1. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 1 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

2. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 2 ATLAS A Large Particle Detector for the Large Hadron Collider

3. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 3 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

4. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 4 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.

5. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 5 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 

6. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. quill jewels beam splitter variable path fixed path delivery fibre return fibre support structure

7. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 7 Demonstration System Splitter Tree and APD box Fibres Power Square Grid

8. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 10 Square Grid

11. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 11 Calibration of Jewel Internal Offsets

12. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 12 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

13. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 13 Reconstruction

14. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 14 Reconstruction of Jewel C Translation (Square Grid) Std Dev = 400 nm

15. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 15 Correlation Plots for ‘all lines’

16. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 16 Square Grid Tetrahedral Grid Jewel C raised up by 100mm Now sensitive to Z coordinate, allowing three dimensional coordinate reconstruction

17. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 17 Tetrahedral Grid Reconstruction Results

18. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 18 Node C Three Dimensional Coordinate Reconstruction (Stationary Stage)

19. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 19 Node C Three Dimensional Coordinate Reconstruction (Stage translated in X)

20. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 20 Reconstruction of Jewel C Translation (Tetra Grid)

21. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 22 Barrel Grid Simulations Lines of sight for one quadrant of Alignment Grid FEA model of carbon fibre support structure 70 35  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

23. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 23 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

24. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 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. S. M. Gibson, P. A. Coe, Photon02, 5 th September 2002 26 Steve sends his apologies from Pylos…