13.02.2008 warsaw university licas linear collider alignment & survey iwaa08, g. moss 1 the...
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IWAA08, G. Moss
113.02.2008
WarsawUniversity
LiCAS
Linear Collider Alignment & Survey
The LiCAS LSM SystemFirst measurements from the Laser Straightness Monitor
of the LiCAS Rapid Tunnel Reference Surveyor.
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Contents LiCAS Overview Straightness Monitor
Basics Produced system Beam Fitting Stability The Ray tracer Reconstruction Calibration Autocalibration Conclusions
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Sensitivity of Internal Components
Component
TrX TrY TrZ RotX RotY
RotZ
LSM √ √ √ √
FSI ± ± √ ± ±
Inclinometer
√(not used)
√
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Straightness Monitor Basics
LSM is used to measure:- Transverse translations- Rotations
Require 1µm precision over length of train
z
y Translation:Spots move same direction
Rotation:Spots move opposite directions
CCD Camera
Retro reflectorIncoming beam
Outgoing beam
The train needs to know how it is aligned internally.
Achieved by internal FSI and the Laser Straightness Monitor.
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Beam FittingMultiple beams fitted on each image
(to deal with reflections)
Typical difficult image Differences from data and fit (range of 2/256)
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Beam Fitting Real life beams fitted over 40 hours to: 1.28μm horizontally 0.54μm vertically Difference not understood – possibly
beam jitter
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Stability Large amount of data taken with no
planned movement
2 x 10 images every 10 minutes Data taken for 4 days
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Stability
Laser power increased here
0.78μm Standard deviation
0.55μm Standard deviation per camera. (Same as earlier)
Camera 2Camera 0 + Camera 2Camera 0 + Camera 2 added
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Stability
Launch/car1 are unstable to the order of 4 micro-radians over 4 days.
Motion of ~35μm on car3 (9.2m away)
Motion of ~15μm on car2 (4.7m away)
Motion of ~1μm on car1 (0.2m away & attached)
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Ray Tracer•Ray tracer used to calculate spot positions
•Highly flexible
•Agrees with completely independent Simulgeo simulation
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ReconstructionRay tracer is used as a part of a fit function for
the Minuit fitting package
Position & orientation of each LSM unit used as the fit parameters
CCD spots fitted by Chi-squared Minimisation Precise to ~0.5xSpot uncertainty for translations
~0.3 microns Precise to ~5xSpot uncertainty for rotations
~3 microradians Easy to take many images, average, then fit or fit
then average.
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Reconstruction
Orientation Parameters
Do Ray-trace
Traced BSSMeasured BSS
Compare
Difference isthe chi squared
Set Orientationin RayTracer
Change orientationparameters until chi-squared is a minimum
Orientation parametersin model should match their real life counterparts
Measured data
Variables changed
Data produced by ray-tracer
Start
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Internal Geometry
Model used needs correct geometry Camera positions & orientations Pellicle positions & orientations
These are the calibration constants Measured to 5-10 microns with CMM Need to know some better
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Constant ImportanceFractional Effect of Calibration Constant Errors
on X Reconstruction
-1.92E -05
-2.44E -05
-8.62E -05
-3.46E -05
0.0137672
0.0242108
0.00922344
0.00674144
-0.0137672
0.00236188
-0.00638842
0.00330743
0.00901177
-0.0179043
-0.00471597
-0.00426068
0.247563
-0.00162873
-0.00285011
-0.00681383
0.000784621
0.00940945
0.25524
-0.000568239
0.00261698
0.00384359
-4.70E -06
0.249913
0.00137205
0.00175043
0.0206908
-0.00990215
0.00122841
0.248757
-0.00119316
0.00416492
0.00387589
0.00299668
-0.0164883
0.00380746
-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30
Ca
lib
rati
on
Co
ns
tan
t
Fractional Effect
Fractional Effect of Calibration Constant Errors on Y Reconstruction
0.000232296
7.54E -05
-3.61E -05
1.16E -04
-0.0393707
0.542851
0.510581
-0.0186342
0.0354872
0.0321918
0.017355
0.51903
0.519738
0.0298428
0.00218116
-0.016493
-0.0112241
-0.0227298
-0.237067
-0.0186867
0.0091897
0.00853597
0.00627214
0.00698782
-0.233642
-0.0124712
0.0349322
0.0315577
-0.032755
-0.237208
-0.000936036
-0.0289897
0.00751996
0.0611489
-0.00809303
-0.245866
0.0279941
-0.0152319
0.0284279
0.0282809
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
Ca
lib
rati
on
Co
ns
tan
t
Fractional Effect
Fractional Effect of Calibration Constant Errors on X Rotation Reconstruction
0.00148791
0.00170907
0.000508503
0.000896225
-0.142667
2.40725
2.52964
0.524659
-0.0344198
0.0575502
-0.173775
-2.44857
-2.43335
0.393972
0.0327378
-0.0911257
0.0690915
-0.0982474
-0.0549693
-0.36683
-0.0802124
0.0984274
0.102507
-0.0780714
-2.63525
0.162835
-0.00473015
0.101802
0.0347473
2.47235
0.265889
0.174575
-0.150524
-0.0888212
-0.101556
0.187312
0.0177157
-0.00983479
-0.0433176
0.0211725
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00
Ca
lib
rati
on
Co
ns
tan
t
Fractional Effect
Fractional Effect of Calibration Constant Errors on Y Rotation Reconstruction
-0.000338973
-0.000396597
-0.000436897
-1.22E -05
-0.069971
0.0331497
0.0226464
0.0808236
0.18408
-0.249641
-0.120422
0.0440838
0.0320906
0.0664203
0.255743
-0.233498
0.0151639
0.0233963
-0.0565556
0.0145145
-0.0210639
-0.0481545
-2.43072
0.00614492
0.0153731
0.0758632
-0.162739
2.42701
-0.103565
0.00711689
-0.0102406
-0.0353695
-0.055106
-0.0834477
0.0763176
0.0233914
0.0407057
-0.0744809
-0.0576272
-0.027149
-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00
Ca
lib
rati
on
Co
ns
tan
t
Fractional Effect
Important Constants
CCD Y positions
CCD Z positions
Pellicle Y positions
Pellicle Z positions
1 micron error in parameter gives 0.25 – 0.5 micron / 2.5 – 5.0 microradian error in reconstructed parameter
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Classical Calibration
•This method compares spot positions generated using a set of calibration constants, to the measured values (knowing the correct orientation).
•Many orientations are used
•It changes the calibration constants until the difference between the measured spots is minimised.
•Complements linear algebra method (see presentation by A. Reichold.)
True Orientation (measured by laser tracker)
Setup RayTracer
Calibration Constants
Do Ray-trace
Traced BSSMeasured BSS(taken by cameras)
Compare
Add difference tototal chi squared
Set Correct Orientation
For n Orientations
Change calibration constants until chi-squared is a minimum
Calibration constantsin model should match their real life counterparts
Measured data
Variables changed
Data produced by ray-tracer
Start
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Classical Calibration Simulation run with typical values:
1μm camera resolution 3μm/10μradian observation error 80 orientations used 1mm component uncertainty
Important constants found to < 1 μm Other constants found to <100 μm (not
that useful)
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Classical Calibration Now USE the fitted constants Reconstruct many times and compare to the truth Mean residual gives systematic error of that system Standard Deviation is dominated by camera resolution – gives
statistical error of that system
Offset: 0.18μm
Offset: 0.69μ radians
Offset: -0.36μm
Offset: 2.80μ radians
Example run shown on right.
However – this is only one example. Would like to know what to expect in general.
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Classical Calibration Run simulation many times (with 0.1
mm component uncertainty) Collect the mean and standard
deviation values of the histograms produced
Create a histogram of these values For the mean histogram the standard
deviation gives the accuracy For the standard deviation histogram
the mean gives the precision
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Auto-Calibration
E = External unknowns (reconstructed variables) I = Internal unknowns (calibration constants) M = Measurements
M = F(E,I) Eg for a single LSM reading
8 measurements (CCD spot positions) 4 external unknowns 18 internal constant unknowns
(this is underconstrained) For 10 readings
80 measurements 40 external unknowns 18 internal constant unknowns
(This is overconstrained by 22 DoF)
We use the large overconstraint found with many readings to determine the calibration constants.
Complements both classical calibration methods Can be used with much more data and can show how constants change.
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Auto-Calibration
This method incorporates the calibration constants as part of the fitting process
Many runs are fitted en-masse and the individual chi-squareds summed
The constants that give the lowest total chi-squared are chosen.
S etup R ayTracer
C a lib ra tion C ons tan ts
M easured B S S(taken by cam eras)
R econstruc t
A dd to to ta l ch i squa red
F or n se ts o f beam spots
C hange ca lib ra tion cons tan ts un til to ta l ch i-squa red is a m in im um
C a lib ra tion constantsin m ode l shou ld m atch the ir rea l life coun terpa rts
M easured da ta
Variab les changedD a ta p roducedby reconstructo r
S ta rt
R econstruc tedO rien ta tion
D isca rdedC h i-S quared from fit
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Auto-Calibration Simulations have been performed using
typical uncertainties 40 runs 1μm camera resolution 0.1mm constant uncertainty
Find most important constants to <0.3μm (after corrections)
Problems (as expected) with scaling & offsets
Still a useful addition to calibration