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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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 3
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.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 4
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.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 5
Prototype Events: Compton @ 2 MeV
.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 6
Prototype Events: Pairs @ 49 MeV
.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 7
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 8
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 9
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 10
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!
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 11
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 12
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 13
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 →
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 14
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 15
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“
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 16
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!
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 17
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 18
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.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 19
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!
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 20
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°
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 21
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
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 22
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°
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 23
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!
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 24
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)
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 25
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.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 26
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.
Andreas Zoglauer - Basic principles of the data analysis for the MEGA prototype - Compton workshop at Kloster Seeon 2003May 29, 2003 27
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