveforms relative to photon
arrival time. This delay includes PMT transit time plus signal
delays between the PMT output and the digitizer. The PMT transit
time is found to vary according to the square root of the applied
voltage,pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð2Þ
Ttransit ðVPMT Þ ¼ T0 þ 2kV0 V0 =VPMT
where k ¼ 0:017 ns=V is the slope at V0 ¼1500 V. The voltage
applied to each PMT is set for a design gain 107, which is achieved
between 1050 and 1600 V in 99.9% of PMTs. The resulting RMS
spread of the overall time offset is 2.7 ns. We ﬁnd 5% of DOMs
more than 5 ns away from the mean, so the DOM-to-DOM
corrections are currently included in reconstruction.

8. Two-dimensional photocathode scan
The number of photons arriving at the PMT is calculated fromthe observed photoelectron signals via the PMT optical efﬁciency.
This is separated into an overall ‘‘absolute efﬁciency’’ and anangular dependence. The dominant factor in angular dependence
is just the amount of photocathode area which can be seen fromvarious directions. However, this has to be adjusted for the factthat the photocathode surface is very large and different portions
do not all yield the same efﬁciency.
We have systematically analyzed the variation of efﬁciency
with photocathode position at 25 3 C, using a two-dimensional
scan system. A UV LED (370 nm) with collimator produced a 1 mm
spot which was moved along the curved PMT surface, maintaining
normal incidence of the light. The LED delivered approximately
125 photons per 80 ns pulse. The anode voltage was set for gain
107 at the center of the photocathode, as measured by the SPE
charge peak (q0 in Eq. (1)). The PMT pulse charge for each position
was then measured by an integrating ADC triggered by the LED
pulser.
Fig. 7 shows typical response maps on the cathode surface. The
measured charge is proportional to the net photomultiplierefﬁciency and reﬂects the combined position dependence ofphotocathode quantum efﬁciency, collection efﬁciency, anddynode multiplication. PMT to PMT variation of the efﬁciency at
a given spot on the photocathode may be as great as 40%,
however, the spread in the area-integrated efﬁciency from PMT to
PMT is much smaller, of order 10% (see Section 9). The average

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Fig. 7. Position dependence of the light pulse response for three example PMTs, and the average of 135 PMTs (lower right). The X–Y coordinates measure distance from thecenter of the photocathode along the curved PMT face. The value at each X–Y position indicates the PMT output pulse charge in units of the SPE charge, averaged over many
pulses.

map shows a uniform falloff in the edge region, except for a small
bias in the + X direction. All PMTs were measured in the sameorientation, so this bias could be associated to the ﬁrst dynode
position or the geomagnetic ﬁeld.
A small part of the variation seen in the scans can be attributed
to systematic errors, which arise mainly from the geomagnetic
ﬁeld and LED luminosity variance. The geomagnetic ﬁeld of
462 mG is attenuated by about 50% with a shield made of m- metal
sheet and wire, as also used in IceCube DOMs. By comparing
measurements with the PMT rotated from its standard orientationin various ways, we determined the ﬁeld’s effect on the efﬁciency
variation is about 10%. Because the magnetic shield is the same,the overall results are representative of what is expected for
deployed IceCube DOMs. (The ﬁeld at the South Pole is 553 mG,and more vertical relative to the PMT axis.) The time dependenceof LED luminosity affected the shape of each scan by less than 2%,
as seen by reproducibility of the scan results.
By reducing the light intensity to give only SPE hits, a similar
map has been constructed for gain variation. The gain can vary as
a function of position because the corresponding photoelectron
trajectories arrive differently at the ﬁrst dynode, leading todifferent yields of secondary electrons. The observed gain (deﬁned
by q0 in Eq. (1)) varies within 7 10% over the active region whenhigh voltage is set for gain 5  107 at the center. However, thelow-charge contribution to the SPE charge spectrum (Pe in Eq. (1))
was found to also vary with position, so that the peak-to-valley
ratio decreases close to unity near the edge of the photocathode.
In this way, the average charge delivered per photoelectron wasobserved to decrease by up to 30% at nominal gain 107. Because of
these effects, the detection efﬁciency map for single photons
using a speciﬁc discriminator threshold can differ somewhat fromthe maps of Fig. 7.
The integrated sensitivity for a broad beam of photons incident
from a particular direction follows from the cathode efﬁciency
maps by averaging over the surface seen from that direction [27],with correction for non-normal incidence on surface elements asappropriate [28]. For this purpose the relative efﬁciency map isassumed not to vary with wavelength, i.e., each position isassumed to obey the spectral response curve given by the
manufacturer [16]. The averaging substantially reduces the effectof variations over the surface so the sensitivity is not strongly
dependent on direction at moderate polar angles. Only light that
arrives at large polar angles relative to the PMT axis will primarily
illuminate the equator region and therefore show strong azimuthal dependence. Likewise, the variation in charge spectrum
from center to edge has little effect after averaging.
The scans were performed on a small fraction of the IceCube
PMTs, so only the average variation with polar angle is used in

ARTICLE IN PRESS

9.1. Technique
Our setup for measuring a PMT’s UV photon detection efﬁciency isshown in Fig. 8. A pulsed 337 nm laser beam is passed through achamber containing pure nitrogen gas, and the PMT to be calibrated isilluminated by the tiny amount of light that is Rayleigh scattered atabout 901 from the beam. The PMT is rotated inside the dark box toprobe different positions on the photocathode surface. The primarybeam intensity is measured with a calibrated silicon photodiode‘‘energy probe’’, and sets the fundamental scale for our efﬁciency
measurement. A pressure gauge and temperature sensor provide thegas density. Beam intensity, geometry and gas density are then foldedwith the well-known Rayleigh scattering cross-section to obtain theabsolute number of photons per pulse incident on the PMT. Individual
photon detections are counted in each pulse and divided by the
number incident to obtain the optical sensitivity at 337 nm.
Additional corrections (Section 9.4) are needed to obtain DOM
efﬁciency at wavelengths around 400 nm where IceCube is mostsensitive.
The measurement combines effects of quantum efﬁciency andcollection efﬁciency, and can be directly applied in IceCube
analysis. It is different from the usual quantum efﬁciency
measurement, which is based on cathode current response to acalibrated DC light source [16,30].
The laser (Spectra-Physics VSL-337ND-S) emits 4 ns pulses
containing  1010 photons, as measured by the silicon photodiode probe (Laser Probe, Inc., RjP-465). After a warm-up delay,
pulse energies are stable to within 72%.
The beam width is 1 mm, so the illuminated gas volume may beconsidered as a line source of Rayleigh scattered light. Apertures
between the beam and the PMT deﬁne a source region with effective
length of about 1 cm and a spot size on the PMT of about 1.5 cm.
Photons can reach the PMT if they are scattered from the source
region into a solid angle of about 7.6  10  4 sr around the 903

147

Photodiode 2

Iris (1mm)
Shutter
Neutral Density Filter (1%)
Neutral Density Filter (0.1%)
Polarizer (45°)
Depolarizer
Chamber, 60cm DIA

9. Absolute efﬁciency calibration
The absolute calibration of PMT optical efﬁciency is importantbecause IceCube uses the observed number of photons to estimate
energy in reconstructed neutrino interactions. Showers initiatedby electrons or tau leptons yield light in proportion to the energy,
and so do muons above 1 TeV where energy loss is dominated bydirect pair production, photonuclear interactions and bremsstrahlung [5,6].
Optical efﬁciency can be studied after deployment by using
light from muons (produced in cosmic ray showers above
IceCube) or from calibrated beacons deployed in the ice nearby.
However, it is hard to isolate the PMT response from the effects oflight scattering and attenuation in the ice, which have someuncertainties [7].
Here we describe the laboratory calibration of standard PMTs
installed in 16 IceCube DOMs distributed throughout the array.
The calibrated PMTs provide direct information for the energy
calibration of IceCube, and will also help clarify the ice effects inother studies, which is an important subject on its own.

337 nmsimulation and reconstruction. For IceCube, the remaining PMTto-PMT variation in directional sensitivity has very small
consequences, because light is typically scattered after travelingabout 25 m through the ice, and additional scattering takes placein the refrozen ice in the hole where the DOMs are deployed. The
PMT-to-PMT variation, as well as the position dependence itself,
could be more important for detectors deployed in water where
scattering lengths are much longer [29].

Laser

R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Backward
PMT (H7195)

R7081-02 PMT

Forward
PMT (H7195)

Rotation Stage

Photodiode 1
Fig. 8. Schematic view of the absolute calibration system. Photodiode 1
establishes the beam intensity, which is used to predict the amount of Rayleighscattered light reaching the R7081-02 PMT. The Hamamatsu H7195 PMTs and theother photodiode are for monitoring. Optical bafﬂes deﬁne the scatteringgeometry, and chamber windows are anti-reﬂection coated UV quartz (R o 0:1%
at 337 nm).

direction, while other scattered photons are eventually absorbed on
bafﬂes or other surfaces inside the chamber.
The Rayleigh scattering cross-section for a circularly polarized
beam on nitrogen gas is taken as [31]dsR
3¼
ð1þ cos2 yÞ  ð3:50 7 0:02Þ  1026 cm2
dO
16p

ð3Þ

with y as the polar angle relative to the beam direction. The
geometrical integration over the source region and corresponding
solid angles is handled in a detailed ray-tracing calculation. Afteraccounting for pressure and temperature, this yields the overall
number of scattered photons reaching the PMT, typically 0.5 perpulse. With detection efﬁciency around 20%, this corresponds to 0:1 SPE per pulse.
For counting photon detections, the PMT output charge is
integrated for each laser pulse with a CAMAC ADC. The gatingtime is 184 ns which is long enough to include the late PMT pulses
described in Section 7. The PMT gain is set close to 108 as deﬁned
by the SPE peak, q0 in Eq. (1). We then count the number of eventswith charge q greater than a threshold qth ¼0.5q0, which can beclearly discriminated in the charge histogram. A small correction
for events with multiple photoelectrons yields the number ofdetected photons with q 4qth .
The PMT efﬁciency Z for qth ¼0.5q0 is then given by comparing
the number of detected photons to the number reaching the PMT.
The efﬁciency for other charge thresholds can be computed byextrapolation with the SPE charge response model, Eq. (1).
9.2. Results
Fig. 9 shows the measured detection efﬁciency as a function of
distance from the cathode center. It also shows that the absolute

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

Fig. 9. Detection efﬁciency as a function of distance from the cathode center for three different PMTs. The points with error bars show absolute efﬁciency measurements
extrapolated to qth ¼ 0. The histogram curves show corresponding results from the 2D relative efﬁciency scans (Section 8) after normalization. Systematic uncertainties forthe histograms are described in Section 8.

Table 2
Measured photon detection efﬁciency (Z) and photon effective area (Aeff) at 25 3 C
for four different PMTs at wavelength 337 nm and gain 108.
PMT

TA1895
TA2086
TA2349TA2374(qth ¼ 0)

Aeff (cm2)(qth ¼ 0.5q0)

Aeff (cm2)(qth ¼ 0)

18.6
18.8
17.6
17.8

84
87
77
83

119
120
112
114

Zcenter (%)

Zwhole (%)

Zwhole (%)(qth ¼0.5q0)(qth ¼0.5q0)

16.4
16.5
15.1
16.4

13.2
13.6
12.1
13.0

Values for qth ¼ 0 were extrapolated using Eq. (1), where model parameters wereﬁt independently for each PMT.

efﬁciency measurements follow closely the shape expected fromthe 2D relative efﬁciency scans (Section 8). Consequently, therelative efﬁciency scans can be normalized to the absolutemeasurements and used to estimate the absolute efﬁciency
averaged over any given area of the photocathode surface.
Table 2 lists measured efﬁciencies at the center and averaged
over the whole photocathode area. The latter is deﬁned to include
all points within 15 cm of the PMT axis, measured along the
curved surface. Table 2 also includes the photon ‘‘effective area’’
which means the amount of ideal surface with 100% efﬁciency
that corresponds to the actual convolution of area and efﬁciency.
Here it is quoted for light uniformly spread over the PMT surface,with normal incidence. For use in IceCube analysis, a similarcalculation is performed for unidirectional beams as a function of
the beam angle, folding in the variation of cathode response andoptical effects at material boundaries.
The detection efﬁciencies in the central area of the photocathode are close to 20% if extrapolated to qth ¼ 0. These values
have been compared on a PMT-by-PMT basis with measurements
by Hamamatsu using cathode response to DC light sources. We
ﬁnd very good agreement, which implies that the collection
efﬁciency is not much less than 100% at the cathode center.
IceCube PMTs operate at lower voltages than used in thismeasurement (gain 107 instead of 108), so collection efﬁciency is
expected to be slightly lower. However, this effect is expected tobe concentrated at the edges where the electron optics are lessideal, and the efﬁciency falloff near the edges is obtained from the2D relative efﬁciency scans (Section 8). Since those scans weredone at gain 107, no additional correction is necessary for the
results in Table 2.
9.3. Uncertainties
The overall systematic uncertainty DZ=Z of the PMT detection
efﬁciency measurement is 7.7%, as detailed in Table 3. In addition,
the measurement of each position on the PMT face has a typicalstatistical uncertainty of about 5%, set by the number of SPE hits
recorded. This is reduced to about 2% when calculating efﬁciency

Table 3
Systematic error budget for the PMT efﬁciency calibration.
Source

DZ=Z (%)

Laser beam energy
Aperture
Ambient magnetic ﬁeld
Pressure and temperature
Polarization
Rayleigh cross-section
Dark noise/cosmic rays

5
4
4
1
1
0.5
0.2

Overall

7.7

for the whole PMT by combining information from the individual
face positions, but the extrapolation relies on the 2D map (Section8) which has comparable uncertainties.
The dominant contributions to systematic error arise from thelaser beam energy measurement, the geometry of the scatteringchamber, and the geomagnetic ﬁeld. The ﬁrst two enter directly
into the calculation of the number of photons reaching the PMT.
The beam energy comes from the laser energy probe, which wasfactory calibrated to within 5% at 337 nm. The aperture uncertainty of 4% comes from geometrical survey of the chamber,which is used in the ray tracing program.
The ambient geomagnetic ﬁeld is 462 mG and is unshielded in
the current setup. By changing the orientation of the PMT, we
showed that it affects the point-to-point response map at the 20%
level but the average over the surface varies by only 4%.
The Rayleigh scattering angular distribution depends on thepolarization of the laser beam [32], so care was required to limit
any polarization effect. The effect can be strong because the PMT
only sees a Rayleigh scattering signal from the vertical componentof polarization: the horizontal component induces a dipole
moment oscillating perpendicular to the beam in the horizontal
plane, which cannot emit power to the PMT which is in the same
direction. On the other hand the energy probe reads the total
power regardless of polarization, so the fraction of power in thevertical direction must be under control. In our setup (Fig. 8), thelaser beam is ﬁrst linearly polarized at 453 and then passed
through a quartz l=4 waveplate to convert it to 100% circularpolarization. By rotating a linear polarizer in the beam, we
veriﬁed that the resulting horizontal and vertical components areequal to within better than 1%, which leads to a limit of 1% for thecorresponding systematic effect on the efﬁciency measurement.
Several analyses were performed to show that the scatteredphotons are coming from Rayleigh scattering and not othersources such as residual suspended dust. We checked for
expected scaling with gas density down to low pressure,symmetry of scattered light seen in forward and backward

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

9.4. Additional corrections
There are additional steps to obtain the detection efﬁciency of
DOMs from the PMT efﬁciency measurements, and these will bereported separately along with other studies on assembled DOMs.
Corrections include attenuation of light in the glass pressure
housing and the gel used for optical and mechanical coupling,
wavelength dependence in both the PMT sensitivity (quoted by
the manufacturer [16]) and the attenuation factors, and thegeometry of incident rays. These effects are included in a detailed
optical simulation of the DOMs [27,33] which will be compared tolaboratory measurements on assembled DOMs. A full detector
simulation can be used to combine the absolute efﬁciencies at
337 nm, the wavelength dependences, and the spectrum of lightreceived from neutrino interactions. Investigations of the combined effect show that IceCube detects signal photons in a broad
range centered on about 400 nm. These studies will be presented
elsewhere.
Our measurements were at 25 3 C, and some temperaturedependence can be expected. The manufacturer quotes a temperature coefﬁcient of 0:2%= 3 C for cathode sensitivity [16]. This is being
directly addressed by relative measurements of optical efﬁciency ofassembled DOMs at 45, 20 3 C and room temperature.

10. PMT linearity and saturation behavior
For most neutrino interactions expected in IceCube, any one
PMT will not detect more than a handful of photons. For such
events, and even when up to a few hundred are detected, the PMT
output is proportional to the number of photons detected.
However, some of the most interesting signal events would be
expected to deposit large amounts of energy within tens of metersof individual PMTs, and then the PMT response can be less thanproportional. Optimal reconstruction requires measuring thelinearity limit and modeling the nonlinear saturation behavior.
To study saturation behavior, PMTs were illuminated with LED
pulses of various durations and brightnesses. The duration of thelight pulses was varied from 3 ns to 1 ms, as measured with a fast PIN
photodiode (1 ns response time). A set of calibrated neutral density
ﬁlters was used to control the light level. For a given LED brightness,
illumination was ﬁrst measured by the PMT signal, using a ﬁlter
with sufﬁcient attenuation to allow linear operation of the PMT. The
observed signal was converted to a photoelectron rate and a total
number of photoelectrons (p.e.) using the SPE charge q0, determinedin a separate step. Then the illumination level was increased byusing different ﬁlters, with the new number of p.e. calculated fromthe ratio of ﬁlter attenuation coefﬁcients.
Fig. 10(a) shows the observed peak anode current I as afunction of the ideal peak current I0, deﬁned as the peak p.e. ratetimes the SPE charge. At gain 107, the PMT response is linear
within 10% up to currents of about 50 mA (31 p.e./ns), but
saturates completely at about 150 mA. Peak responses todifferent light pulse widths from 3 to 400 ns lie along a single
curve. The 3 and 20 ns width pulses were approximately Gaussianin shape, so the observation of identical peak response supports asaturation model where the observed current is a direct function

102
Ideal (linear)
Width 400 ns
I = Measured Current (mA)monitoring PMTs (see Fig. 8), and repeatability of measurements
after long time intervals.
The main systematic uncertainties in our method could be
reduced if desired, comparable to the current statistical precisionof about 2%. To accomplish this, one would calibrate the silicon
photodiode ‘‘energy meter’’ at the 1% level; measure the aperture
geometry more precisely; and provide good shielding from thegeomagnetic ﬁeld.

149

Width 20 ns
101

Width 3 ns
Fit

102

Gain 107
Gain 5×106

101

Gain 5×105
Gain 105
101

102

103

104

I0 = Ideal Current (mA)
Fig. 10. (a) PMT saturation curve for gain 107. The measured current is plottedagainst the instantaneous light level, deﬁned in terms of the current that would be
expected for an ideal (linear) device. Data points correspond to peak currents forthe indicated pulse widths. The ﬁt curve is given by Eq. (4), with parameterschosen optimally for this PMT (serial number SA2747). (b) Effect of PMT gain on
the saturation curve. Data points correspond to peak currents for 200 ns pulses for
PMT serial number AA0020. The curves show the ﬁtted parameterization, Eq. (5).

of the instantaneous illumination, with little cumulative effectfrom previous illumination. In particular the data are inconsistent
with models expressed in terms of total pulse charge, which wereused in some older versions of the IceCube simulation software.
The 400 ns pulses were approximately rectangular in shape andthe output current mirrored this shape well even in the saturation
region, again as expected for an instantaneous current saturation
model. Even long light pulses near saturation level show only
about 5% decline from 100 mA after 1 ms of steady illumination.
(Note this small history effect is independent of the transient gain
loss due to discharge of the dynode capacitors, which remains
below 1% for such a pulse.)
The same saturation behavior was found to apply regardless ofwhat part of the cathode was illuminated, even at 30 3 C, whichindicates that photocathode surface resistance [16] is notimportant on the relevant time scales.
The instantaneous current response is well parameterized by
the following:ln I0 ¼ ln I þ C

ðI=AÞBð1I=AÞ1=4:

ð4Þ

The parameters A, B and C differ substantially from one PMT toanother (Table 4), so the model should not be used to invert
observed saturated pulses unless each PMT is fully characterized.
Fig. 10(b) shows additional measurements at a range of lower
gains down to 105, relevant for IceTop DOMs. The model of Eq. (4)continues to apply over the full range if the parameters are scaled
approximately as powers of the gain, as shown by the curves
which are scaled by g  Gain=106 :AðgÞ ¼ 285g0:52 =ð1 þ g1=4 Þ2BðgÞ ¼ 13g0:18 =ð1 þ g1=4 Þ2CðgÞ ¼ 0:32g0:13 ð1þ g1=4 Þ2 :

ð5Þ

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

The given parameters apply to a single measured PMT, but similar
scaling behavior can be expected for other examples; as a ﬁrst
estimate one would adjust the leading coefﬁcients in eachparameter to match measurements at a particular gain, andretain the same scaling with gain. Note the good numericalbehavior of the scaling equations allows them to be used also for
estimates outside the given range of gain.
The instantaneous current model also helps understand how
the response to narrow light pulses (3 ns FWHM) broadens as
intensity increases (Fig. 11). With the light pulse strongly
attenuated (220 p.e.), the PMT output pulse width is similar to
the SPE response, about 10 ns. As more light is allowed to reachthe PMT (3700 p.e.), ﬁrst a gradual broadening occurs to about
20 ns width. This broadening follows from Eq. (4) because thepeak current is more attenuated than the rising and trailing edges.
At this point a tail is visible, along with a second peak delayed byabout 60 ns relative to the main peak. These are consistent withthe late photoelectron responses seen in SPE time resolution
measurements (Section 7), except that the relative sizes of main
peak and tail are altered by saturation in the main peak. At still
higher light levels (210,000 p.e.), the second tail peak iscomparable in size to the fully saturated main peak, and thetotal width is dominated by the combination of the two peaks.
The highest light level in Fig. 11 also exposes a small pre-pulse
30 ns before the main peak, as well as a substantial afterpulse
starting several hundred ns later (see Section 11). The pre-pulse isascribed to photoelectrons ejected from the ﬁrst dynode, and issomewhat exaggerated in Fig. 11 because the light source wasaimed at the center of the cathode with the dynode directly

behind. The individual quanta comprising the pre-pulse wereseparately studied using SPE-level illumination, and were foundto be between 1/10 and 1/20 of the SPE pulse size, occurring at
less than 1% of the SPE rate. The ratio between sizes of SPE pulses
and pre-pulse quanta is similar to the typical ﬁrst dynode gain
reported by the manufacturer [24]. Because individual pre-pulse
quanta are below threshold for triggering DOMs, they have asmall impact on event reconstruction. The combined pre-pulses
from many photons would only be observable for a large, narrow
light pulse (  5000 photons detected within 30 ns). Pulses
originating more than  25 m from a DOM would generally bebroader than this, due to scattering in the ice [7].
The saturation model (Eq. (4)) can be important for reconstruction of very high energy neutrinos that produce electromagnetic or hadronic showers. Ideally, reconstruction would rely
most heavily on the PMTs closest to a shower, because the lightpulse is broadened and attenuated as it travels through the ice[7]; however, these PMTs can be saturated for high energy events.
The energy where saturation effects become important can be
estimated by choosing a characteristic distance of 60 m, which isabout half the inter-string spacing. At this distance, simulations[20] show that a 600 TeV shower yields peak intensity of 30 p.e./ns, equivalent to the linearity limit of 50 mA. Above this energy,
signals in close PMTs require a correction for saturation. Above 10 PeV, many nearby PMTs are badly saturated and the shower
energy measurement must rely mostly on far-away PMTs.
However, even badly saturated PMTs measure the beginningand end of the pulse, which can be used to constrain the event
geometry.

Table 4
Saturation curve parameters for three PMT samples, as deﬁned for Eq. (4).

11. Afterpulses

PMT serial no.

A (mA)

B

C

AA0020
SA2747
SA2749

126
138
138

2.02
2.05
1.82

2.98
3.23
2.67

63 nsec

I = Measured Current (mA)

0

c
–40

–80

220 PEsb–120

3,700 PEs
210,000 PEs

a
0

200

400
600
Time (ns)

800

1000

Fig. 11. Average waveforms observed in PMT serial number SA2747 for 3 ns
(FWHM) light pulses with progressively higher intensity: (a) main peak; (b)secondary peak due to unusual electron trajectories and (c) pre-pulse.

As shown in Figs. 6 and 11, the prompt response to a lightpulse has a tail extending to about 100 ns. Afterpulses are seen in
the range of 300 ns to 11 ms. Such afterpulses are a common
feature of PMTs, and are attributed to ionization of residual gases
by electrons accelerated in the space between dynodes [34]. Ions
created in this way can be accelerated back to the photocathode,causing ejection of electrons which are subsequently ampliﬁed
like the original photoelectrons. Some ions strike one of thedynodes instead, but the corresponding ejecta are ampliﬁed muchless and could easily go undetected.
Afterpulse measurements were made at 25 3 C with LED pulsesof 40 ns width, using calibrated optical attenuators to control theintensity, as for the saturation measurements (Section 10). In abright LED ﬂash, many individual ions are created, and their
responses add up to an afterpulse waveform with well deﬁned
peaks and valleys (Fig. 12). The various peaks are believed tocorrespond to ions of different masses, according to theirindividual ﬂight times in the accelerating ﬁeld [34]. Prominent
afterpulse peaks for this PMT occur around 600 ns, 2 and 8 ms after
the main response peak. The peaks are fairly wide and no period isentirely devoid of afterpulses until after 11 ms.
The average afterpulse waveform grows almost linearly with
the ﬂash brightness even up to the highest intensity studied(4:4  106 p:e: in 40 ns), where the primary response is completely
saturated at  1000 p:e:=ns (Fig. 10). This suggests that observed
afterpulses arise primarily from ions generated in earlier stages ofthe multiplier, whose electron currents continue to rise evenwhen later stages have saturated.
Up to primary pulses of 1  106 p.e., the integral from 300 ns to11 ms corresponds to 0.06 SPE per primary photoelectron.
For dimmer ﬂashes, individual events have a small number ofafterpulse electrons. These appear as separate single afterpulses
distributed in time, with probability that can be approximately

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R. Abbasi et al. / Nuclear Instruments and Methods in Physics Research A 618 (2010) 139–152

an event with coincident arrival of one or more downgoing muons
from cosmic ray showers above the detector, which calls fordisentangling the hits originating from multiple tracks, andtherefore also the afterpulses. Multiple muons can also arise froma single shower, and when the resulting tracks are well separated
they can yield multiple hits. More intriguing is the possibility of nt
interactions which can create two showers of particles separated
by hundreds of meters [36]. In such a case some PMTs can see
pulses of light separated by a few microseconds, so effects ofafterpulses should be considered carefully. The late pulses
described in Section 7 should also be considered in these contexts.

0.0
c

–2.0
Measured Current (mA)d
3.0 x 103 PEs

b

–4.0

1.6 x 104 PEs–6.0

1.1 x 105 PEs

a

0
c

–40
–80

12. Summaryd
2.0 x 105 PEsb

1.0 x 106 PEs–120

4.4 x 106 PEs

a
0

5

151

10

Time (μs)
Fig. 12. PMT afterpulse waveforms for bright ﬂashes lasting 40 ns. Each curve isaveraged over many ﬂashes. The primary response (a) is off-scale and saturated atmost of these intensities. Brightness of ﬂashes is determined by the method ofSection 10, which is independent of PMT saturation effects. Prominent afterpulse
peaks are seen around (b) 600 ns, (c) 2 ms and (d) 8 ms after the primary response.
The afterpulse waveforms grow nearly linearly with ﬂash intensity up to the
maximum intensity measured. The PMT was operated at gain of 107, with theanode at 1326 V. Some variation in afterpulse waveforms is observed from one
PMT to another of the same type. Measurement of tails at very late times is slightly
affected by an AC coupling time constant of 80 ms.

predicted from the average waveforms of Fig. 12. Because
different ions are associated with different time ranges, andbecause some ions eject multiple electrons from the photocathode, each afterpulse delay range will be characterized by adifferent fundamental charge distribution. We have observed
corresponding peak charges from 1 SPE to 13 SPE, consistent witha recent more detailed study of individual ion afterpulses [35].
The above observations are from study of only a few PMT
samples, and the numbers quoted pertain to only one (serial
AA0020). Although quantitative differences are seen from one
sample to another, the information allows one to assess whether
afterpulses affect IceCube event reconstructions, and to limit
small systematic errors. If a particular physics analysis thenappears sensitive to afterpulses, a larger sample of PMTs would
have to be studied quantitatively to provide the necessary
corrections.
Given the small ratio of charge between afterpulse andprimary pulse, it can be expected that most IceCube analyses
will not be strongly sensitive to the details of afterpulses. Typical
IceCube events yield hits in each PMT that are spread over timesof a few hundred nanoseconds, well before the main part of theafterpulse distribution. For very high energy events (e.g. electronenergy 1 PeV in the deep ice), signals are likely to be seen by PMTs
500 m away where arrival times are dispersed over 2 ms (FWHM),
and then the afterpulse distribution becomes more relevant.
However, the main effect is a minor distortion of the late part ofthe pulse, which already has an intrinsically long tail due toscattering. Generally one does not lose much information bydisregarding details of the waveforms at late times.
However, some events can have multiple peaks in the photon
time distributions, and then a characterization of afterpulses canbe important for proper reconstruction. The most common case is

The R7081-02 PMT has been characterized and key ﬁndings
were discussed in the context of IceCube physics goals. We
observe a single-photoelectron time resolution of 2.0 ns averaged
over the face of the PMT. A small fraction of the pulses arrive
much later, with about 4% between 25 and 65 ns late. We also
observe prepulsing and afterpulsing, with afterpulsing occurring
up to 11 ms late. The single photoelectron charge spectrum is wellﬁt by a Gaussian corresponding to charge resolution near 30%,
plus a contribution at low charge which is represented by an
exponential. The dark rate was measured to be 300 Hz in thetemperature range 40 to 20 3 C. A new method for opticalsensitivity calibration has been demonstrated, which uses
Rayleigh scattering to scale from the intensity of a primary laser
beam to the much smaller number of photons reaching a target
PMT. Measurements of dark rate, single photon detection
efﬁciency, single photoelectron waveform and charge, time
resolution, large pulse response, and afterpulses will serve as
input for detailed simulation of IceCube physics events.

Acknowledgements
We acknowledge support from the following agencies: U.S.
National Science Foundation-Ofﬁce of Polar Program, U.S. National Science Foundation-Physics Division, University of Wisconsin Alumni Research Foundation, U.S. Department of Energy, andNational Energy Research Scientiﬁc Computing Center, theLouisiana Optical Network Initiative (LONI) grid computing
resources; Swedish Research Council, Swedish Polar Research
Secretariat, and Knut and Alice Wallenberg Foundation, Sweden;
German Ministry for Education and Research (BMBF), Deutsche
Forschungsgemeinschaft (DFG), Research Department of Plasmas
with Complex Interactions (Bochum), Germany; Fund for Scientiﬁc Research (FNRS-FWO), FWO Odysseus programme, Flanders
Institute to encourage scientiﬁc and technological research inindustry (IWT), Belgian Federal Science Policy Ofﬁce (Belspo);
Marsden Fund, New Zealand; Japan Society for the Promotion of
Science (JSPS); M. Ribordy acknowledges the support of the SNF(Switzerland); A. Kappes and A. Groß acknowledge support by the
EU Marie Curie OIF Program; J.P. Rodrigues acknowledge support
by the Capes Foundation, Ministry of Education of Brazil.
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