Time-Delay Interferometry [TDI] for LISA (2/2)
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Video Lecture 65 of 69
Copyright Information: This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen. The full course, including this and many other lecture videos, exercises, solutions to exercises, and lists of relevant reading, are available on the web at http://elmer.caltech.edu/ph237/
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### Lecture Description

Time-Delay Interferometry [TDI] for LISA - Week 18, Lecture 34  [by John Armstrong (JPL)]

1. The context:
1. Review of LISA; its main noise sources and their magnitudes
2. Why conventional Micheson-interferometer method of cancelling laser frequency noise will not work for LISA: large, time-varying difference in arm lengths

Basic idea of TDI

1. View unequal-arm LISA as symmetric system of 12 one-way links
2. From 12 data channels with appropriate time delays based on estimates of arm lengths, construct TDI observables which cancel the leading noises while keeping GW signals

Details of TDI

1. The nature of each data channel: fractional frequency shift of incoming laser light compared to local laser
2. Noises on each channel: laser phase noise, shot noise, proof-mass acceleration noise, noise in metrology data
3. Noise-cancelling combinations of time-delayed channel signals
1. GW-carrying combinations
2. Sagnac combination

Computation of LISA sensitivity to periodic waves -- sensitivity averaged over sky and over GW polarizations

1. Computation is done for each GW-carrying, noise-cancelling combination of data channels, using Monte Carlo sampling of sky directions and polarizations
2. Resulting sensitivity curves for the various GW combinations
3. Dependence of sensitivity on arm length
4. How sensitivity curves change if spacecraft triangle shape is changed

Uses of TDI:

1. On-orbit calibration of instrumental noise
2. Separation of GW background from instrumental noises

Practical problems due to:

1. Frequency offsets of lasers with respect to each other
2. Spacecraft relative motion
3. Noise in oscillators used for downconverting photodetector fringe rates, ...
4. How to deal with these problems

Summary

### Course Description

Caltech's Physics 237-2002: Gravitational Waves
A Web-Based Course organized and Designed by Kip S. Thorne, Mihai Bondarescu and Yanbei Chen.

This course contains all the materials from a graduate-student-level course on Gravitational Waves taught at the California Institute of Technology, January through May of 2002. The materials include Quicktime videos of the lectures, lists of suggested and supplementary reading, copies of some of the readings, many exercises, and solutions to all exercises. The video files are so large that it may not be possible to stream them from most sites, but they can be downloaded. Alternatively, the course materials on DVD's can be borrowed via Interlibrary Loan from the Caltech Library (click on CLAS, then on Call Number, then enter QC179.T56 2002 ).

Questions and issues about this course and website can be directed to Mihai Bondarescu or Yanbei Chen.