Development & validation of an absolute FSI network

1. Development & validation of an absolute FSI network STATUS & NEXT STEPS SU internal meeting 16 July 2015 Solomon William KAMUGASA

2. Content • N≈ 2 glass retroreflectors • First FSI prototype • Calibration alternatives • Proposal for next generation prototype • FSI multilateration redundancy study • Some simulations results based on 8 channel FSI

3. N≈2 retroreflector Pros • Wide viewing angle • Allows good geometry • Can be machined accurately • Sphericity λ/10 Cons • Limited return intensity • N varies with λ • Difficult to get in ‘standard’ sizes

4. Understanding N≈2 • Beam lost • Path followed by returned beam Transmitted Reflected Transmitted 0.8889 0.8889 * 0.1111 * Return intensity = Return intensity = 8.78% of emitted light

5. N≈2 reflector constant Reflector constant

6. N≈2 return intensities 10mm S-LAH79 Gain 8 average intensity [%] 30mm Etalon F=37.13mm collimator F=18.75mm collimator Distance [mm]

7. S-LAH79 lateral tolerance Vertical displacement [mm] Horizontal displacement [mm]

8. N≈2 Market study Ready for order • S-LAH79 (max diameter =10mm) • Etalon (current diameter =30mm) Awaiting info • TaFD55 can be done in diameter = 0.5”(12.7mm) • P-SF68 – awaiting slab dimensions

9. First prototype enabling centring of optical fibre end • Aluminium spherical support • Proof of concept • Existing 1.5” supports • Distances in different directions from same point

10. Offset definition Error caused by 0.1mm y-offset at various distances Offset definition Two possible offsets Along the beam (x-offset) Effect: significant - a constant Perpendicular to beam (y-offset) Effect: negligible - decreases with distance Distance error [nm] True distance [m]

11. X-offset calibration X-offset residuals Number of samples Residual [µm]

12. 1st FSI network

13. Alternative calibration strategy • Improvement of existing strategy • More stable supports • More data • Consider more than 3 points • Cheaper (existing components) • LSA solution based on CMM and FSI measurements • Both x & y offsets determined • Based on accurate CMM measurements • More costly (CMM time)

14. Proposal for motorised FSI prototype XY stage Ceramic sphere FSI collimator Ball bearings Support frame 3 ball bearing support Articulation arm y x • Advantages: • Easy calibration • Possible to measure distances in various directions from same point • Can be measured by QDaedalus & CMM

15. FSI redundancy study Observations from all FSI stations to all targets Global relative redundancy [%] Number of targets • Multilateration in general = low redundancy = low reliability • Reliability can be tremendously increased by: • Using more stations &/or targets • making multiple observations along a given line of sight

16. Optimal geometry for 4 channel FSI • 4 channel system, 1 target • Short tetrahedron with equilateral triangle base • 4th station – same x, z as target but extruded y • 4 stations minimum for LSA solution • 4 is half the number of existing channels (4 on each side of magnet) y z x xy error ellipse based on 10µm a priori sigma x z Semi minor axis sigma [µm] y Semi major axis sigma [µm] A priori sigma = 10µm Sx=Sy=Sz=9µm

17. Fiducialisation Simulation • Object: 300×400×300mm • 8 stations, 16 targets • 6 targets on each side ‘seen’ by 4 stations each • 2 targets on top of object & 2 to the extremes ‘seen’ by all 8 stations z y x

18. Simulation results Input: A priori stdev: 10µm Observations between most stations One entry per line of sight Total observations: 94 Unknowns: 72 6 constraints not included in calculation of precision

19. Simulation results Input: 2 entries per line of sight Number of observations:188 Number of unknowns:72

20. Simulation results Input: 1 entry per line of sight No observations between stations Number of observations:80 Number of unknowns:72

21. Simulation results Input: 2 entries per line of sight No observations between stations Number of observations:160 Number of unknowns:72

22. Next steps • Better understanding of N=2 • Prototype development • Further simulations • Measurements & inter-comparisons

23. Thank you for your attention http://pacman.web.cern.ch/