photon propagation and ice properties bootcamp 2012 @ uw madison dmitry chirkin, uw madison r air...

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Photon propagation and ice properties Bootcamp 2012 @ UW Madison Dmitry Chirkin, UW Madison r air bubble photon

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Photon propagation and ice properties

Bootcamp 2012 @ UW Madison

Dmitry Chirkin, UW Madison

r

air bubble

photon

Scattering and Absorption of Light

Source is blurred

Source isdimmer

scattering

absorption

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

Mie scattering theoryContinuity in E, H: boundary 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

A better approximation to Mie scattering

fSL

Simplified Liu:

Henyey-Greenstein:

Mie:

Describes scattering on acid, mineral, salt, and soot with concentrations and radii at SP

Properties of photon propagation

Locally at x,y,z and for a given wavelength:

• group refractive index propagation speed• phase refractive index Cherenkov angle

• absorption coefficient• scattering coefficient• scattering function

• ice properties defined everywhere• for any wavelength

Photon spectrum

Fla

sher

405

nm

For

muo

ns:

fold

ed w

ith

Che

renk

ov s

pect

rum

Angular profile of photons from muons

Propagating photons in IceCube

Photonics: 2000 – up to now Photon propagation code PPC: 2009 - now

Photonics: conventional on CPU

• 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)

Direct photon tracking with PPC

propagate photons directly when needed

photon propagation code

insert photon

length to absorption distance to next scatter

propagate to next scatterscatter

check for intersection with OMs

Check for distance to absorption

hit lost

IceCube simulation with PPC on GPUsphoton propagation codegraphics processing unit

PPC simulation on GPUgraphics processing unit

execution threads

propagation steps(between scatterings)

photon absorbed

new photon created(taken from the pool)

threads completetheir execution(no more photons)

Running on an NVidia GTX 295 CUDA-capable card,ppc is configured with:

448 threads in 30 blocks (total of 13440 threads)average of ~ 1024 photons per thread (total of 1.38 . 107 photons per call)

Photon Propagation Code: PPCThere are 5 versions of the ppc:

• original c++• "fast" c++• in Assembly• for CUDA GPU• C++ with OpenCL

All versions verified to produce identical results

comparison with i3mcmlhttp://icecube.wisc.edu/~dima/work/WISC/ppc/

Also compare to clsimCLaudio SIMulator

developed by Claudio Kopper

Written in C++ with OpenCL

GPU scalingOriginal: 1/2.08 1/2.70CPU c++: 1.00 1.00Assembly: 1.25 1.37GTX 295: 147 157GTX/Ori: 307 424C1060: 104 112C2050: 157 150GTX 480: 210 204

On GTX 295: 1.296 GHzRunning on 30 MPs x 448 threadsKernel uses: l=0 r=35 s=8176 c=62400

On GTX 480: 1.401 GHzRunning on 15 MPs x 768 threadsKernel uses: l=0 r=40 s=3960 c=62400

On C1060: 1.296 GHzRunning on 30 MPs x 448 threadsKernel uses: l=0 r=35 s=3992 c=62400

On C2050: 1.147 GHzRunning on 14 MPs x 768 threadsKernel uses: l=0 r=41 s=3960 c=62400

Uses cudaGetDeviceProperties() to get the number of multiprocessors,Uses cudaFuncGetAttributes() to get the maximum number of threads

Cudatest: lean and meanice fitting machine

cudatest:

Found 6 devices, driver 2030, runtime 20300(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32)

l1 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)1(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32)

l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)2(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32)

l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)3(1.3): GeForce GTX 295 1.296 GHz G(938803200) S(16384) C(65536) R(16384) W(32)

l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)4(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32)

l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)5(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32)

l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1)

3 GTX 295 cards, each with 2 GPUs

PSU

0 and 14 and 52 and 3

nvidia-smi -lsa

GPU 0:Product Name : GeForce GTX 295Serial : 1803836293359PCI ID : 5eb10deTemperature : 87 C

GPU 1:Product Name : GeForce GTX 295Serial : 2497590956570PCI ID : 5eb10deTemperature : 90 C

GPU 2:Product Name : GeForce GTX 295Serial : 1247671583504PCI ID : 5eb10deTemperature : 100 C

GPU 3:Product Name : GeForce GTX 295Serial : 2353575330598PCI ID : 5eb10deTemperature : 105 C

GPU 4:Product Name : GeForce GTX 295Serial : 1939228426794PCI ID : 5eb10deTemperature : 100 C

GPU 5:Product Name : GeForce GTX 295Serial : 2347233542940PCI ID : 5eb10deTemperature : 103 C

As fast as 900 CPU cores

Measuring the ice properties

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

Experimental setup (SPICE)

Flasher dataset

Ice layer parametrization

10 m

In each 10-meter layer define:• scattering • absorption

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!

Likelihood description of data: SPICE Mie

Find expectations for data and simulation by minimizing –log of

Regularization terms:

Measured in simulation: s and in data: d; ns and nd: number of simulated and data flasher events

Sum over emitters, receivers, time bins in receiver

Statistical description

There is an obvious constraint

which can be derived, e.g., from the normalization condition

Suppose we repeat the measurement in data nd times and in simulation ns times. The s and d are the expectation mean values of counts per measurement in simulation and in data.

With the total count in the combined set of simulation and data is s + d , the conditional probability distribution function of observing s simulation and d data counts is

Two hypotheses:If data data and simulation are unrelated and completely independent from each other, then we can maximize the likelihood for s and d independently, which with the above constraint yields

On the other hand, we can assume that data and simulation come from the same process, i.e.,

We can compare the two hypotheses by forming a likelihood ratio

Derivation for multiple bins

Example: exp(-x/5)/5

To enhance the differences between the two likelihood approaches, consider that the amount of simulation is only 1/10th of that of data

200

2000

Using full range of the data and simulation Simulated exp(-x/5.0) with mean of 5.0

Optimal binning is determined by desire to:capture the changes in the ratemaximize the combined statistical power of the bins

The conditional probability (given the total count D) is

if the bins are considered independently i=di.

if the rate is constant across all bins, =i=D/L.

The likelihood ratio is

This never exceeds 1! so we use 1/L! or 8.

Bin size

Limiting case of near-constant rate

Small bin description

Single large bin of length L:

We prefer a single large bin if:

Optimal binning

typical

Optimal binning: flasher data

-log(8)log(L!)

Initial fit to sca ~ abs

Starting with homogeneous “bulk ice” properties iterate until converged minimize q

2

1 simulatedevent/flasher 4 ev/fl 10 ev/fl

Fit to scaling coefficients sca and abs

Both q2 and t

2 have same minimum!

• Absolute calibration of average flasher is obtained “for free” no need to know absolute flasher light output beforehand no need to know absolute DOM sensitivity

1 statistical fluctuations

Minima inpy, toff, fSL

Dust logger: tilt of the ice layers

Dust logger

IceCube in-ice calibration devices

3 Standard candles56880 Flashers7 dust logs

Ice tilt in ppc

Measured with dust loggers (Ryan Bay)

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

Ice anisotropy?

Geometry around string 63

Evidence in flasher data

62

54

55

6471

70

53

4556

72

77 69

Dependence with distance

What is Ice anisotropy

Direction of more scatteringDire

ctio

n of

less

sca

tter

ing

Naïve approximation: multiply the scattering coefficient by a function of photon direction, e.g., by

1 + ( cos2- 1/3 )

However, this is unphysical:

(nin,nout) = (-nout,-nin) (time-reversal symmetry)

(nin,nout) = (-nin,-nout) (symmetry of ice)

(nin,nout) = (nout,nin)

A possible parameterizationThe scattering function we use is f(cos ), a combination of HG and SL.

How about this extension: f(cos )= f(nin . nout) f(Anin . Anout)

0 0A = 0 0 in the basis of the 2 scattering axes and z ( are, e.g., 1.05). 0 0 1/

However, function f(cos ) is well-defined for only cos between -1 and 1.

A possible modification is nin Anin/| Anin | nout A-1nout/| A-1nout |.

This introduces two extra parameters: (in addition to the direction of scattering preference).

The geometric scattering coefficient is constant with azimuth. However, the effective scattering coefficient receives azimuthal dependence as:

Scattering example (5% anisotropy)

Fitting for the anisotropy coefficients

1=0.040, 2=-0.082

Effect of anisotropy on simulation

=1.0 =1.04, =0.92

How important is anisotropy?

from SPICE paper

threshold: > 0, 1, 10, 100, 400 p.e.

30%

21%

so-so

awesome!

threshold: > 10 p.e.

Can we resolve ice anisotropy?

8% more scattering36o NW

N

EIce flow direction

41o NW

C13

0-S

kyw

ay

History of SPICE model evolution

11/19/09 SPICE (also known as SPICE1): first version

seeded with AHA as initial solution AHA is used for extrapolation above and below the detector relies on AHA for correlation relation between be(400) and adust(400).

02/01/10 SPICE2:

fixed the hdh bug (see ppc readme file) seeded with bulk ice as initial solution dust logger and EDML data is used for extrapolation dust logger data is used to extend in x and y, taking into account layer tilt.

02/17/10 SPICE2+:

fixed the "x*y" option hit counting in ppc be(400) vs. adust(400) relation is determined with a global fit to arrival time distributions.

04/28/10 SPICE2x:

improved charge extraction in data: improved merging of the FADC and ATWD charges implemented saturation correction fixed the alternating ATWD bug updated DOM radius 17.8 --> 16.51 cm (cosmetic change: modifies only the meaning of py) fixed the DOM angular sensitivity curve (removed upturn at cos(theta)=-1).

06/09/10 SPICE2y:

Fixed code determining the closest DOMs to the current layer (when using tilted ice) Iterations (after timing fits) are combined (improving description in the dust layer) Randomized the simulation based on system time (with us resolution).

07/23/10 SPICEMie:

Much improved treatment of oversized DOMs in ppc Fits scattering function to a linear combination of HG and SAM functions, using higher g=0.9 Perform a global fit for py, overall time offset, scattering and absorption correlation coefficients Tilt map is estimated with respect to (0, 0) in IceCube coordinates (simplifies use with photonics).

04/16/12 SPICE Lea:

Improved data processing with the new feature extraction Improved likelihood description and optimized binning Introduced and fitted ice anisotropy effect

SPICE1:

Relies on AHA as a first guess, and for correlation between be and adust.

SPICE2:

Adds extrapolation with dust logger and EDML, ice tilt map from Ryan

SPICE2+:

Use full arrival time distributions, full fit for both be and adust.

SPICE Mie:

Fit for toff and shape of the scattering function

SPICE e-a:

New NNLS-based feature extraction. Fitted ice anisotropy

Older ice models: AHA, WHAM

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

Ice models vs. flasher data

Describing the data

Ice model must describe the data to which it was fit,

Ice model is built using the calibration in-situ light flasher data

ice model must describe the flasher data.

Here I quantify the (dis)agreement with a width of the distribution of the charge ratio qsimulation/qdata for all pairs of emitters and receivers in a flasher data set.

SPICE 1threshold: > 0, 1, 10, 100, 400 p.e.

29.2%

SPICE Miethreshold: > 0, 1, 10, 100, 400 p.e.

27.7%

SPICE e-athreshold: > 0, 1, 10, 100, 400 p.e.

20.0%

AHA(fixed ppc table)

threshold: > 0, 1, 10, 100, 400 p.e.

55.2%

WHAMthreshold: > 0, 1, 10, 100, 400 p.e.

42.4%

Remarks on comparison

Ice model error in description of the light deposition in the range of 125-250 meters away from the emitters:

SPICE 1: 29.2%SPICE Mie: 27.7%SPICE Lea: 20.0%

AHA: 55.2%WHAM: 42.4%

Well, what about timing?

See full collection of plots at http://icecube.wisc.edu/~dima/work/IceCube-ftp/ppc/lea/.

lea vs. wham: 63,5 flashing

lea vs. wham: 63,15 flashing

lea vs. wham: 63,25 flashing

lea vs. wham: 63,35 flashing

lea vs. wham: 63,45 flashing

lea vs. wham: 63,55 flashing

Direct Hole Ice simulation

Hole radius = ½ nominal DOMradius

Hole effective scattering ~ 50 cmHole absorption ~ 100 m

Do we need more detailed DOM simulation, including info about both the direction and point on the DOM surface?

Perhaps not, if the scattering length in the hole is not much shorter than the hole radius (speculation).

Traditional “hole ice” angular sensitivity

DOM 20,20 20,19: nz=cos.

nominal

direct hole ice

DOM 20,20 20,21: nz=cos.

DOM 20,20 20,19: xz

Ratio direct hole ice/nominal

nominal

hole ice

deficit

enhancement

DOM 20,20 20,21: xz

enhancement

deficit

nominal

hole ice

Remarks on the hole ice

Effect of the hole ice is quite subtle:• The number of photons is reduced on the side facing the emitter, and enhanced in the direction away from the emitter.

• The traditional “hole ice” implementation via the angular sensitivity modification reduces the number of photons in the direction into the PMT, and enhances the number of photons arriving into the back of the PMT.

If the emitter is inside the hole ice, the enhancement of photons received on the same string is dramatic.

Either effect is much smaller when receiver is on the different string can decouple measurement of bulk ice properties from the hole ice