Status of PSA investigation and optimization · 2015-09-28 · Status of PSA investigation and...

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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1000

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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

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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

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tau_cov - tau_chi [ns]-50 -40 -30 -20 -10 0 10 20 30 40 50

Cou

nts

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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

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diff cov-ratio

Optimization

Before (left) and after (right) complete Optimization

Exemplarily for det 1, z=10-12 mm. All energies

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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

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cov dist

tau [ns]20 25 30 35 40 45 50 55 60 65 70

Cou

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ratio dist

tau [ns]20 25 30 35 40 45 50 55 60 65 70

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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

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1250

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# loops0 1 2 3 4 5 6 7 8

Cov

2

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910×

# loops0 1 2 3 4 5 6 7 8

Rat

io

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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

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610×

dt [0.1 ns]2 4 6 8 10 12 14 16 18 20

Rat

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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

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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

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p0.5 1 1.5 2 2.5

Cov

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610×

p0.5 1 1.5 2 2.5

Rat

io

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0.042

0.044

0.046

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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

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