1. Intra-Tower Tracker Alignment Instrument Analysis Workshop 4
Gamma-ray Large Area Space Telescope
Intra-Tower Tracker Alignment
Michael Kuss
INFN Pisa
Instrument Analysis Workshop 4
SLAC
15 July 2005

2. Towers …
the ideal tower
the real tower
a rotation
a horizontal shift
a vertical shift

3. Class Residual Class Residual is used for alignment:
Residual(const TString="MyRootFile.root", const TString="residual.root", const TString geo="");
~Residual() { delete myEvent; delete myTracker; }
void Go(int lastEntry=-1);
// general for DrawXxx: residual is h_abs - h_abs_ext
// ***********
// draws the residual, top without fitting, bottom with gauss fit
void DrawResidual(TString plane, TCut="");
// draws top the slope vs. residual, bottom the profile with pol1 fit
void DrawResSlope(TString plane, TCut="");
// draws top the other coordinate vs. residual, bottom profile with pol1 fit
void DrawResOrd(TString plane, TCut="");
// draws the slope profiles for all planes
void DrawResSlopeAll(TCut="abs(h_abs_ext-h_abs)<1");
// draws the ordinate profiles for all planes
void DrawResOrdAll(TCut="abs(h_abs_ext-h_abs)<1");
// attempt to do a "statistical" (not event be event) correction of rotZ of
// planes. 2x3 histograms. Left uncorrected, right rotZ corrected. Top
// ordinate vs. residual, middle profile of that, bottom residual.
void DrawResOrdCorr(TString plane, TCut="");

4. What does it do? What does it not do?
aligns planes horizontally, along the measured coordinate
aligns planes vertically
does an estimate of the rotation around z
What does it not do?
doesn’t align planes horizontally, parallel to the strips
doesn’t determine rotations around x and y

5. General Procedure user> source cmt/setup.sh
user> rh9_gcc32opt/runTreeMaker.exe digi.root recon.root ”” tree.root
user> root
root [0] .x compile.C
root [1] Residual* r = new Residual(”tree.root”,”res.root”,”geo.txt”)
… opens tree.root for reading, res.root for writing, and reads the geometry from geo.root.
root [2] r->Go()
... reads events from the tree file. Fits a straight tracks, discarding the clusters of both planes of the tray to which the plane to be studied belongs. For each cluster(!), fills a small tree with
plane name
measured horizontal position of cluster (vertical to the strips)
measured vertical position of cluster (i.e., elevation of the plane)
extrapolated horizontal position of cluster vertical to the strips (track fit)
extrapolated horizontal position of cluster parallel to the strips (track fit in the other view)
inverse slope of track
and saves the small tree in the residual file.
root [3] r->Draw...() // e.g. r->DrawResSlopeAll()
utilizes one of the Draw... methods. And saves a new geometry to disk.

6. selecting tracks

7. Residual r->DrawResidual(”X5”, ”abs(h_abs-h_abs_ext)<1”)
horizontal displacement: 59m

8. Residuals vs. slope (horizontal and vertical alignment)
r->DrawResSlope(”Y9”, ”abs(h_abs-h_abs_ext)<1&&abs(invSlope)<1”) X4 X3 X2 X1 X0
real
position
ideal
res = x + z · cot(θ) θ
horizontal displacement: 157m
vertical displacement: 81m
Aligns:
horizontal ( to strips)
vertical

9. Residuals vs. slope of track (all planes)
r->DrawResSlopeAll()

10. Residuals vs. position in other view
r->DrawResOrd(”Y9”, ”abs(h_abs-h_abs_ext)<1”)
Y, real position
Y, ideal position X
horizontal displacement: 65m
rotation around z: 0.54mrad

11. Residuals vs. position in other view (all planes)
r->DrawResOrdAll()
r->DrawResOrdCorr(”Y9”)
res_x%y
res_x-p0-y*p1%y

12. Alignment results

13. How To Align Alignment is an iterative process. Before RA v8r3p1:
run with 10k events till convergence
run with 20k events till convergence
run with 50k events till convergence
run with 100k events till convergence
initially, convergence was defined as maximum deviation of any parameter of two consecutive geometries to be less than 10μm (but not more than 5 iterations)
1 iteration for 100k events takes about 1h CPU
Since RA v8r3p1:
run with 100k events till “real” convergence
“reaI” convergence is achieved if a geometry repeats (but not more than 50 iterations)
1 iteration for 100k events takes about 6 min CPU
result is “perfect” geometry

14. Alignment: 1st try

15. Intra-Tower Alignment Blindness
Attention
Intra-tower alignment is blind versus:
translation
shearing
vertical scaling (horizontal is fixed by strip dimensions)
rotation
translation of the planes of one view vs. the other
rotation of the planes of one view vs. the other
After every iteration, separately in each view, I “correct” for:
∑posh = 0 (horizontal translation)
∑posh2 min. (shearing)
∑(posv-posv,ref) = 0 (vertical translation)
∑(posv-posv,ref)2 min. (vertical scaling)
∑rotz = 0 (rotation around z)

16. Alignment: 3rd try

17. 1st 100k

18. 1st 100k

19. 2nd 100k

20. 3rd 100k

21. 4th 100k

22. 5th 100k

23. Reproducibility: vertical
absolute position / mm
deviation / um
plane #0 #1 #2 #3 #4
avg
#0-avg
#1-avg
#2-avg
#3-avg
#4-avg Y0
42.610
42.581
42.587
42.612
42.605
42.599 11
-18
-12 13 6 X0
44.710
44.702
44.692
44.701
44.689
44.699 3 -7 2
-10 X1
74.402
74.383
74.373
74.394
74.377
74.386 16 -3
-13 8 -9 Y1
76.751
76.743
76.749
76.753
76.750 -6 4 1 Y2 X2 7 X3 -4 Y3 -2 -5 Y4
-11 15 X4 X5 Y5 Y6 X6 -1 X7
-14 Y7 Y8 5 X8 12 X9 -8 Y9
Y10
X10
X11
Y11
Y12
X12
X13
Y13
Y14
X14
X15
Y15
Y16
X16
X17 10
-15 9
Y17
STDEV:

24. Reproducibility: horizontal
absolute position / mm
deviation / um
plane #0 #1 #2 #3 #4
avg
#0-avg
#1-avg
#2-avg
#3-avg
#4-avg Y0
-0.064
-0.062
-0.054
-0.051
-0.053
-0.057 -7 -5 3 6 4 X0
-0.068
-0.072
-0.076
-0.070 -4 2 X1
-0.089
-0.087
-0.097
-0.092 5 Y1
-0.067 -2 1 Y2
-0.023
-0.025
-0.024 -1 X2
0.129
0.134
0.125
0.128 X3
0.124
0.126
0.122 Y3
0.153
0.147
0.149
0.148 Y4
0.151
0.150 -3 X4
0.132
0.133
0.130 X5
0.115
0.114
0.119
0.117
0.120 Y5
-0.078
-0.077
-0.080
-0.081
-0.082 Y6
-0.042
-0.040
-0.046
-0.047
-0.044 X6
-0.090
-0.086 X7
-0.075
-0.084 Y7
-0.052
-0.048
-0.055 Y8
-0.032
-0.031
-0.035
-0.033 X8
-0.071
-0.069 X9
-0.119
-0.121
-0.115
-0.118
-0.117 Y9
0.111
0.106
0.109
0.112
Y10
0.142
0.144
0.141
0.143
X10
-0.083
-0.085
X11
-0.108
-0.105
-0.102
-0.107
-0.104
Y11
-0.106
Y12
X12
0.045
0.043
0.046
X13
0.035
0.034
0.037
Y13
-0.018
-0.016
-0.015
-0.019
-0.017
Y14
-0.026
-0.029
X14
0.016
0.011
0.013
0.014
X15
0.005
0.004
0.000
0.002
0.003
Y15
0.017
0.019
0.018
Y16
0.023
0.025
0.024
X16
0.072
0.074
0.066
0.071
X17
0.041
0.038
0.036
Y17
0.020
STDEV:

25. The Future of LeaningTower
can only analyze single tower runs
introduces ambiguities for the resulting geometry
doesn’t iterate on rotations
people don’t like it anyway
 merge with AlignmentContainer

26. Intra-Tower Alignment Blindness (revisited)
Intra-tower alignment is blind versus:
translation
shearing
vertical scaling (horizontal is fixed by strip dimensions)
rotation
translation of the planes of one view vs. the other
rotation of the planes of one view vs. the other

27. Translation SOLVED Intra-tower alignment:
absolute position of a single tower is ambiguous
Inter-tower alignment:
tracks passing tower gaps fix the relative positions
SOLVED

28. Rotation SOLVED Intra-tower alignment:
rotation of a single tower with respect to some coordinate system is ambiguous
Inter-tower alignment:
tracks passing tower gaps fix the rotation of one tower vs. the others
SOLVED

29. There is no way to correct for shearing from data!
Metrology measurements?
Average over all towers?
Do we care? 50μm vs 554mm for a perpendicular track = 0.1 mrad

30. There is no way to correct the vertical scale from data!
Vertical Scaling
There is no way to correct the vertical scale from data!
Metrology measurements?
Average over all towers?
Do we care? 70μm vs 554mm for a 45° track = 0.1 mrad