A Proposal of the DOM response implementation method for the Photonics tableproduction
Kotoyo Hoshina∗ and Shigeru Yoshida†

Department of Physics, Faculty of Science, Chiba UniversityChiba 263-8522, Japan(Dated: April 27, 2004)
In order to implement the DOM response without increasing size of the photonics table, a simple
analytical formula of the wave length spectrum is proposed. Its validity has been investigated by
the toy Monte Carlo simulation code, and we found that a systematic error in the photoelectron
intensity estimation resulted from this approximation is within 5 %, which is probably better than
the accuracy of our absolute detector calibration we are able to achieve.
I.
A POSSIBLE ALGORITHM TOIMPLEMENT THE DOM RESPONSE

In AMANDA, the photonics table has integrated thedetection processes all the way down to the photoelectron level to save computer memory. The photoelectron ﬂuctuation, however, would not be able to betaken into account, except the statistical one. The IceCube DOM is being measured in lab carefully to understand its behavior and it is important to implement theirmeasured results properly in the detector MC even in thecase when it has to rely on the pre-produced photonics
table. A possible solution to achieve this goal without
enlarging the table size further would be to let the photonics calculate number of photons (not photo-electrons)arriving at individual DOM locations. The conversion
process to photoelectrons including the angular factor
is simulated in the DOM Monte Carlo module in “realtime” manner in the event generator. In this approach,the photonics consider a DOM as a perfect 4π detector
with 100 % collection eﬃciency. An algorithm for theDOM simulator to calculate number of photo electrons
in the event generation chain will be something like:
1. Assume a photon beam is parallel from the lightemission point to the DOM location.
2. Sample the hit location of photons at the DOM
glass sphere.
3. Ray-trace a photon until it hits the PMT photocathode or somewhere else in the DOM sphere.
This can be done using the pre-calculated table tosave CPU time.
4. Simulate the PMT/DOM electronics response.
5. Repeat this procedure for all the photons the photonics table predicted.

∗ Electronicaddress:
hoshina@hepburn.s.chiba-u.ac.jp;
URL: http://www.ppl.phys.chiba-u.jp/research/IceCube/† Electronic address: syoshida@hepburn.s.chiba-u.ac.jp

A drawback of this method is that you are not able
to know wavelength of an individual photon because thewavelength factor is convoluted in the photonics table,
although the DOM response depends on the wavelength.
II.
THE ANALYTICAL WAVELENGTH
SPECTRUM AFTER THE PROPAGATION AND
ITS VALIDITY

The wavelength spectrum for photons propagating in
ice can be approximated as
dNγ1 2 exp [−d a(λ)b(λ)],
dλλ(1)

where d is the distance from the light origin to a DOMlocation, a(λ) and b(λ) are the coeﬃcient of the absorption and the scattering of photons, respectively. If thisapproximation works good enough, the DOM simulator
can assign a wavelength for an individual photon following this spectrum.
In order to see how well this formula would reconstruct
the real wavelength distribution, we built a toy Monte
Carlo simulation code where we ray-traced photons running in ice with uniform property. The ice property ischaracterized by the coeﬃcients a and b in Eq. 1 and we
took them from the Ped’s PhD thesis [1]. Three cases
are assumed. One is to represent the “homogeneous” icecase, the second is supposed to follow the AMANDA ice
at depth of 1690 m as the representative “clean” ice, andthe last is to assume those at depth of 1740 m as a “dust”
ice. We run photons in these three cases but compare theresults with the analytical model, Eq. 1, of the “homogeneous” ice case only, because the DOM simulator does
not know the accurate ice proﬁle of a given photon pathin our proposed algorithm anyway because of limitationof the photonics table dimension, even if we had a perfectknowledge of the ice characteristics.
FIG. 1 shows the direct comparison. Although theanalytical mode is very simple, it reconstructed the simulation results reasonably well, but not perfectly. Notethat the analytical model represented by Eq. 1 predicts
both the intensity of photons without being absorbed
and the wavelength distribution. The photon intensity

4

Number of Photons at d[m] from the right source

10Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

d = 0[m]d = 50[m]d = 50[m]310

d = 50[m]d = 150[m]d = 150[m]d = 150[m]

300

350

400
450
500
550
600
Wave Length of Photon [nm]0.008

distance = 50m

0.006
0.004
0.002
300

350

400
450500550
Wave Length of Photon [nm]Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.010.008

distance = 150m

0.006
0.0040.002
300

350400450500550
Wave Length of Photon [nm]Number of Photons (normalized)

Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.01

Number of Photons (normalized)

Number of Photons (normalized)

FIG. 1: Number of Photon spectra and their intensity. Both numerical results obtained by the toy Monte Carlo and the simple
analytical formula are shown for comparison.
Homogeneous Model
Homogeneous ice (MC)0.01

at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.008

distance = 300m

0.006
0.004
0.002300350

400
450500550
Wave Length of Photon [nm]FIG. 2: The relative photon wavelength spectrum. The normalized numerical data and the (normalized) simple model prediction
are shown. Here three case in distances are plotted: 50, 150, and 300 m from the light source to the “OM”.

0.0025

distance = 50m

0.002
0.00150.001
0.0005
300

350

400

450

500

Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.00350.003
0.0025

distance = 150m

0.002
0.00150.001
0.0005550

300

Wave Length of Photon [nm]

350

400

450500

Probability of # of Generated p.e.

0.003

Probability of # of Generated p.e.

Probability of # of Generated p.e.

Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.0035

Homogeneous Model
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.00350.003
0.0025

distance = 300m

0.002
0.00150.001
0.0005

550

300

350

400

450500550

Wave Length of Photon [nm]Wave Length of Photon [nm]FIG. 3: Same as in FIG. 2, but the quantum eﬃciency shown in FIG. 4 is convoluted.

0.25

Absolute QE

0.2
0.15
0.10.05
300 350 400 450 500 550 600
Wave Length of Photon [nm]Np.e.(Model) / Np.e.(Monte-Carlo)

FIG. 4: QE of HAMAMATSU R7081-02 used in this study.
1.2
1.15
1.1
1.05
10.95
Homogeneous ice (MC)at 1690m (clean ice, MC)
at 1740m (dust ice, MC)

0.9
0.85
0.805

0100

150

200250300

350lengths below 350 nm. But the optical sensitivity of theDOM below 350 nm decreases rapidly. An example isshown in FIG. 4 where the PMT quantum eﬃciency isplotted. So this discrepancy would not be signiﬁcant at
all in the end.
To demonstrate this hypothesis, FIG. 3 shows the spectrum of photoelectrons by integrating the QE curve to thephoton wavelength spectrum. You can see that now theagreement is quite good.
The area of the curves shown in FIG. 3 corresponds toexpected number of photoelectrons. We should check
if we have a systematics of number of photoelectrons
by introducing approximated analytical formula of wavelength spectrum. In FIG. 5 is plotted the ratio of the“real” number of photoelectrons (which corresponds tothe area of the MC curve in FIG. 3) to those estimatedby assumption that the incoming photons at DOMs follows the wavelength spectrum estimated by our analytical model (which corresponds to the area of the black
curve in FIG. 3). The systematics diﬀerence is within
5 % for d ≤ 200 m. Systematic errors in cases of thelonger distances would probably be smeared out by low
statistics of photons and systematic uncertainty of theice proﬁle in the actual event generation.

400

Distance [m]FIG. 5: Ratio of number of photoelectrons obtained by thereal photon wavelength spectrum to those calculated by themodel spectrum as a function of distance.

are told by the photonics table itself, and the DOM simulator would use Eq. 1 as a probability distribution tosample the wavelength. It is, therefore, more appropriate to compare the simulation data with the analyticalmodel normalized to the data. FIG. 2 shows this comparison. Now the matching becomes much better evenfor the cases of longer propagation.
You may be concerned that the case of “clean” ice exhibits some discrepancy between the Monte Carlo data
and the analytical model prediction at the shorter wave-III.

CONCLUSION

The simple wavelength spectrum model would allow
the DOM simulator to fully simulate the DOM response
including the angular eﬃciency and the photoelectron
ﬂuctuation in the Monte Carlo event generation basedon the photonics table. It also allows the event generator
to use a diﬀerent DOM simulator (say, a newer version,or the one to implement the wavelength shifter) without
repeating the photonics table production eﬀorts.
The systematic shift of the number of photoelectrons
would be 5 %. This is comparable to our most optimistc goal of the absolute detector calibration and would
certainly be better than the uncertainty due to our incomplete knowledge of the IceCube ice proﬁle.

[1] Predrag Miocinovic, PhD Thesis (University of California,Berkeley, 2001).