Coordinate Measurement in 2D and 3D Geometries using FSI

1
Coordinate Measurement in 2-D and 3-D Geometries
using FSI
ATLAS Group, University of OxfordS. M. Gibson,
P. A. Coe, A. Mitra, D. F. Howell, R. B.
Nickerson

• Overview

• Motivation the alignment of ATLAS
• Demonstration system
• Square Grid
• Tetrahedral Grid
• Grid simulations
• Future Work

2
ATLASA Large Particle Detector for theLarge
Hadron Collider
3
Motivation the alignment of ATLAS
What is alignment? The procedure in which the
positions of the detector elements are determined
Inner Detector Geodetic Grid Physics requires 3-D
shape variations to be measured to 10 mm
ATLAS A Toroidal LHC ApparatuS LHC Large
Hadron Collider
4
Requirements for ATLAS

• Each arm of the geodetic grid must be measured to
  1 mm.
• 800 such 1-D length measurements to be made
  simultaneously.
• Minimal mass components within the inner
  detector.
• Radiation hard.
• No maintenance for 10 years.

5
FSI Length Measurement
DETECTOR
M1
M2
To interferometer with OPD to be measured
Reference Interferometer with fixed OPD
DQ 2p/cDDn
DF 2p/cLDn
Ratio of phase change Ratio of OPDs
6
Interferometers inside ATLAS

• Each line of the alignment grid inside ATLAS will
  consist of a quill (two optical fibres beam
  splitter) and a retro-reflector.

7
Demonstration System
Splitter Tree and APD box
Fibres Power Square Grid
8
Demonstration system Square Grid

• 6 simultaneous length measurements made between
  four corners of the square.
• 7th interferometer to measure stage position.
• Displacements of one corner of the square can
  then be reconstructed.

9
Overview of Measurements Reconstruction

• Simultaneous line of sight measurements
• Calibration of jewel internal offsets
• Check calibration by systematic removal of one
  line of sight in analysis
• Check precision of reconstruction

10
Square Grid
11
Calibration of Jewel Internal Offsets
12
Model Degrees of Freedom
Node C is free in X and Y
Node D is free in X and Y
Node A defines the origin
Node B defines the X axis
13
Reconstruction
14
Reconstruction of Jewel C Translation(Square
Grid)
Std Dev 400 nm
15
Correlation Plots for all lines
16
Square Grid
Tetrahedral Grid
Now sensitive to Z coordinate, allowing three
dimensional coordinate reconstruction
Jewel C raised up by 100mm
17
Tetrahedral Grid Reconstruction Results
18
Node C Three Dimensional Coordinate
Reconstruction (Stationary Stage)
19
Node C Three Dimensional Coordinate
Reconstruction(Stage translated in X)
20
Reconstruction of Jewel C Translation(Tetra Grid)
21
Grids for ATLAS

• The grid for ATLAS will contain
• eight hundred lines of sight
• in a complex geometry.
• A quarter of the Barrel grid
• One of the two Endcap grids
• The error propagation through these grids has
  been simulated.

22
Barrel Grid Simulations
Lines of sight for one quadrant of Alignment Grid
FEA model of carbon fibre support structure
23
Single Barrel Grid Simulation Results
Result without radial lines to modules
Central jewels constrained in rotation

• NB rigid end flanges assumed currently
  repeating with increased number of degrees of
  freedom.
• 1 micron precision assumed throughout.
• Fixed inner barrel.

24
Cross-check of Grid Simulations

• Full barrel grid simulations should predict
  errors on all nodes of grid, for given
  measurement precisions.
• Idea
• Take FEA model of perfect barrel
• Extract grid line lengths
• (add random errors to lengths)
• Pass to reconstruction software for calibration
  of model
• Distort FEA model eg, twist and/or multipole
  distortions
• Extract new lengths
• (add random errors to lengths)
• Pass to reconstruction software
• Calculate reconstructed node co-ordinates and
  compare with those in FEA model
• Repeat later including interpolation software.

25
Future Work

• Continuing studies with the tetrahedral grid
• More detailed full barrel grid simulations
• Cross check of simulations using distorted FEA
  model
• References
• ref1 used with kind permission of the author
• L. Brunel, SIMULGEO Simulation and
  reconstruction software for opto-geometrical
  systems, CERN CMS Note 1998/079.

26
Steve sends his apologies from Pylos