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Status of PSA investigation and optimizationAGATA Week 2015 Valencia
Lars Lewandowski, Benedikt Birkenbach, Peter Reiter
IKP Cologne
22.09.2015
Outline
PSA performance characterization
ClusteringHigh statistic grid pointsInvestigation of grid search
PSA optimizationInput parameters
Detector propertiesProper setup of algorithm
Exemplarily shown for optimization of transfer function
PSA characterization
Distribution of hits
If unexpected behavior:Segment/Detector/general?
Dependence on interactionposition and energy
Clustering!
PSA characterization
Distribution of hits
If unexpected PSA results:Segment/Detector/general?
Dependence on interactionposition and energy
High Statistic Grid Points(HSGP)!
PSA characterization
Distribution of hits
If unexpected PSA results:Segment/Detector/general?
Dependence on interactionposition and energy
Detector 0 (A004),z=10-12 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
2000
4000
6000
8000
10000
z=10-12mm
PSA characterization
Distribution of hits
If unexpected PSA results:Segment/Detector/general?
Dependence on interactionposition and energy
E [keV]
FO
M /
E0.
6
Problems with: Lowenergies, front of thedetector, segmentborders, edge of detector
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
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4500
z=54-56 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=56-58 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
z=58-60 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=60-62 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=62-64 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=64-66 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=66-68 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=68-70 mm
Visualization of Grid Search
Consider χ2(~r) of ONE event
Local χ2 minima?
E = 257 keV, Segment=22, x=-32.25 mm, y=-6.25 mm,z=59.25 mm
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
-40
-30
-20
-10
0
10
20
30
40
0
500
1000
1500
2000
2500
3000
3500
4000
4500
z=70-72 mm
Visualization of Grid Search
Radial dependence of χ2(~r) (± 10 mm from minimum)
Radial position seems reliable. Angular resolution difficult
Depth of minimum = χ2min/χ
2max ⇒ reliability of PSA result
r [mm]0 5 10 15 20 25 30 35 40
chis
q
0
500
1000
1500
2000
2500
Visualization of Grid Search
Energy dependence of depth of minimum (10k events)
Small energies problematic
E [keV]0 200 400 600 800 1000 1200
chis
q_m
in /
chis
q_m
ax
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0
1
2
3
4
5
6
7
8
9
PSA optimization
Detector and electronics properties:
Transfer function of preamplifier and digitizer (rise times)
Preamplifier decay times for every segment and core (Scaling of database)
Differential Crosstalk
Space Charge (impurity concentrations)
PSA optimization
Setup of the algorithm:
Distance metric χ2 =∑
t |Simulation(t)−Measurement(t)|p
Time alignment:
Constant shift for every segment/coreDynamic Shift during PSA on event by event basis
Stopping criteria (number of loops, min/max shift)Number of ticks included (only ≈ rise time)Metric χ2 =
∑t |Simulation(t) - Measurement(t + tshift)|p
How to chose parameters
No information on real interaction position
χ2
Comparison with expected hit distribution (known for source runs -
statistical fluctuation)
Clustering/Correlation (Covariance)High statistic grid points (Ratio)
How to chose parameters
No information on real interaction position
χ2
Comparison with expected hit distribution (known for source runs -
statistical fluctuation)
Clustering/Correlation (Covariance)
High statistic grid points (Ratio)
How to chose parameters
No information on real interaction position
χ2
Comparison with expected hit distribution (known for source runs -
statistical fluctuation)
Clustering/Correlation (Covariance)High statistic grid points (Ratio of hits inside HSGPcompared to rest)
Example of optimization - Transfer function
Transfer function of preamplifier and digitizer
’Effective’ τ
Performed for every 540 segments (and 15 cores)
Impact on hit distribution
Results with different optimization methods
Detector 1, z=0-2 mm
Transfer Function
Minima positions are similar, but do not coincide 100%
Differences of optimal τ values derived via differentdetermination methods
tau_chi - tau_ratio-50 -40 -30 -20 -10 0 10 20 30 40 50
Cou
nts
0
20
40
60
80
100
tau_cov - tau_chi [ns]-50 -40 -30 -20 -10 0 10 20 30 40 50
Cou
nts
0
20
40
60
80
100
diff cov-chi
Transfer Function
τchi is systematically bigger than τcov and τratio
τcov and τratio coincide very wellτcov+τratio
2 is used for optimizing all 555 channels
tau_cov - tau_ratio [ns]-50 -40 -30 -20 -10 0 10 20 30 40 50
Cou
nts
0
20
40
60
80
100
120
140
160
180
200
220
diff cov-ratio
Optimization
Before (left) and after (right) complete Optimization
Exemplarily for det 1, z=10-12 mm. All energies
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
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x [mm]-40 -30 -20 -10 0 10 20 30 40
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Summary and Outlook
Summary
Characterization and optimization of PSA performance
Clustering and non physical allocation of hits could be reduced...
...but not removed
Outlook:
Reiteration of optimization (input parameters are not independent)
Measure transfer function of digitizer and preamplifier
Use scanning table data / collimated source measurements
Impact of PSA optimization on tracking performance
Thank you for your attention
Transfer function
Distribution of found τ values (one for each segment)
tau [ns]20 25 30 35 40 45 50 55 60 65 70
Cou
nts
0
10
20
30
40
50
60
cov dist
tau [ns]20 25 30 35 40 45 50 55 60 65 70
Cou
nts
0
10
20
30
40
50
ratio dist
tau [ns]20 25 30 35 40 45 50 55 60 65 70
Cou
nts
0
10
20
30
40
50
60
70
chi dist
PSA characterization
Distribution of hits
Distribution of final χ2(~r ,E)(’Figure of Merit’)
If unexpected PSA results:Segment/Detector/general?
Dependence on interactionposition and energy
Non homogeneous!
Comparison of hit distribution and mean χ2
Segment and detector performance
Distance of High Statistic Grid Points (HSGP)
Investigate relative position of HSGPs
Same or similar spot in all detectors?
Distance of High Statistic Grid Points
Search for HSGP segment wise
HSGP positions at characteristic spots
General problem that exists for every detector
The AGATA Data Library
The AGATA Data Library (ADL)contains the signals for everypossible interaction point
Consider impurity concentrationof the crystal
Not constant over whole crystal
Assumptions: cylindricalsymmetry, no radial change,linear gradient from front to back
Two dimensional optimizationproblem: Iterative method
Impurity concentration in theorder of 1010/cm3
Optimization of the Impurity Concentration
Use average χ2 of best fit of allinteractions of source run asminimization variable
Imp. concentration is givenrelative to start value provided bymanufacturer
Imp. Concentrations for back andfront not independent and cannotbe evaluated separately
Iterative method uses output ofprevious step as input
Optimization of the Impurity Concentration
Results of the optimization
Comparison of Measurement and Simulation
Amplitudes of measurement and simulation do not coincide
Systematic deviation
Calibration of calculated signals
Amplitude of simulation depends on decay time τ of preamplifier
Energy shift of simulation
Variation of τ for every preamplifier: 555 parameters!
τnew = τ(1−m), m = mean of distribution
Impact on PSA
Improvement of HSGP at highlighted spots
Maximum number of loops
Vary allowed number of maximum loops for TA after PSAAlgorithm converges X
# loops0 1 2 3 4 5 6 7 8
Chi
2
1100
1150
1200
1250
1300
1350
1400
# loops0 1 2 3 4 5 6 7 8
Cov
2
3
4
5
6
7
8
9
10
11
910×
# loops0 1 2 3 4 5 6 7 8
Rat
io
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Minimum Shift
If minimal time shift dt is reached, the algorithm stops(Obviously) small dt are preferred, but change is very small (std value=1.5 ns)
dt [0.1 ns]2 4 6 8 10 12 14 16 18 20
Chi
2
1176.5
1177
1177.5
1178
1178.5
1179
dt [0.1 ns]2 4 6 8 10 12 14 16 18 20
Cov
3500
3520
3540
3560
3580
3600
3620
3640
3660
610×
dt [0.1 ns]2 4 6 8 10 12 14 16 18 20
Rat
io
0.055
0.0552
0.0554
0.0556
0.0558
0.056
0.0562
Local time alignment
For a fast algorithm the time alignment assumes a convexfunction
The next time shift is only performed if χ2 improved in theprevious step
If χ2[n] is not a convex function only a local minimum will befound
χ2 of time shift n
χ2[n] =21∑i=0
(Am[i + n]− As [i ])2
Global time alignment
Therefore a global time alignment was implemented that evaluates the χ2 forevery time shift and then searches the minimumGood news: The global time alignment gives nearly the same results as the fastalgorithm ⇒ χ2[n] behaves like a convex function
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
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x [mm]-40 -30 -20 -10 0 10 20 30 40
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Standard and global time alignment algorithms (with nearly same results) [det1, z0]
Time alignment after PSA
TA after PSA uses χ2 like parameter
Reminder: χ2 in PSA is determined with set distance metric
Figure of Merit
χ2 =∑ti ,j
|Amj [ti ]− As
j [ti ]|p
Measured Am and simulated signal As of segment id j and time ti
In the time alignment only the sqare of the differences is used⇒ Room for improvement?
Distance metric in the time alignment
The χ2 in the TA is now derived in the same way as in the PSAThe distance metric parameter p is variedCompared to PSA significantly higher values seem to be favored
p0.5 1 1.5 2 2.5
Chi
2
1112
1112.5
1113
1113.5
1114
1114.5
1115
1115.5
p0.5 1 1.5 2 2.5
Cov
2450
2500
2550
2600
2650
2700
610×
p0.5 1 1.5 2 2.5
Rat
io
0.04
0.042
0.044
0.046
0.048
0.05
0.052
Impact of distance metric on hit distributions
Detector 1,z=6 mm
The timealignment seemsto favor highervalues for p
Even beyondEuclidian metric
Preprocessing time alignment
Before the first PSA and time alignment afterwards, a constant timeshift is applied to each core (and therefore to each segment)
Values used from dissertation Birkenbach, choosing the values insuch a way that the PSA TA has to shift minimal
Shifts of PSA with and without preprocessing TA are shown for one
Axis in ns + arbitrary offset
Preprocessing time alignment
With (left) and without (right) preprocessing time alignment
x [mm]-40 -30 -20 -10 0 10 20 30 40
y [m
m]
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