WP3The LiCAS Laser Straightness

Monitor (LSM)Greg Moss

Contents

• Introduction• The LSM ray tracer• Reconstruction• Calibration Constants• Determining Calibration Constants• Planned work

• (Marker Reconstruction simulation)

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.

Sensitivity of Internal Components

Component TrX TrY TrZ RotX RotY RotZ

LSM √ √ √ √

FSI ± ± √ ± ±

Inclinometer √(not

used)

√

Ray Tracer•Ray tracer written in C++

•Open GL interface

•Highly flexible

•Agrees with Fortran version

•Can use many setups:

-Lab

-Car

-‘Virtual’ setups

-Any general setup

A ‘virtual’ setup has a mirror/camera combination replaced by the image of the camera in the mirror. It is mathematically equivalent (if the CCD X axes are inverted).

Reconstruction

Ray tracer is used as a part of a fit function for the Minuit fitting package

– Position & orientation of the LSM block used as the fit parameters

– CCD spots fitted by Chi-squared Minimisation– 100% effective to within nm with good

convention choice and no noise

Reconstruction• If perfectly set up reconstruction is limited by

beam spot fit precision (limited by camera noise)

• 0.7 microns currently used (Lab in air)• Gives reconstruction

precision of 0.24

microns & 1.67

micro-radians

Calibration

• Still need to know the exact position of the components

• These are the calibration constants

• The errors on the constants give the systematic error

• There are different possible sets of constants

Effect of Errors in Constants

• A large set of ray traces with many different calibration constants was taken.

• Error on the reconstructed parameters then plotted against each calibration constant.

• The gradient gives the dependence on

the constant.

With Standard SetupReconstruction Dependence on Calibration Constants - Standard Lab Setup

-3.00E+00 -2.00E+00 -1.00E+00 0.00E+00 1.00E+00 2.00E+00 3.00E+00

lsmBlockX

lsmBlockY

lsmBlockRotXpp_s

lsmBlockRotYp_s

Re

co

ns

tru

cti

on

Pa

ram

ete

r

Error Correlation

CCD3RotZ_s

CCD3RotYp_sCCD3RotXpp_s

CCD3Z

CCD3YCCD3X

CCD2RotZ_sCCD2RotYp_s

CCD2RotXpp_s

CCD2ZCCD2Y

CCD2X

CCD1RotZ_sCCD1RotYp_s

CCD1RotXpp_s

CCD1ZCCD1Y

CCD1X

CCD0RotZ_sCCD0RotYp_s

CCD0RotXpp_sCCD0Z

CCD0Y

CCD0XBS1RotZ_s

BS1RotYp_s

BS1RotXpp_sBS1Z

BS1Y

BS1XBS0RotZ_s

BS0RotYp_s

BS0RotXpp_sBS0Z

BS0YBS0X

lsmBlockRotYp_s

lsmBlockRotXpp_slsmBlockY

lsmBlockX

With Virtual Setup

Reconstruction Dependence on Calibration Constants - Virtual Lab Setup

-3 -2 -1 0 1 2 3

lsmBlockX

lsmBlockY

lsmBlockRotXpp_s

lsmBlockRotYp_s

Rec

on

stru

ctio

n P

aram

eter

Error Correlation

CCD3RotZ_s

CCD3RotYp_s

CCD3RotXpp_s

CCD3Z

CCD3Y

CCD3X

CCD2RotZ_s

CCD2RotYp_s

CCD2RotXpp_s

CCD2Z

CCD2Y

CCD2X

CCD1RotZ_s

CCD1RotYp_s

CCD1RotXpp_s

CCD1Z

CCD1Y

CCD1X

CCD0RotZ_s

CCD0RotYp_s

CCD0RotXpp_s

CCD0Z

CCD0Y

CCD0X

lsmBlockRotYp_s

lsmBlockRotXpp_s

lsmBlockY

lsmBlockX

Calibration Constant Determination

• Constants are being measured using a CMM• To determine the calibration constants more

accurately a brute force method is in development.

• The LSM block produces data in many different orientations

• Using externally measured orientation data (from a laser tracker) the calibration constants can be determined

• See next slide for details

Calibration Constant Determination

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

•This method compares spot positions generated with a set of calibration constants with the measured values (knowing the correct orientation).

•Many orientations are used

•It changes the calibration constants until the difference between the measured spots are the same as the calculated spots

Calibration Constant Determination

• Problems with Standard model – constants are heavily dependent on each other: correct minimum not found easily

• Virtual model gives correct answers to O(10-14)m if given perfect data

• If given realistic data some constants are found to O(10-7)m, some fail to be found within 10-5m.

• However, the constants that are found well are the ones the reconstruction is sensitive to!

• Reconstructing using these constants as the only source of error gives precision of 0.037 microns & 0.25 micro-radians. (Currently only done twice – complete test planned)

• Adding 0.7 micron error to spot positions gives errors of 0.23 microns & 1.6 micro-radians - remaining miscalibration has no effect

Planned Work

• Some CMM measurements not made yet• Errors on laser tracker data not accounted for• Optimal number of measurements to take yet to

be found• Advanced error propagation not completed• Detailed investigation into covariance not

completed• Real Data to be taken in May• Combine with calibration of other RTRS

elements

Conclusions

• The LSM is a critical part of the LiCAS RTRS

• Highly precise & accurate reconstruction needed

• Needs to be well calibrated

• Some Calibration constants critical

• They can be found to the accuracy required

Marker Reconstruction Simulation

• The following are slides from Grzegorz Grzelak

• They show how a complete simulation of a tunnel survey is performed

• After the process the (mis)alignment can be put into PLACET and a beam simulation effected.

https://savannah.cern.ch/projects/placet/

Partially Calibrated Reconstruction

Virtual Setup – partially calibrated

Reconstruction Dependence on Calibration Constants - Virtual Setup with Camera positions known to 0.1 microns

-3.00E+00 -2.00E+00 -1.00E+00 0.00E+00 1.00E+00 2.00E+00 3.00E+00

lsmBlockX

lsmBlockY

lsmBlockRotXpp_s

lsmBlockRotYp_s

Rec

on

stru

ctio

n P

aram

eter

Error Correlation

CCD3RotZ_s

CCD3RotYp_s

CCD3RotXpp_s

CCD3Z

CCD3Y

CCD3X

CCD2RotZ_s

CCD2RotYp_s

CCD2RotXpp_s

CCD2Z

CCD2Y

CCD2X

CCD1RotZ_s

CCD1RotYp_s

CCD1RotXpp_s

CCD1Z

CCD1Y

CCD1X

CCD0RotZ_s

CCD0RotYp_s

CCD0RotXpp_s

CCD0Z

CCD0Y

CCD0X

lsmBlockRotYp_s

lsmBlockRotXpp_s

lsmBlockY

lsmBlockX