WP3 Frequency Scanning Interferometry Analysis Techniques for the LiCAS RTRS John Dale

Introduction Aims and Requirements LiCAS-Rapid Tunnel Reference Surveyor (RTRS) Overview Current Status Frequency Scanning Interferometry (FSI)

Aims and Requirements ILC will have ~70km of beam lines. LiCAS will survey straight sections. Keep machine downtime to an acceptable level. –5m of tunnel per minute (7km of tunnel per day) –~ 30 times faster than a team of three surveyors using a laser tracker. Fully remote controlled –1 operator for multiple RTRS’s Required to enable alignment to 200 μm over 600m vertically (a betatron wavelength) 500 μm over 600m horizontally

produced by Dr Armin Reichold collider component LiCAS Concept Tunnel Wall Reconstructed tunnel shapes (relative co- ordinates) wall markers external FSI internal FSI LSM beam

LiCAS RTRS Train

Current Status Prototype shipped to DESY in spring Calibration to begin in May Prototype running and data taking over summer 2007

Tunable Laser Reference Interferometer Measurement Interferometer FSI Sub-System FSI sub-system uses 2 interferometers, with the same tuneable laser Reference Interferometer has a precisely known optical path length. As laser tunes interference fringes are produced. ω gli / ω ref =D gli /D ref 35.5 fringes 11.5 fringes Measurement Length 6*11.5/35.5= 1.94m Reference Length 6m

FSI Sub-System Reference Interferometers Laser EDFA Splitter Tree External FSI

Current Analysis Steps Reference Interferometer Phase Extraction using Carre algorithm –Analytical method to determine phase –Requires 4 points equally spaced in phase –Problem 1: points are evenly spaced in time not in phase, causes errors in the extracted phase. –Problem 2: Extracted phase in range 0-2π, requires unwrapping, can lead to unwrapping errors Spectral Analysis of Intensity vs. Extracted Phase –using the Lomb Periodogram Peak Fitting to give frequencies –Gaussian peak fitting

Analysis Techniques Under Development Extended Kalman Filtering (EKF) techniques for phase extraction –Recursive filter which estimates the state of a dynamic system. –Initial have φ i and Δφ i –Can guess by φ i+1 =φ i + Δφ i and Δφ i+1 = Δφ i –Improves guess by looking at residuals in data and sin(φ i+1 ) –Leads in incorrect improvement in region of π/2 and 3π/2 –Improved by running filter forwards and then backwards –Advantage 1: No phase unwrapping required –Advantage 2: Computationally quicker

Comparison between Carre and EKF 0.005% Noise 0.01% Noise

Preliminary comparison of length analysis between Carre and EKF Two analysis chains set up 1) Carre, Lomb, peak fitting, length calculation 2) EKF, Lomb, peak fitting, length calculation Preliminary results show EKF increases the length measurement precision by ~20%

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