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ITS Track based Alignment
By
Bjørn S. NilsenThe Ohio State University
Contents
• Quick overview– What are the mis-alignments– Track model assumptions– Re-alignment form
• Results from perfect tracking/detectors
Mis-Alignment overview
• There are 2198 ITS Si detector
• Each detectors can be mis-positioned in all of 6 different ways.– Collection of detectors may be
effected in similar/correlated ways, whole ladders…
– SDD also has an additional possible mis-alignment, “Jitter”, or better t0
• ITS must also be aligned with respect to the rest of ALICE, TPC.
Track model
• Not dependent on a specific track model– Must return point of intersection with an
arbitrary plane, including error matrix– Must return direction of track at that point– Should be refit excluding points from a specific
detector, quickly
• with no ambiguity as to which points belong to track i.
€
tμi s;M{xν
i0L xνij L }( )
Re-Aligning
• For ITS is the thin detector/plane direction in the detector (local) coordinate system.
• Where i is the index for different tracks, and j is the index for different detectors. Together they define a RecPoint.
€
χ 2 = tμij (s j;M{xξ
ik≠ j L }) − (ΔRμτj 0 xτ
ij − ΔTμj )( )
1
σ μνij
( )2
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟tν
ij (s j ;M{xξik≠ j L }) − (ΔRντ
j 0 xνij − ΔTν
j( )
ij
∑
€
0 xμij ≡0Rμτ
j l xτij −0Tμ
j f xμij = ΔRμτ
j 0 xτij − ΔTμ
j
€
s j ( f ) n j = ΔRμτ
j 0Rτνj )
y νj , f Tμ
j = ΔRμτj 0Tτ
j + ΔTμj )
€
) y
€
∂χ 2
∂ΔTηl
= 0ηl
€
∂χ 2
∂ΔRηυl
= 0ηυl
Perfect Tracks & Detectors3000 events with 5 tracks each
____
__T
rack
s___
___
____
__D
etec
tors
____
_
Miss-alignedDet=885 x=0.1cm z=1.0E-7cm
3000 events with 5 tracks each
____
__D
etec
tors
____
___
____
Tra
cks_
____
_
Det=885
Det=885
After Re-Alignment__
____
Det
ecto
rs__
____
____
_Tra
cks_
____
_
Perfect — Re-Aligned__
____
Det
ecto
rs__
___
____
__T
rack
s___
___
1E-15
Numbers
€
0R =
1 0 0
0 −1 0
0 0 −1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟€
0T = 0 −38.5684 1.9754( )
€
χ 2 j= 885= 2.0081E −10
Perfect Alignment
€
mR =
1 0 0
0 −1 0
0 0 −1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟€
mT = −0.1 −38.5684 1.9753999( )
€
χ 2 j= 885= 244.451
Mis-Alignment
€
rR =
1 −8.59E − 20 −4.96E − 9
6.08E − 7 −1 1.27E − 6
−7.46E − 9 −2.54E − 21 −1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟€
rT = −3.35432E − 9 −38.5684026 1.975399991( )
€
χ 2 j= 885= 2.3579E −11
Re-Alignment
Realignment Results1E-8 to 1cm in x & z
1 0
0
0
0
0
0-1
-1
-38.57
0
1.975
Conclusion
• In plane displacements realignment good
• Progress is under way
• Must take into account track angles
Additional Slides
SDD “Jitter”Better t0
• ALICE SDD readout clock synchronous with Beam.– Jitter poor choice of word– t0 fix for all events– t0 may differ by detector
(half detector)
• Test Beam SDD readout clock asynchronous with Beam– Jitter varies event by event– Must be measured
Solution for In-plane
Equation for Full
€
) Q μν
ij ≡ΔRμτ
j Qτνij
ΔRρςj Qςρ
ij
Wμνij ≡ δμν +
) Q μν
ij
Yμνij ≡ δμν −
) Q μν
ij
Qμνij ≡0 )
n μj cos(θν
i )
χ2 After Re-aligning
Z
X
1.0 0.1 0.01 1.0E-3 1.0E-4 1.0E-5 1.0E-6 1.0E-7 1.0E-8 0.0
1.0 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.76e-11
0.1 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
0.01 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-3 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-4 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-5 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-6 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-7 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
1.0E-8 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11 2.36e-11
Differ at the 0.1% level