Revised Unbiased Alignment Procedure for Precision Plane Alignment

Revised Unbiased Alignment Procedure for Precision Plane Alignment
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The revised unbiased alignment procedure ensures accurate alignment of planes by utilizing B=0 field data and minimizing errors. By following a systematic process of fitting errors, positions, rotations, and Euler angles iteratively, the alignment results in precise positioning of the detector planes. This method, as demonstrated in the Lepton Collider meeting presentation by Peter Kluit, guarantees a fully aligned detector relative to the reference plane, particularly suitable for straight lines in B=0 field conditions.

  • Precision Alignment
  • Unbiased Procedure
  • Detector Planes
  • Iterative Fitting
  • Lepton Collider
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  1. Revised Unbiased Alignment The revised unbiased alignment procedure is followed: - Only the B=0 field data is used - First the errors in planes 3-4 are put to mm in order not to biases the fit results in planes 0-1 - The position residuals in plane 0, then 1 are fitted (3 iterations) - The then positions in 0 and 1 are fixed and the rotations are fitted in planes 0 and 1 (2 iterations) - This gives an unbiased alignment of planes 0-3 - Then the errors in planes 3-5 are put to their nominal values - After that the planes 3-5 are aligned in position (3 iterations) - Finally, the 6 Euler angles of planes 3-4 are fitted (2 iterations) - Note that the Euler angles in plane 5 are fixed to 0 and in plane 5 only the positions are fitted! Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 1

  2. Alignment B=0 T run 6905 Euler angles = 0 100 150 200 250 100 200 300 400 500 50 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 0 residual y (mm) MIMOSA 0 residual x (mm) - - Std Dev Mean Entries Std Dev 0.005507 Mean Entries - - 0.000868 0.001333 0.01046 6787 6787 The plane rotations cause a broadening of the residual distributions 100 100 120 140 160 180 200 220 20 40 60 80 20 40 60 80 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 1 residual y (mm) MIMOSA 1 residual x (mm) - - Std Dev 0.02478 Mean Entries Std Dev 0.01266 Mean Entries 0.004169 0.003321 6787 6787 100 120 140 100 150 200 250 20 40 60 80 50 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 2 residual y (mm) MIMOSA 2 residual x (mm) - - Std Dev Mean Entries Std Dev 0.01004 Mean Entries - - 0.002422 0.01957 0.00293 6787 6787 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 2

  3. Alignment B=0 T run 6905 Euler angles = 0 100 150 200 250 300 350 100 200 300 400 500 600 50 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 3 residual y (mm) MIMOSA 3 residual x (mm) - - Std Dev Mean Entries Std Dev 0.006253 Mean Entries - 0.0003322 0.001016 0.01028 6787 6787 The plane rotations cause a broadening of the residual distributions 100 150 200 250 100 200 300 400 500 50 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 4 residual y (mm) MIMOSA 4 residual x (mm) - - Std Dev Mean Entries Std Dev 0.005758 Mean Entries - 0.002143 0.002624 0.0101 6787 6787 100 200 300 400 500 600 100 200 300 400 500 600 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0.2 - 0.15 0.1 - 0.05 0 0.05 0.1 0.15 0.2 0 - 0 - MIMOSA 5 residual y (mm) MIMOSA 5 residual x (mm) - - Std Dev 0.006346 Mean Entries Std Dev 0.005743 Mean Entries - 0.001774 0.001821 6787 6787 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 3

  4. Revised Unbiased Alignment This gives detector that is fully aligned wrt the reference plane. Note that this can only be done with straight lines (B=0 field) The results for angles etc. are different from the Table on slide 1. One can then fit all the B=0 field data with a curved fit and plot the residuals. This in order to compare later to the B=0.5 and 1 T data sets. In checking the alignment procedure it was found that there was a bug (shifts) in the calculation of the (local) residual code I AnalysisTelescope that produces the plots on these slides. After fixing the bug, the minuit fit procedure and plots correspond to each other. Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 4

  5. Full Alignment B=0 T run 6905 zoom 1000 1200 1400 1600 1800 1000 1200 200 400 600 800 200 400 600 800 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 0 residual y (mm) MIMOSA 0 residual x (mm) 0 0 Std Dev 0.002023 Mean Entries Std Dev 0.003632 Mean Entries 0.01 0.01 2.477e 0.0001942 6258 6258 0.02 0.02 05 - 100 200 300 400 500 600 700 800 900 100 200 300 400 500 600 700 800 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 1 residual y (mm) MIMOSA 1 residual x (mm) 0 0 Std Dev 0.003461 Mean Entries Std Dev 0.003925 Mean Entries 0.01 0.01 - 4.184e 3.718e 6258 6258 0.02 0.02 05 - 05 - 1000 1200 1000 200 400 600 800 200 400 600 800 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 2 residual y (mm) MIMOSA 2 residual x (mm) 0 0 Std Dev 0.002965 Mean - Entries Std Dev 0.004047 Mean Entries 0.01 0.01 - 0.0001007 3.98e 6258 6258 0.02 0.02 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 5

  6. Full Alignment B=0 T run 6905 zoom 1000 1200 1400 200 400 600 800 100 200 300 400 500 600 700 800 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 3 residual y (mm) MIMOSA 3 residual x (mm) 0 0 Std Dev 0.002788 Mean Entries Std Dev Mean Entries 0.01 0.01 2.869e 5.765e 0.0049 6258 6258 0.02 0.02 05 - 05 - 1000 200 400 600 800 100 200 300 400 500 600 700 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 4 residual y (mm) MIMOSA 4 residual x (mm) 0 0 Std Dev 0.003257 Mean Entries Std Dev 0.004137 Mean Entries 0.01 0.01 1.194e 2.699e 6258 6258 0.02 0.02 05 - 05 - 1000 1200 1400 1000 200 400 600 800 200 400 600 800 - - 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 5 residual y (mm) MIMOSA 5 residual x (mm) 0 0 Std Dev 0.003357 Mean Entries Std Dev 0.002971 Mean Entries 0.01 0.01 - - 1.903e 4.461e 6258 6258 0.02 0.02 05 - 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 6

  7. Full Alignment B=0 T run 6905 100 200 300 400 500 600 700 1 - 0 0.5 - q/p (1/GeV) B = 1T 0 Std Dev 0.01274 Mean - Entries 0.5 range -0.01 to 0.01 rms = 0.004 0.000293 6258 1 1000 1200 200 400 600 800 0 0 10 Std Dev 5.608 Mean Entries 20 chi2/ndof 2.937 6258 30 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 7

  8. Procedure for Alignment in B field Starting point is the B=0 field positions and rotations. First, the positions of planes 0,1,3,4,5 are fitted in three iterations Secondly, the 6 Euler angles in planes 0-1 and subsequently the 6 Euler angles in 3-4 are fitted in two iterations. The Euler angles in plane 2 and 5 are fixed to zero. At an earlier stage the B field angle was fitted and fixed to -0.0175 From the fits it is clear that rotations are need in all planes. The shifts in positions are smaller but non zero. The results of this procedure is shown in the following plots and Table. Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 8

  9. Alignment B=0.5 T run 6963 1000 1200 1400 1600 1800 1000 1200 1400 200 400 600 800 200 400 600 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 0 residual y (mm) MIMOSA 0 residual x (mm) - - Std Dev 0.001845 Mean Entries Std Dev 0.002493 Mean Entries - 9.103e 1.987e 5486 5486 05 - 05 - 100 200 300 400 500 600 700 800 900 100 200 300 400 500 600 700 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 1 residual y (mm) MIMOSA 1 residual x (mm) - - Std Dev 0.003062 Mean Entries Std Dev 0.003216 Mean Entries - 0.0001028 5.664e 5486 5486 05 - 1000 1200 1400 1000 200 400 600 800 200 400 600 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 2 residual y (mm) MIMOSA 2 residual x (mm) - - Std Dev 0.002406 Mean Entries Std Dev 0.002661 Mean Entries - 3.755e 2.818e 5486 5486 05 - 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 9

  10. Alignment B=0.5 T run 6963 1000 1200 1400 1600 1000 200 400 600 800 200 400 600 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 3 residual y (mm) MIMOSA 3 residual x (mm) - - Std Dev 0.001984 Mean Entries Std Dev 0.002802 Mean Entries - 3.656e 1.304e 5486 5486 05 - 05 - 1000 200 400 600 800 100 200 300 400 500 600 700 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 4 residual y (mm) MIMOSA 4 residual x (mm) - - Std Dev Mean Entries Std Dev 0.003016 Mean Entries 5.114e 5.38e 0.00272 5486 5486 05 - 05 - 1000 1200 1400 1600 1000 1200 200 400 600 800 200 400 600 800 - - 0 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0.02 0.015 0.01 0.005 0 0.0050.010.0150.02 0 - - - - MIMOSA 5 residual y (mm) MIMOSA 5 residual x (mm) - - Std Dev 0.001964 Mean - Entries Std Dev 0.002553 Mean Entries - 5.533e 2.64e 5486 5486 05 - 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 10

  11. Alignment B=0.5 T run 6963 100 120 20 40 60 80 1 - 0 0.5 - 0 Std Dev 0.06931 Mean Entries q/p (1/GeV) 0.5 p = 5 GeV - 0.1988 5486 1 1000 1200 1400 1600 200 400 600 800 0 0 10 Std Dev 4.024 Mean Entries 20 chi2/ndof Spread comes from beam 1.396 5486 30 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 11

  12. Alignment B=1 T run 6986 100 200 300 400 500 100 150 200 250 300 350 400 - - 50 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 0 residual y (mm) MIMOSA 0 residual x (mm) 0 0 Std Dev 0.001953 Mean Entries Std Dev 0.002098 Mean Entries 0.01 0.01 2.737e 0.0001497 1443 1443 0.02 0.02 05 - 100 150 200 250 100 120 140 160 180 200 220 - - 50 20 40 60 80 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 1 residual y (mm) MIMOSA 1 residual x (mm) 0 0 Std Dev 0.003115 Mean Entries Std Dev 0.002922 Mean Entries 0.01 0.01 - - 7.442e 0.0002889 1443 1443 0.02 0.02 05 - 100 150 200 250 300 350 400 100 150 200 250 300 - - 50 50 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 2 residual y (mm) MIMOSA 2 residual x (mm) 0 0 Std Dev 0.002216 Mean Entries Std Dev 0.002445 Mean Entries 0.01 0.01 3.015e 6.128e 1443 1443 0.02 0.02 05 - 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 12

  13. Alignment B=1 T run 6986 100 150 200 250 300 350 400 450 100 150 200 250 300 350 - - 50 50 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 3 residual y (mm) MIMOSA 3 residual x (mm) 0 0 Std Dev 0.002003 Mean Entries Std Dev 0.002429 Mean Entries 0.01 0.01 2.222e 0.0001799 1443 1443 0.02 0.02 05 - 100 150 200 250 300 100 120 140 160 180 200 220 240 - - 50 20 40 60 80 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 4 residual y (mm) MIMOSA 4 residual x (mm) 0 0 Std Dev 0.002526 Mean Entries Std Dev 0.002969 Mean Entries 0.01 0.01 - 1.572e 0.0003035 1443 1443 0.02 0.02 05 - 100 200 300 400 500 100 150 200 250 300 350 - - 50 0.02 0.02 0 0 - - 0.01 0.01 MIMOSA 5 residual y (mm) MIMOSA 5 residual x (mm) 0 0 Std Dev 0.001574 Mean Entries Std Dev 0.002505 Mean Entries 0.01 0.01 - 0.0001286 6.815e 1443 1443 0.02 0.02 05 - Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 13

  14. Alignment B=1 T run 6986 100 20 40 60 80 1 - 0 0.5 - 0 Std Dev 0.01232 Mean Entries q/p (1/GeV) 0.5 p = 5 GeV - 0.1678 1443 1 Distribution cut? 100 range -0.16 to 0.18 rms = 0.005 mean = -0.1685 200 300 400 500 0 0 10 Std Dev 4.005 Mean Entries 20 chi2/ndof 1.249 1443 30 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 14

  15. Alignment results plane B pos x pos y pos z euleryz eulerxz eulerxy (T) (um) (um) (mm) (deg) (deg) (deg) MIMOSA26_0 0 -25.984 -45.495 0.04 -0.1377 -0.7064 -0.5012 0.5 -20.747 -47.457 0.04 1.26458 1.8144 -0.5400 1.0 -16.338 -47.206 0.04 -0.0457 1.8785 -0.5240 MIMOSA26_1 0 -199.698 121.753 23.94 -1.2805 -0.47618 -0.77429 0.5 -197.475 121.121 23.94 -2.06528 -1.39395 -0.79131 1.0 -194.658 120.531 23.94 -1.42099 -1.66358 -0.77744 MIMOSA26_3 0 -154.309 53.843 369.81 4.24436 -1.76821 -0.040393 0.5 -151.583 51.971 369.81 1.9812 -4.49577 -0.011917 1.0 -147.91 48.582 369.81 -1.0040 -3.11723 -0.016902 MIMOSA26_4 0 63.521 176.188 392.27 2.74687 -1.91574 0.15911 0.5 65.102 178.319 392.27 1.47227 -3.70921 0.17223 1.0 66.342 178.385 392.27 -0.90756 -2.68643 0.17114 MIMOSA26_5 0 -40.305 -19.455 415.84 0 0 0 0.5 -50.079 -25.056 415.84 0 0 0 1.0 -59.234 -21.706 415.84 0 0 0 Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 15

  16. Interpretation of the alignment results The shift in position are largest for plane 5: 19 and 6 um (x y) Other planes also move e.g. plane 0: 8 and 2 um plane 3: 8 and 5 um The change in rotations in euleryz and eulerxz are far larger than Eulerxy that is rather stable. In planes 0-1 euleryz changes by 1 degrees and xz by 2.5 degrees. In planes 3-4 euleryz changes by 5 degrees and xz by 3 degrees. In Summary: shifts due to the field are observed in planes (up to 20 um) Rotation changes due to the field are large up to 5 degrees in the last three planes, in the first planes they go up to 2.5 degrees. These are modest changes that have to be applied for a high precision Si telescope with residuals 2-3 um. Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 16

  17. Momentum resolution telescope The momentum measurement in the Telescope comes basically from the angular rotation in the field in the two sets of planes. The momentum resolution at 1 T: 1) in the core of the 1 T data one finds ?(1/p) = 0.005 GeV-1 2) in the core of the 0 T data (assuming 1 T) ?(1/p) = 0.004 GeV-1 This corresponds at 6 GeV to a relative momentum resolution of ?p/p = 2.9% and 2.4% The momentum resolution in the 1 T is slightly worse, because of the presence of elelectrons with lower momenta. NB: In the 0.5 T data the momentum spectrum of the beam is rather spread out. That makes the estimate of the momentum resolution difficult. Lepton Collider meeting 13 December 2021 Peter Kluit (Nikhef) 17

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