1. Spatial Resolution of DEPFET Matrices
TB2008 Analysis in Prague –
Spatial Resolution of DEPFET Matrices
Zdeněk Doležal, Zbyněk Drásal, Peter Kodyš, Peter Kvasnička
Charles University in Prague

2. Contents Description of analysis
Results of example scan No.1318 (verification of analysis)
Conclusions from the edge scan
Conclusions from the bias scan
Resolution in the angle scan
Comments and open questions (messages to R&D community)
Conclusion

3. Description of analysis

4. Description of analysis
Pre-tracking steps:
Common mode noise correction
Every 16th frame removed (small bug on readout sequence)
Gain correction
COG production (position error estimations)
Alignment and corrections in several steps
Full resolution analysis with residuals, resolution analysis, track precision estimation, telescope resolutions etc.
Verification of analysis with simulated data
GEANT4 simulation (TB2008 geometry, experimental detector resolutions simulated by Gaussian smear, analyzed in a standard way)
Agreement in resolutions of all detectors within ±5% (±0,1 µm)‏
Alignment and corrections in several steps (for hardcore TB analysts)
first alignment from COG, exclude mod#2 (smaller area), edge cut 250 microns
calculate and apply large scale response (LSR) corrections, no edge cut, exclude mod#2 and mod#4, do first tracking
mod#4: calculate and apply LSR correction
mod#2: alignment, calculation + LSR correction
h correction based on tracking residuals
new alignment and final analysis

5. Large scale response (LSR) correction
Before correction…
Plots are residuals vs. position; edge effect and “V” effect are visible
Module 1
Module 0
Module 2
Module 3
Module 5
Module 4
Y axis: ±50m

6. Large scale response (LSR) correction
… and after correction
LSR correction (red) after gain correction, edge effect and “V” effect are corrected
Module 1
Module 0
Module 2
Module 3
Module 5
Module 4
Y axis: ±50m

7. Gain correction on module 4
Gain correction, periodic effects every 4 row in response
Hit map in 2D
Corrections in rows (+40% -15%)
Corrections in columns (+50% -12%)
Large variations in occupancy over rows and columns, so correction is not precise for every pixel (due to different statistics). Calibration outside of TB is required!
Hit map in x
Hit map in y

8. Gain correction on module 4
Gain correction, periodic effects every 4 row in response
Original data:
Structure with period 4 is visible on rows
Correction with period 4 in rows – response gain is more homogeneous
Standard correction in rows and columns

9. Residuals: non-Gaussian tales at a 1 percent level
Module 0
Module 1
Module 2
Module 3
Module 4
Module 5

10. COG level resolution inside pixel
Projection of resolution in x and y
Cluster COG analysis: Lower bound of resolution based on noise and cluster cut level, signals on pixels and cluster size.
Areas of single pixel cluster size
Module 0
Module 1
Module 2
Module 3
Module 0
Module 1
Module 2
Module 5
Module 4
Resolution map inside pixel in x and y direction
Color scale: m
Module 3
Module 4
Module 5
Average resolution = sqrt (resX2 + resY2)

11. TB resolution results inside pixel
Sub pixel analysis from tracks, resolution plots:
Module 0
Module 1
Telescopes 4 and 5 are worse than telescopes 0 and 1. DUT 3 is the best in both directions.
Green boxes show variations of resolutions.
Module 2
Module 3
Resolution
Module 0
Module 1
Module 5
Module 4
Module 2
Module 3
Residuals
Color scale: m
Module 4
Module 5
Results are in agreement with COG level resolution analysis on previous slide
Color scale: m

12. Verification of analysis with simulation data
Resolutions reproduced from analysis of simulated data for best estimates from the real TB 2008 data. Errors in resolutions are ~0.1μm, values are averages over pixel area

13. Residuals and resolution Detailed table of results
Results after individual steps – averages, direction x:

14. Residuals and resolution Detailed table of results
Results after individual steps – averages, direction y:

15. Conclusion from the edge scan
Changing edge voltage does not influence the edge effect in LSR
Edge offset: 0V
Edge offset: 2V
Edge offset: 1V
Edge offset: 3V

16. Conclusion from bias scan
Changing bias affects seed and cluster size
Does not affect cluster charge and resolution
Cluster charge
Seed
Cluster size
Residuals
Resolutions

17. Cluster charge and seed in the angle scan
Expected behaviour:
rising cluster charge between 0 and ±4 deg (longer path)
effects of larger cluster size above ±4 deg
here 2x2 pixels summed only

18. Cluster size in the angle scan
Linear increase of cluster size above ±1 deg.

19. Resolution in the angle scan
Best resolution within ±1 deg (agreement with simulations from Ariane’s talk from Bonn workshop – see next slide)

20. Point Resolution in Z Point Resolution in Z At shallow angles cluster
size gets extremely large
and simple centre-of-gravity
approach yeilds poor
resolution due to inter-pixel
charge fluctuations. Resolution is improved by means of
η-algorithm (edge-technique)
In many cases at normal incidence
only one row is fired :
resolution is limited by pixel size
When track is inclined more than one
row is fired -> resolution gets better
A. Frey, MPI München /08/ DEPFET Workshop Bonn

21. Comments and open questions (important messages to R&D community)
Every 16th frame wrong in Linux DAQ or also in Windows DAQ? (Is it fixed?)
Gain correction:
Why does gain periodically change with period 4? (Switcher issue? Geometry layout of DEPFET?)
Why mainly in telescopes? (common powering?)
Gain correction should be done during characterization for every pixel
Why is there LSR effects? “V” and “Edge” effects? (design issue?) Laser test for measurement of those effects are done and will be evaluated soon, need to repeat it on telescope modules
Mechanical movement of modules was observed in level of 10 hours (~few tens of microns)
Lack of good telescopes for routine testing of DUT. Systematic effects coming from non-diagonal elements of correlation matrix between detectors have influence to alignment, fitting of tracks and residual plot shape. Simulation of geometry and all effects is needed for confirmation of results and elimination of systematic effects.

22. Conclusions Analysis of DEPFET TB2008 in Prague almost complete
Presented final results for:
individual detector resolutions
resolution vs. interpixel position
influence of edge voltage
resolution vs. bias
resolution vs. incidence angle
Summary:
To do:
energy scan

23. Backup slides

24. Gain correction
Gain correction, plot of seeds (green) and all pixels (red)
Non-Gaussian distribution
Median of quartile analysis for correction
Need few cycles of tuning:
Made correction for rows and cols (multiplication factor)
Recalculate signals in every cluster
COG cluster analysis
Check hit map homogenity
Check gain homogenity

25. Correlation matrices
Correlation matrix, non-diagonal correlations shows some effects

26. Influence of corrections to final position of hit
Corrections influence to impact point position: gain correction (upper plot) and h correction (button plot)
h correction: X-range is in +- 10m
gain correction: X-range is in m, module 4 have range 10x higher

27. Stability of measurement
Mechanical movement of modules in range of few tens microns in axis 0 over 10 hours in 43 sub runs of scan 1318

28. Stability of measurement
Mechanical movement of modules removed after individual alignment of sub runs (one sub run ~ 15 minutes)

29. COG level resolution inside pixel
Cluster COG analysis: Lower bound of resolution based on noise and cluster cut level, signals on pixels and cluster size.
Areas of single pixel cluster size
Plots are on period of 2 pixels

30. TB analysis results inside pixel
Sub pixel analysis from tracks, support plots:
Cluster size
Cluster charge
Seed

31. Gain correction on module 0
Gain correction, final correction, module 0, small periodical structure was observed

32. Gain correction on module 1
Gain correction, final correction, module 1, no periodical structure was observed

33. Gain correction on module 2
Gain correction, final correction, module 2, no periodical structure was observed

34. Gain correction on module 3
Gain correction, final correction, module 3, no periodical structure was observed

35. Gain correction on module 4
Gain correction, final correction, module 4, big periodical structure was observed

36. Gain correction on module 5
Gain correction, final correction, module 5, small periodical structure was observed

37. LSR corrections of edge effects and “V”
No data at this stage! (Step 2 of alignment)

38. LSR corrections of edge effects and “V”

39. LSR corrections of edge effects and “V” (Run 1318-032)
Description of analysis from Residuals to Resolution
Example of LSR corrections: After correction :

40. LSR corrections of edge effects and “V”
(Whole run 1318)

41. Before h correction
!!!

42. h correction functions

43. …after h correction

44. Calculation of detector resolutions
Detector resolution = RMS error of position measurement in the detector
Notes:
- „Mean“ square here also means averaging over the detector surface
- Detector resolution is NOT the best positon error we can achieve – if we have a track going through several detectors, we can obtain position estimates with errors smaller than the resolutions of individual detectors.
We calculate detector resolutions from the covariance matrix of fit residuals.
Each fit residual is a linear combination of detector measurement errors and multiple scattering deflections => residual covariance is a linear combination of measurement error covariance and multiple scattering covariance.
H is a projector
to the residual space
u are local hit cooridnates
G describes the geometry of multiple scattering
Σ and Δ are diagonal matrices of MS scatt.deflections and squared detector resolutions

45. Calculation of detector resolutions (cont'd)‏
This is the same as on previous slide.
RMS multiple scattering deflections can be calculated using the Moliere formula, so this allows us to express detector resolutions in terms of residual correlations and RMS multiple scattering deflections.
The procedure is somewhat complicated by the fact that H doesn't have full rank: its rank is 2 x (number of points on the track) – 4.
We can either use some matrix algebra to directly express the resolutions, or maximize likelihood.

46. Collected results presented on TIPP09 in Tsukuba (Japan)
1.8
2.5
2.1
1.3
1.4
1.7
1.5
2.0
Resolutions σ [μm]
2.8
3.4
2.4
3.0
Residuals σ [μm]
928
958
1050
1315
1028
1111
Seed [ADU]
3.2
3.3
4.5
4.1
3.9
Cluster Size 88 92
124
127
112
117
S/N Ratio
13.7
13.0
14.8
Noise [ADU]
1213
1259
1614
1884
1453
1599
Signal [ADU] 24 32
Pixel size [μm]
Axis y
Axis x
Detector 5
Detector 4
Detector 3
Detector 2
Detector 1
Detector 0