WP3 The 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 reflector Incoming 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 ComponentTrXTrYTrZRotXRotYRotZ 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 Setup

With Virtual Setup

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

Partially Calibrated Reconstruction

Virtual Setup – partially calibrated