9th october 2003james loken – oxford university1 sct x-ray alignment software a first look
TRANSCRIPT
9th October 2003 James Loken – Oxford University 1
SCT X-ray Alignment Software
A First Look
9th October 2003 James Loken – Oxford University 2
Complete Tomograph-set-up-
9th October 2003 James Loken – Oxford University 3
9th October 2003 James Loken – Oxford University 4
9th October 2003 James Loken – Oxford University 5
Hardware Layout Head ess. as for
complete system X-ray tube Collimation system,
~80m and ~330m wide beams
Rotary stage, precise to 0.36’’
9th October 2003 James Loken – Oxford University 6
Parameters: R, Ψ1 and Ψ2
Measured: Φ1 and Φ2
Result coordinates: r and φ
Accuracy achieved with the XTomo2D(at r ~ 500mm) :
σ(rφ) = 5 μmσ(r) = 20 μm
[see NIM, A457 (2001) 43-51]
Measuring tool: AEROTECH Rotary Stage, σ(φ) = 1’’
Two Dimensional X-rayTriangulation Scheme
9th October 2003 James Loken – Oxford University 7
Detector Orientation
9th October 2003 James Loken – Oxford University 8
X-ray Alignment Current Methods
Simulation (of Hits) HitToStrip (real data could enter here) StripToHit Reconstruction (from Hits) Analysis
Future Incorporate Position and Tilt sensors Diagnostic tools for Problem Solving Calibration of X-ray Gun
CopyHits (for debug)
9th October 2003 James Loken – Oxford University 9
Simulation
Loop over all 12 z positions Generate beams (2) at 201 phi
values Loop over barrels 3 – 6
Intersect beam with barrel radius Find appropriate detector and
intersect with beam Write accurate strip hit (and gun
pars) to hit list
Write modules hit to scan list
,
g
g gx y
,d
d dx y
0,0
9th October 2003 James Loken – Oxford University 10
HitToStrip
Read Scan list for modules hit Read hit list for hit and gun pars
Generate 10K strips with Gaussian for r-phi and u/v-phi dets (beam 0.5 mrad x 20 mrad (?))
Add 20% (?) random background strips Store as histogram
Save histograms (8) as root file
Repeat for each Scan (201 x 12)
9th October 2003 James Loken – Oxford University 11
Module Strip Data
Strip Number (+768 for U/V-Phi)
0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,5000
200
400
600
800
1,000
1,200
1,400
1,600
1,800
2,000
2,200 Entries : 22000 OutOfRange : 0 Mean : 937.17 Rms : 382.18
Module Strip Histogram for one scan
9th October 2003 James Loken – Oxford University 12
StripToHit
Read Scan list for modules hit Find Root file
Find Histogram for each module Search histogram (in each half) for largest peak Fit limited range around peak to Gaussian Extract peak value as accurate hit Write accurate strip hit (and gun pars) to hit list
Repeat for each module
Repeat for each Scan (201 x 12)
9th October 2003 James Loken – Oxford University 13
Fit to Strip Data
Strip Number
550 552 554 556 558 560 562 5640
100
200
300
400
500
600
700
800
900
1,000
1,100
1,200 Entries : 9864 OutOfRange : 0 Mean : 557.19 Rms : 3.3189
amplitude : 1140.6 mean : 557.21 sigma : 3.4966
U-Phi strips
Strip Number
578 579 580 581 582 583 584 585 586100
200
300
400
500
600
700
800
900
1,000
1,100
1,200
1,300
1,400
1,500
1,600
1,700
1,800
1,900
2,000
2,100
2,200 Entries : 9832 OutOfRange : 0 Mean : 582.33 Rms : 1.7699
amplitude : 2121.6 mean : 582.37 sigma : 1.8803
R-Phi strips
9th October 2003 James Loken – Oxford University 14
Reconstruction Equations
,
g
g gx y
2 2 1/ 2
From gun beam:
cos
sin
(( ) ( ) )
From detector strips:
cos
sin
where p = pitch = 80mu
s = Strip Number
Want to find , , by minimisin
b g g
b g g
b g b g
s d d
s d d
d d d
x x R
y y R
R x x y y
x x p s
y y p s
x y
0 0 0
0 0 0
g "b-s" above.
Have starting values , , , and can expand
; ; ;
Can linearize, and iterate fit.
d d d
d d m d d m d d m
x y
x x x y y y
,d
d dx y
0,0
9th October 2003 James Loken – Oxford University 15
…getting lazy now…
9th October 2003 James Loken – Oxford University 16
…and now…
9th October 2003 James Loken – Oxford University 17
Reconstruction Equations
00 01 02 0
10 11 12 1
220 21 22
m
m
m
c c c x v
c c c y v
vc c c
200 0 0
01 1 1
02 1 0 0 0
10 2 2 1
211 3 3
12 3 0 2 0
where
and w (1 cos )
and w ( cos sin )
( cos sin )
and w
and w (1 sin )
( cos sin
g
g g
d d
g
d d
c w
c w
c w w p s
c w w
c w
c w w
20 4 4 0 0 1 0
21 5 5 2 0 3 0
22 5 0 4 0
)
and w ( sin cos )
and w ( sin cos )
( cos sin )
d d
d d
d d
p s
c w w w p s
c w w w p s
c w w p s
1
m
m
C T V
T C V
or
0 0 0 1 1
1 0 2 1 3
2 0 4 1 5
0 0 0
1 0 0
( )
( )
( )
and
( cos cos )
( sin sin )
g g d d
g g d d
v a w a w
v a w a w
v a w a w
a x R p s x
a y R p s y
9th October 2003 James Loken – Oxford University 18
Some Results
dZ, microns
-200 -150 -100 -50 0 50 100 150 2000
1
2
3
4
5
6
7
8
9
10 Entries : 32 OutOfRange : 0 Mean : -1.6657 Rms : 18.317
Error in Z (barrel 3)
R*dPhi, microns
-20 -15 -10 -5 0 5 10 15 2002468
10121416182022
Entries : 32 OutOfRange : 0 Mean : 0.042256 Rms : 0.43248
Error in R*Phi (barrel 3)
dR, microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16
18
20 Entries : 32 OutOfRange : 0 Mean : -0.055209 Rms : 0.97847
Error in R (barrel 3)
dPhi, 0.1*mrad
-20 -15 -10 -5 0 5 10 15 2002468
1012141618202224
Entries : 32 OutOfRange : 0 Mean : 0.30633 Rms : 0.63630
Error in DetPhi (barrel 3)
9th October 2003 James Loken – Oxford University 19
…and with Banana Distortions
Strip number
dR, microns
0 100 200 300 400 500 600 700-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
100
Entries : 380 OutOfRange : 0 XMean : 389.46 XRms : 202.75 YMean : -4.1862 YRms : 26.984
Distortions in Plane (barrel 3)
Strip number
dR, microns
0 100 200 300 400 500 600 700-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
70
80
90
100
Entries : 380 OutOfRange : 0 XMean : 389.46 XRms : 202.72 YMean : 0.12399 YRms : 3.8308
Distortions in Plane (barrel 3)
9th October 2003 James Loken – Oxford University 20
Goodness of Fits
Chisq
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18 Entries : 56 OutOfRange : 0 Mean : 1.6748 Rms : 1.5328
Chisq for fits (barrel6)
Chisq
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14 Entries : 48 OutOfRange : 0 Mean : 2.3156 Rms : 1.3149
Chisq for fits (barrel5)
Chisq
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10 Entries : 40 OutOfRange : 0 Mean : 2.2863 Rms : 1.3042
Chisq for fits (barrel4)
Chisq
0 2 4 6 8 10 12 14 16 18 200123456789
1011
Entries : 32 OutOfRange : 0 Mean : 1.8463 Rms : 1.0096
Chisq for fits (barrel 3)
9th October 2003 James Loken – Oxford University 21
X-ray Gun off centre
Phi, radians
microns
0 1 2 3 4 5 6-5,000-4,000-3,000-2,000-1,000
01,0002,0003,0004,0005,000
moduleY - nominal
Phi, radians
microns
0 1 2 3 4 5 6-5,000-4,000-3,000-2,000-1,000
01,0002,0003,0004,0005,000
moduleX - nominal
Phi, radians
microns
0 1 2 3 4 5 6-5,000-4,000-3,000-2,000-1,000
01,0002,0003,0004,0005,000
moduleR - nominal
9th October 2003 James Loken – Oxford University 22
Recon Gun Shifted
Phi, radians
microns
0 1 2 3 4 5 6-500-400-300-200-100
0100200300400500
moduleY - nominal
Phi, radians
microns
0 1 2 3 4 5 6-500-400-300-200-100
0100200300400500
moduleX - nominal
Phi, radians
microns
0 1 2 3 4 5 6-500-400-300-200-100
0100200300400500
moduleR - nominal
9th October 2003 James Loken – Oxford University 23
Results from this for Barrel 3
microns
-200 -150 -100 -50 0 50 100 150 2000
2
4
6
8
10
12
14
16
18 Entries : 32 OutOfRange : 0 Mean : -0.82524 Rms : 19.389
Error in Z (barrel3)
0.1*mrad
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16
18 Entries : 32 OutOfRange : 0 Mean : 0.17450 Rms : 0.62137
Error in DetPhi (barrel3)
microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16
18
20 Entries : 32 OutOfRange : 0 Mean : -0.069691 Rms : 0.43359
Error in R*Phi (barrel3)
microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16 Entries : 32 OutOfRange : 0 Mean : 6.5117E-3 Rms : 1.1456
Error in R (barrel3)
9th October 2003 James Loken – Oxford University 24
…and Barrel 4
microns
-200 -150 -100 -50 0 50 100 150 2000
2
4
6
8
10
12
14 Entries : 40 OutOfRange : 0 Mean : -2.3696 Rms : 25.637
Error in Z (barrel4)
0.1*mrad
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16 Entries : 40 OutOfRange : 0 Mean : -0.060439 Rms : 1.4557
Error in DetPhi (barrel4)
microns
-20 -15 -10 -5 0 5 10 15 200
5
10
15
20
25 Entries : 40 OutOfRange : 0 Mean : 2.1388E-4 Rms : 0.68262
Error in R*Phi (barrel4)
microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14 Entries : 40 OutOfRange : 0 Mean : 8.8847E-3 Rms : 1.4005
Error in R (barrel4)
9th October 2003 James Loken – Oxford University 25
…and Barrel 5
microns
-200 -150 -100 -50 0 50 100 150 2000
1
2
3
4
5
6
7
8
9 Entries : 48 OutOfRange : 0 Mean : -3.2908 Rms : 31.961
Error in Z (barrel5)
0.1*mrad
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14
16
18
20 Entries : 48 OutOfRange : 0 Mean : 0.11069 Rms : 2.1072
Error in DetPhi (barrel5)
microns
-20 -15 -10 -5 0 5 10 15 200
5
10
15
20
25 Entries : 48 OutOfRange : 0 Mean : 0.058815 Rms : 1.0248
Error in R*Phi (barrel5)
microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12 Entries : 48 OutOfRange : 0 Mean : -0.38326 Rms : 4.1840
Error in R (barrel5)
9th October 2003 James Loken – Oxford University 26
…and Barrel 6
microns
-200 -150 -100 -50 0 50 100 150 2000
1
2
3
4
5
6
7
8
9
10 Entries : 56 OutOfRange : 0 Mean : -1.8592 Rms : 45.492
Error in Z (barrel6)
0.1*mrad
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12
14 Entries : 56 OutOfRange : 0 Mean : -0.74921 Rms : 4.1444
Error in DetPhi (barrel6)
microns
-20 -15 -10 -5 0 5 10 15 200
5
10
15
20
25
30 Entries : 56 OutOfRange : 0 Mean : 0.017796 Rms : 1.2875
Error in R*Phi (barrel6)
microns
-20 -15 -10 -5 0 5 10 15 200
2
4
6
8
10
12 Entries : 56 OutOfRange : 0 Mean : 1.4398 Rms : 4.9042
Error in R (barrel6)
9th October 2003 James Loken – Oxford University 27
Conclusions(Observations)
A good start has been made But much work to be done
If the Hardware works well, the Software can extract good results
It’s worrying to wait until 2005 to test it But we should get some test data sooner
A good Calibration of the Gun is needed