S. M. Gibson, P. A. Coe, Photon02, 5 th September Coordinate Measurement in 2-D and 3-D Geometries using FSI Overview ATLAS Group, University of Oxford S. M. Gibson, P. A. Coe, A. Mitra, D. F. Howell, R. B. Nickerson Motivation – the alignment of ATLAS Demonstration system Square Grid Tetrahedral Grid Grid simulations Future Work

S. M. Gibson, P. A. Coe, Photon02, 5 th September ATLAS A Large Particle Detector for the Large Hadron Collider

S. M. Gibson, P. A. Coe, Photon02, 5 th September Motivation – the alignment of ATLAS ATLAS = A Toroidal LHC ApparatuS LHC = Large Hadron Collider 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  m

S. M. Gibson, P. A. Coe, Photon02, 5 th September Requirements for ATLAS Each arm of the geodetic grid must be measured to ~1  m. ~800 such 1-D length measurements to be made simultaneously. Minimal mass components within the inner detector. Radiation hard. No maintenance for 10 years.

S. M. Gibson, P. A. Coe, Photon02, 5 th September FSI Length Measurement TUNABLE LASER sweep  To interferometer with OPD to be measured DETECTOR M1 M2 Reference Interferometer with fixed OPD I MEASURED   I REF   Ratio of phase change = Ratio of OPDs  /c]D   /c]L 

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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. quill jewels beam splitter variable path fixed path delivery fibre return fibre support structure

S. M. Gibson, P. A. Coe, Photon02, 5 th September Demonstration System Splitter Tree and APD box Fibres Power Square Grid

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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.

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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

S. M. Gibson, P. A. Coe, Photon02, 5 th September Square Grid

S. M. Gibson, P. A. Coe, Photon02, 5 th September Calibration of Jewel Internal Offsets

S. M. Gibson, P. A. Coe, Photon02, 5 th September Model Degrees of Freedom Node A defines the origin Node B defines the X axis Node C is free in X and Y Node D is free in X and Y

S. M. Gibson, P. A. Coe, Photon02, 5 th September Reconstruction

S. M. Gibson, P. A. Coe, Photon02, 5 th September Reconstruction of Jewel C Translation (Square Grid) Std Dev = 400 nm

S. M. Gibson, P. A. Coe, Photon02, 5 th September Correlation Plots for ‘all lines’

S. M. Gibson, P. A. Coe, Photon02, 5 th September Square Grid Tetrahedral Grid Jewel C raised up by 100mm Now sensitive to Z coordinate, allowing three dimensional coordinate reconstruction

S. M. Gibson, P. A. Coe, Photon02, 5 th September Tetrahedral Grid Reconstruction Results

S. M. Gibson, P. A. Coe, Photon02, 5 th September Node C Three Dimensional Coordinate Reconstruction (Stationary Stage)

S. M. Gibson, P. A. Coe, Photon02, 5 th September Node C Three Dimensional Coordinate Reconstruction (Stage translated in X)

S. M. Gibson, P. A. Coe, Photon02, 5 th September Reconstruction of Jewel C Translation (Tetra Grid)

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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.

S. M. Gibson, P. A. Coe, Photon02, 5 th September Barrel Grid Simulations Lines of sight for one quadrant of Alignment Grid FEA model of carbon fibre support structure  m0m0m Simulgeo ref1 model of Alignment Grid nodes (jewels) ASSUME: end flanges are rigid rings & central jewels constrained in rotation Z X Y

S. M. Gibson, P. A. Coe, Photon02, 5 th September Single Barrel Grid Simulation Results NB: rigid end flanges assumed – currently repeating with increased number of degrees of freedom. 1 micron precision assumed throughout. Fixed inner barrel. Central jewels constrained in rotation Result without radial lines to modules

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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.

S. M. Gibson, P. A. Coe, Photon02, 5 th September 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.

S. M. Gibson, P. A. Coe, Photon02, 5 th September Steve sends his apologies from Pylos…