9th October 2003 Danny Hindson, Oxford University 1

Inner Detector Silicon Alignment

• Simple approach- Align in stages + rely on iteration

• Barrel to Barrel alignment- All 6 degrees of freedom- Update on convergence problems

• Internal Barrel alignment- Full detector demo of rphi and z alignment

9th October 2003 Danny Hindson, Oxford University 2

Barrel to Barrel Alignment• Plot phi residual and z residual surfaces• Fit known functions for each of 6 dof

Eg X Translationgives sine wave on phi residual surface

9th October 2003 Danny Hindson, Oxford University 3

Extract misalignments from surface• Fit these functions to the surfaces:

res = A + Bsin - Ccos + Dzcos - Ezsin- Zres = F + Drsin - Ercos

• Issues- phi movements of SCT modules creating an effect on the z

residual surface (even for =0 tracks)• Possibly caused by iPatRec tolerances affecting rphi and rphi’

differently• Currently derive D and E (X and Y rotations) from phi surface only

– Will retry with iPatRec v6.5.0 very shortly

Eg A=rotation about z axisB=X translation

9th October 2003 Danny Hindson, Oxford University 4

Barrel to Barrel Results• Randomly shuffle 6 dof of the seven barrels

- Rotations, RMS=0.2 mrad- Translations, RMS=100 μm

• Converges on sagitta distortion• Previously had problems with convergence

– Especially x and y rotations– Tried various things

• Multiple scattering? Tried higher energy tracks => no change• Tried limiting tracks to eta<1. Some tracks were hitting endcaps

- Situation much improved (now ~20 iterations rather than 50+)

9th October 2003 Danny Hindson, Oxford University 5

Sagitta Distortions• Sagitta type distortion for each of the 6 dof (tested down to 6 GeV)• Final barrel positions are a combination of all 6

Rotations about z axis X/Y translations

Y rotation~X translation (z)

9th October 2003 Danny Hindson, Oxford University 6

Convergence problems

9th October 2003 Danny Hindson, Oxford University 7

How do I tell if it’s worked?• Sagitta distortions are complicated:

– To visualise– To undo

• Use E/p (need lot of tracks)• In some cases I can’t fully do this

• Plot pt and impact parameter resolution– Plot a 2D profile histogram of pt vs eta– Take width of each bin and plot on simple histogram

• Do this before and after• 1/pt resolution at 40 GeV is ~1 TeV-1 for perfect detector

9th October 2003 Danny Hindson, Oxford University 8

Internal Barrel Alignment

• Adopted simple approach- Align rphi and z within rings- Align rings relative to each other

• Use overlaps to determine relative positions– More tolerant than basic residual to misalignments in other

barrels

• Lot of issues highlighted last time – some progress

9th October 2003 Danny Hindson, Oxford University 9

Internal Barrel Alignment• 1) Pixel z overlaps quite small

- Can`t ignore edge channels, since these are 300 m long (lose 75-90% of overlap hits)

- Have measured bias introduced by keeping them (30-75μm)

• 2) Full ring rotations mimic change in radius- Each overlap gives a non-zero reading- Because overlap residual is a function of (actual incidence angle)-

(fitted incidence angle)

• 3) iPatRec alignment tolerances- Now have v6.5.0.- Not sure if faster convergence compensates for slower speed

9th October 2003 Danny Hindson, Oxford University 10

Internal Alignment Demonstration

• Shuffle all modules in all 7 barrels in rphi– 3530 modules in TDR geometry– RMS of shuffle 0.1 to 0.2 mrad

• 2.5 million 6 GeV muon tracks spread over eta<1.5

• Used v3.0.2 of iPatRec

9th October 2003 Danny Hindson, Oxford University 11

Results

RMS before (mrad) RMS after (mrad)

Barrel 0 0.2 (=8 microns) 0.126

1 0.2 0.055

2 0.2 0.096

3 0.1 0.046

4 0.1 0.036

5 0.1 0.032

6 0.075 (=39 microns) 0.041

Tracks don’t hit all rings

Converged after 6 iterations (pattern recognition => ~24 hours)

9th October 2003 Danny Hindson, Oxford University 12

Example of one ring – Pixel barrel 1

9th October 2003 Danny Hindson, Oxford University 13

Future

• Visualisation tool– Possible to improve 3D behaviour? (ROOT?)

• Aims– Run full demo combining full barrel misalignments

with internal rphi/z misalignments– If time:

• Look at rotations around local z axis• Better approach to z overlaps in pixel detector