WP3Frequency Scanning Interferometry

Analysis Techniques for the LiCAS RTRSJohn 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 FSIinternal 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.

• ωgli/ ωref =Dgli/Dref

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 φi and Δφi

– Can guess by φi+1=φi + Δφi and Δφi+1 = Δφi

– Improves guess by looking at residuals in data and sin(φi+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 up1) Carre, Lomb, peak fitting, length calculation

2) EKF, Lomb, peak fitting, length calculation

• Preliminary results show EKF increases the length measurement precision by ~20%

Thank You