Andreas Zoglauer Outline - Max Planck Society · May 29, 2003 Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003

Andreas Zoglauer

Outline:

Event reconstruction

Image reconstruction

Preliminary results from the MEGA prototype calibration

Data analysis for the MEGA prototype

Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 2

What is MEGA?

MEGA = Medium Energy Gamma-ray Astronomy

Combined Compton and pair telescope designed for the energy range from 400 keV to 50 MeV

The prototype:

For details of the MEGA project see presentation of Gottfried Kanbach


The MEGA calibrationwith the HIγS free electron laser (Duke University, NC)

April/Mai 2003

Monoenergetic (dE/E < 2%), 100% polarized gamma-ray beam at energies from 700 keV up to 49 MeV.

For more details see talk of Robert Andritschke

This is work in progress!

No complete single detector energy calibration available!

No efficiency has been calculated, yet.


How to start the data analysis?

All data needs to pass through 4 different analysis levels:

Event representation

Complete analysis path implemented for MEGA

Data acquisition (Detector / Simulation)

Image reconstruction & high level data

analysis

Calibration & low level data

analysis

Event reconstruction

Analysis task

Hits: Strips, Pixel, ADC-

counts

Hits: Position, energy

Events: Compton,

pair

Images, spectra, etc.


Prototype Events: Compton @ 2 MeV

.


Prototype Events: Pairs @ 49 MeV

.


Simplified outline of algorithm

1. Search for vertex (identifiy pairs)

2. Search for high energy charged particles, e.g. Muons (straight line in tracker)

3. Seperate Comptons from the unidentifiable events

A. Identify tracks and their direction of motion

B. Find Compton-hit-sequence for events with 2 or more Compton interactions

C. Accept or reject Compton event


Characteristics of a good track

Rules:

• Angular scattering according to Molière-scattering

Increase of scattering at end of track (decreasing energy of electron)

• Energy deposit follows Bethe-Bloch-Equation

Increase of deposits at end of track

• First deposit likely to be lower than average deposit (interaction takes place somewhere within layer)

For each track compute probability of compliance

The track with the highest compliance with rules is choosen


Pair reconstruction algorithm

1)

2)3)

4)

1. Search vertex

2. Search straightest continuation for both tracks

3. Exchange / Skip single hits from tracks and test if track parameter suit better to ideal track

4. Follow tracks into calorimeter

Works from 10 to 50 MeV!

Best performance @ 49 MeV for on axis incidence:

83% of pairs found by visual screening are found by program, the rest are narrow pairs without a vertex


Compton events: Tracking

1. Consider all downward combinations (no U-turn)

2. Compute for all combinations the probability of being a „good“ track

3. Choose best combination

4. Follow track down into calorimeter

5. Estimate energy of missing hits (interactions in dead material)

Performance @ 5 MeV on-axis incidence for 3 and more layer tracks:

85% correct identified, from the rest most tracks hit only 3 layers. Problem: energy deposit decreases (instead of increases) along the track path!


Compton sequence reconstruction

g1

E2

E3

ϕ1

ϕ2

g2

g3

( )2coscos geoi

EinT ϕϕ −=

If a event has 3 or more interactions, than the Compton scatter angle ϕ can be computed in two ways:

Via energies:

Via angles:

⇒ Redundant information

⇒ Can be used to determine Compton sequence (orrecover incompletly absorbed events)

E1

++−=i

e

i

eEi E

EEE 001cosϕ

ii

iigeoi gg

ggrr

ro

r

⋅=

−

−

1

1cosϕ

Compute for all possible sequences the squared difference:

and its error ∆Tn (gaussian error propagation of energy and spatial uncertainties).

Knowning Tn and ∆Tn and that in an ideal case T = 0, one can calculate a probability that combination is correctly sequenced and completely absorbed

Choose combination with highest probability. Details see presentation of Uwe Oberlack


Compton sequence reconstruction

Main problem: Energy resolution and spatial resolution of calorimeters limited

Best and second-best solution frequently lay within measurement errors

Standard CSR alone not sufficient to retrieve correct sequence

Solution: Use additional information

1. Track Normally gives correct start point

2. Absorption probabilities Reduction of random coincidences

Event reconstruction finished

Continue with high level data analysis: Polarization, spectrum, imaging, etc


Imaging of basic event types

Reduced Compton circles of events with

electron track

Classical Compton Event Circles

(no electron tracking)

Direct imaging of pair-creation events

← 2 MeV → ← 8 MeV →


Selection of algorithmRequirements:

• Give correct results

• Combine all event types (untracked Compton, tracked Compton, pairs) into one image

• Use all event data as accurately as possible (e.g. no information loss through binning)

• Usable on a Notebook (e.g. no large system matrix, Comptel-type data space for MEGA would need up to 1013 bins)

• Easy change of geometry (tests for simulation)

• Easy change of coordinate system (far-field spherical, near field Cartesian 2D & 3D)

Only one known choice:

List-mode maximum-likelihood expectation-maximization

Original version developped by Scott Wildermann for a medical Compton camera


Iterative reconstruction equation

( )( )

( )∑∑ +=+

nk

nlknk

nnm

m

lml

m btYt

s λλλ 1

Image bin m at iteration level l

Probablility that an event emitted in image bin m is

detected as event n

„Response“ Probability that the event came from image-space (only

for Compton events != 1)

Background

Probability that an event emitted in image bin m is

detected

„Sensitivity“

Projection:

Data space image space

In a way that the expectation of the log-likelihood is maximized

Projection:

Image space data space

„Expectation of log-likelihood“


Complete Response

Response T= tnm determined by the following probabilities:

1. Photon is emitted and leaves object in a certain direction2. It is not absorbed on its way to detector3. It crosses detector unabsorbed to its first interaction 4. It makes a Compton interaction5. The measured energy/position values are detected6. Photon crosses the detector unabsorbed to its second

interaction7. It makes Compton interaction/is fully absorbed8. The measured energy/position values are detected

Too many integrations: Simplification needed!


Simplified Response

( )( ) ( ) ( )( ) ( ) ( )∫ −⋅⋅Ω⋅ΩΩ mmDtot ll

mjjCARMCjSPDKij edlKAWLt 1,,~ *0

µϕσϕσLength of cone-section (uncertainty of electron

track, Molière-scattering)

Width of cone-section (uncertainty of energy

measurement)

Geometry (absorption probabilities)Normalization

Performance:

Accuractely retrieve position of point sources

Recover extended sources

Retrieve point sources on high background (with parallel estimation of background scaling factor)

Reproduce relative intensities

↓ Reproduce absolute flux


Results from the MEGA calibrationwith the HIγS free electron laser (Duke University, NC)

April/Mai 2003

Monoenergetic (dE/E < 2%), 100% polarized gamma-ray beam at energies from 700 keV up to 49 MeV.

For more details see talk of Robert Andritschke

This is work in progress!

No complete single detector energy calibration available!

No efficiency has been calculated, yet.


Polarization measurement @ 710 keV

verticalPolarization E-vector

(horizontal)

Hit distribution in the small side-calorimeters:

Maxima are reached perpendicular to the E-vector of the polarized gamma-rays.

Minor irregularites are due to different efficiencies in the different CsI crystals.

Roughly 50% of all events are background!


Polarization @ 2 MeV

Peaks represent 4 sides of detector

Azimut

Azimut

Duke measurement with beam at 2 MeV. Data is NOT corrected for exposure or background!

Event selections:

Energy: 2 MeV +- 15%

Scatter angle: 0..90°

Lab measurement with 88Y 20 cm above detector.

Event selections:

Energy: 1836 keV +- 15%

Scatterangle: 0..90°


Imaged XY-table pattern @ 25 MeVin the near field in a plane perpendicular to the beam

Beam

Deconvolved image of pair events.

Each XY-table position contains 10000 reconstructed events.

After event selections (Pairs only) roughly 4000 events per position remain.

Weakest point contains only ~3000 events


Beam images @ 0° incidence8 MeV2 MeV 5 MeV

Comptons

Pairs

12 MeV

Increase of incomplete absorption (electron escapes tracker, secondary photons „scatter away“). Effect will be much less prominent with satellite geometry.

Increase of influence of Moliere-scattering and of unknown recoil of nucleus

20°

25 MeV 49 MeV

20°


Single photon angular dispersion: Pairs

Angular dispersion as 68% containment radius around known source position

0

5

10

15

20

10 100Energy [MeV]

Angu

lar d

ispe

rsio

n [d

eg]

MEGA prototype EGRET

MEGA is 2x better than EGRET at 49 MeV!


Beam images @ 49 MeV

for different incidence angles

20°

0° 60°90°

Distance to axis

30°

Event reconstruction and imaging works for angles up to 80°

Extreme wide field of view of MEGA (at least up to 80° off axis)


Reconstructed beam location accuracy @ 49 MeV

0,0

0,5

1,0

1,5

0 30 60 90Incidence angle: Distance to axis [°]

Loca

tion

accu

racy

[°]

Location accuracy MEGA Alignment accuracy

Location accuracy for on axis incidence near the alignment accuracy of MEGA at Duke

Only at high incidence angles beam seems to move towards axis.


Lab measurement: Extended source

Measurement:

Two 88Y sources are located on a rotating propeller and perform a circle with radius 7.5 cm.

This is about equivalent to a circle with 30° diameter at infinity.


Extended source

„MEGA Supernova remnant“Image properties:

• Includes tracked and not tracked events, single and multiple Compton events

• Energy range: 0.8 to 1.0 MeV

• Number of events: ~138000

• First hints for a circular structure visible with ~5000 events

• Minor irregularities result from assuption that all detectors have same efficiency

The End

Documents

Andreas Zoglauer Outline - Max Planck Society · May 29, 2003 Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003