Zden ě k Dole ž al, Zbyn ě k Dr á sal, Peter Kody š , Peter Kvasni č ka

1. 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 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: 0-1.3 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 1.0-2.5 0.9-1.9 Module 2 Module 3 Residuals Color scale: 1.4-4.5 m 0.9-2.5 0.9-1.7 Module 4 Module 5 Results are in agreement with COG level resolution analysis on previous slide 1.0-3.5 1.2-4.1 Color scale: 0.9-4.1 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: 2V Edge offset: 0V 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 3.8.2006 – 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 3/08/2006 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 +- 0.5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 hcorrection !!!

42. hcorrection functions

43. …after hcorrection

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