Photon propagation and ice properties

Bootcamp 2010 @ UW Madison

Dmitry Chirkin, UW Madison

r

air bubble

photon

Propagation in diffusive regime

absorption scattering

r2=A.r1 <r2>=<A.r1>=<r1>

Mie scattering theoryContinuity in E, H: boudary conditions in Maxwell equations

e-ikr+it

e-i|k||r|

r

Mie scattering theory

Analytical solution!

However:

Solved for spherical particles

Need to know the properties of dust particles:

• refractive index (Re and Im)• radii distributions

Mie scattering theory

Dust concentrations have been measured elsewhere in Antarctica: the “dust core” data

• Mie scattering - General case for scattering off particles

Scattering function: approximation

Scattering and Absorption of Light

Source is blurred

Source isdimmer

scattering

absorption

a = inverse absorption length (1/λabs)b = inverse scattering length (1/λsca)

scattered

absorbed

Measuring Scattering & Absorption

• Install light sources in the ice

• Use light sensors to:

- Measure how long it takes for light to travel through ice

- Measure how much light is delayed

- Measure how much light does not arrive

• Use different wavelengths

• Do above at many different depths

Embedded light sourcesin AMANDA

45°

isotropic source

(YAG laser)

cos source

(N2 lasers, blue LEDs)

tilted cos source

(UV flashers)

Timing fits to pulsed data

Fit paraboloid to 2 grid

►Scattering: e ± e

►Absorption: a ± a

►Correlation: ►Fit quality: 2

min

Make MC timing distributionsat grid points in e-a space

At each grid point, calculate2 of comparison between

data and MC timing distribution(allow for arbitrary tshift)

Fluence fits to DC data

d1

d2

DC source

In diffusive regime:

N(d) 1/d exp(-d/prop)

prop = sqrt(ae/3)

c = 1/prop

d

log(Nd)

slope = cc1

c2

c1

dust

No Monte Carlo!

Light scattering in the ice

bubblesshrinkingwith depth

dusty bands

Wavelength dependence of scattering

Light absorption in the ice

LGM

3-component model of absorption

Ice extremely transparentbetween 200 nm and 500 nm

Absorption determined by dustconcentration in this range

Wavelength dependence of dustabsorption follows power law

A 6-parameter Plug-n-Play Ice Model

be(,d )

a(,d )

scattering

absorption

be(,d )Power law:

-

3-component model:

CMdust - + Ae-B/

T(d )

Linear correlation with dust:CMdust = D·be(400) + E

A = 6954 ± 973B = 6618 ± 71D = 71.4± 12.2E = 2.57 ± 0.58 = 0.90 ± 0.03 = 1.08 ± 0.01

Temperature correction:a = 0.01a T

id=301

id=302

id=303

AHA modelAdditionally Heterogeneous Absorption: deconvolve the smearing effect

Is this model perfect?

Fits systematically offPoints at same depth not consistent with each other!

Individually fitted for each pair: best possible fit

Is this model perfect?

Averaged scattering and absorptionFrom ice paper

Measured properties not consistent with the average!Deconvolving procedure is unaware of this and is using the averages as input

When replaced with the average, the data/simulation agreement will not be as good

SPICE: South Pole Ice model

• Start with the bulk ice of reasonable scattering and absorption

• At each step of the minimizer compare the simulation of all flasher events at all depths to the available data set

• do this for many ice models, varying the properties of one layer at a time select the best one at each step

• converge to a solution!

Dust logger

IceCube in-ice calibration devices

3 Standard candles56880 Flashers7 dust logs

Correlation with dust logger dataef

fect

ive

sca

tter

ing

coef

ficie

nt (from Ryan Bay)

Scaling to the location of hole 50

fitted detector region

Improvement in simulation

by Anne Schukraft by Sean Grullon

Downward-going CORSIKA simulation Up-going muon neutrino simulation

Photon tracking with tables

• First, run photonics to fill space with photons, tabulate the result

• Create such tables for nominal light sources: cascade and uniform half-muon

• Simulate photon propagation by looking up photon density in tabulated distributions

Table generation is slow Simulation suffers from a wide range of binning artifacts Simulation is also slow! (most time is spent loading the tables)

Light propagation codes: two approaches (2000)

PTD• Photons propagated through

ice with homogeneous prop.• Uses average scattering

• No intrinsic layering: each OM sees homogeneous ice, different OMs may see different ice

• Fewer tables• Faster• Approximations

Photonics• Photons propagated through

ice with varying properties• All wavelength dependencies

included• Layering of ice itself: each OM

sees real ice layers

• More tables• Slower• Detailed

photonicsBulk PTD Layered PTD

PTD vs. photonics: layering

average ice type 1 type 2 type 3 “real” ice

3

3

3

1

1

2

2

2

2

2

2

Direct photon tracking with PPC

• simulates all photons without the need of parameterization tables

• using Henyey-Greenstein scattering function with <cos >=0.8• using tabulated (in 10 m depth slices) layered ice structure• employing 6-parameter ice model to extrapolate in wavelength

• transparent folding of acceptance and efficiencies

• Slow execution on a CPU: needs to insert and propagate all photons

• Quite fast on a GPU (graphics processing unit): is used to build the SPICE model and is possible to simulate detector response in real time.

photon propagation code