Computational Techniques for
Photon Transport in Ice
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UC BerkeleyPeter NiessenVrÿe Universiteit, Brussel
International Workshop on
UHE Neutrino TelescopeChiba UniversityJuly 30, 2003
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UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Motivation
Photon transport can not be
solved analytically in all cases
Inhomogeneity of transport
medium further complicatesthe problem

1 < Nscat << NdiffusivePγ (r,t)?
γImplementation

Monte Carlo generation ofphoton flux tables
Table parametrization forsimulation and reconstruction
Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Photon flux
Minimalscattering
IntermediatescatteringLarge scattering

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Minimal scattering regime Nscat~1:
treat delayed photons as a perturbation
Majority of flux is"undelayed"P(r,0)∝exp(-d/λa)Simple empiricalpower law-like fit todelayed flux
P(r,t)∝P(r,0)·tα
Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Large scattering regime Nscat≥Ndiffusive:
described by 3D random walk function*
Input parameters:
λe = 2.645 m
λa = 120 m

input values
recovered*B. Price and L. Bergström
Appl. Opt. 36, 4181 (1997)
Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Intermediate scattering regime
1<Nscat<<Ndiffusive
no closed form solution⇒ calculate fluxes numerically**see A. Karle, in proceeding of Simulation and Analysis Methods for Large
Neutrino Telescopes workshop, July 1998, Zeuthen, Germany, p. 174
Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Optical properties between photon sourceand detection point can change!

Variation in icetransparency inAMANDA

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Photonics software package
numerical solution to flux calculation problem

ray-tracing approach to photon transport
handles varying optical properties
highly flexible geometry and runtime configuration
very fast
easily extendable

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Multidimensional tables used to keep results
source location& orientation (2D)

photon orientation& travel time (3D)receiver location (3D)
Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Absorption treated as photon survival probability
speeds up table evaluation
allows treatement of varying optical properties
Scattering treated by Henyey-Greenstein approximation
to Mie scattering theory
survival probability updated

Layer 1next scattering point
recalculated
next scattering
point determinedphoton path

Layer 2Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

light source

flux calculated involume unit-cellsΦγ ∝ Psurv(γ)/A⊥(cell)
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UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

execution speed ~ 106 γ / hour / GHz

speed dependent on
unit-cell density &optical properties

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

But....
Full production table set size is ≥ 1 GB⇒ need to parametrize the tables

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Attractive properties of Neural Networks
model free fitter→ superposition of weighted sigmod functions

DelayPhoton fluenceinterpolation ability

Delay probability

Relative distancePredrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

NN configuration:
Fully connected Multilayer Perceptron Network
timing delay tables 6x10x10x10x1
fluence tables 5x60x60x1 or 5x10x10x10x1

Input coordinates

Output fluxFluence table fitting not finalized
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UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

"hybrid" model for initial evaluationtable lookup for fluence
NN fit to timing delay tables
Hybridsimulated hit-time
distribution agree

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UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

NN performance in detector simulation

Table lookup on
centralized server
incurs large
system overhead

decentralized NN
evaluation

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003

Summary & OutlookMC table generation tested and running well
NN parametrization of flux timing tables isadequate
Fine tune parametrization of fluence tables
proceed with full scale implementation into
AMANDA simulation chain

Predrag Mio inovi

UHE Neutrino Telescope Workshop, Chiba University, 29-30 July, 2003