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

1. The Nature of Gravitational Waves
2. Gravitational Waves Data Analysis
3. Gravitational Wave Sources in Neutron Stars
4. Introduction to General Relativity: Tidal Gravity
5. Mathematics of General Relativity: Tensor Algebra
6. Mathematics of General Relativity: Tensor Differentiation
7. Introduction to General Relativity (4/5)
8. Introduction to General Relativity (5/5)
9. Weak Gravitational Waves in Flat Spacetime (1/6)
10. Weak Gravitational Waves in Flat Spacetime (2/6)
11. Weak Gravitational Waves in Flat Spacetime (3/6)
12. Weak Gravitational Waves in Flat Spacetime (4/6)
13. Weak Gravitational Waves in Flat Spacetime (5/6)
14. Weak Gravitational Waves in Flat Spacetime (6/6); Propagation of Gravitational Waves Through Curved Spacetime (1/5)
15. Propagation of Gravitational Waves Through Curved Spacetime (2/5)
16. Propagation of Gravitational Waves Through Curved Spacetime (3/5)
17. Propagation of Gravitational Waves Through Curved Spacetime (4/5)
18. Propagation of Gravitational Waves Through Curved Spacetime (5/5)
19. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (1/2)
20. Generation of Gravitational Waves by Slow-Motion Sources in Curved Spacetime (2/2)
21. Astrophysical Phenomenology of Binary-Star GW Sources (1/5)
22. Astrophysical Phenomenology of Binary-Star GW Sources (2/5)
23. Astrophysical Phenomenology of Binary-Star GW Sources (3/5)
24. Astrophysical Phenomenology of Binary-Star GW Sources (4/5)
25. Astrophysical Phenomenology of Binary-Star GW Sources (5/5); Post-Newtonian G-Waveforms for LIGO & Its Partners (1/2
26. Post-Newtonian Gravitational Waveforms for LIGO & Its Partners (2/2)
27. Supermassive Black Holes and their Gravitational Waves (1/3)
28. Supermassive Black Holes and their Gravitational Waves (2/3)
29. Supermassive Black Holes and their Gravitational Waves (3/3); Gravitational Waves from Inflation (1/2)
30. Gravitational Waves from Inflation (2/2)
31. Gravitational Waves from Neutron-Star Rotation and Pulsation (1/2)
32. Gravitational Waves from Neutron-Star Rotation and Pulsation (2/2)
33. Numerical Relativity as a Tool for Computing GW Generation (1/2)
34. Numerical Relativity as a Tool for Computing GW Generation (2/2)
35. The Physics Underlying Earth-Based Gravitational Wave Interferometers (1/4)
36. The Physics Underlying Earth-Based Gravitational Wave Interferometers (2/4)
37. The Physics Underlying Earth-Based Gravitational Wave Interferometers (3/4)
38. The Physics Underlying Earth-Based Gravitational Wave Interferometers (4/4)
39. Overview of Real LIGO Interferometers (1/2)
40. Overview of Real LIGO Interferometers (2/2)
41. Thermal Noise in LIGO Interferometers and its Control (1/2)
42. Thermal Noise in LIGO Interferometers and its Control (2/2)
43. Control Systems and Laser Frequency Stabilization (1/2)
44. Control Systems and Laser Frequency Stabilization (2/2)
45. Interferometer Simulations and Lock Acquisition in LIGO
46. Seismic Isolation in Earth-Based Interferometers
47. Quantum Optical noise in GW Interferometers (1/2)
48. Quantum Optical noise in GW Interferometers (2/2)
49. LIGO data analysis (1/2)
50. LIGO data analysis (2/2)
51. The Long-Term Future of LIGO: Facility Limits
52. The Long-Term Future of LIGO: Techniques for Improving on LIGO-II
53. Large Experimental Science and LIGO as an Example (1/2)
54. Large Experimental Science and LIGO as an Example (2/2)
55. Resonant-Mass GW Detectors for the HF Band (1/2)
56. Resonant-Mass GW Detectors for the HF Band (2/2)
57. CAJAGWR talk by W.O. Hamilton on Resonant-Mass GW Detectors
58. Doppler tracking of spacecraft for GW detection in the low frequency band
59. Pulsar timing for GW detection in the very low frequency band
60. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (1/2)
61. LISA (Laser Interferometer Space Antenna) for GW Detection in LF Band: Conceptual Design (2/2)
62. LISA's Lasers and Optics (1/2)
63. LISA's Lasers and Optics (2/2)
64. Time-Delay Interferometry [TDI] for LISA (1/2)
65. Time-Delay Interferometry [TDI] for LISA (2/2)
66. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (1/2)
67. LISA's Distrubance Reduction System (DRS) [Drag-Free System] (2/2)
68. The Big-Bang Observatory [BBO]: A Possible Follow-On Mission to LISA
69. GW's from Inflation and GW Detection in ELF Band via Anisotropy of CMB Polarization

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.

Resources:

• - Part A - Gravitational-Wave Theory and Sources
• - Part B - Gravitational-Wave Detectors - original outline
• - Part B - Gravitational-Wave Detectors - alternative outline with the lectures reordered more logically
• - Course Materials

Credits:
Lectures by Thorne and Guest Lecturers*
Video of lectures by Bondarescu and Chen
Homework problems by Thorne and Guest Lecturers
Homework solutions by Bondarescu and Chen

*John Armstrong (JPL), Barry Barish, Erik Black, Alessandra Buonanno, Yanbei Chen, Riccardo De Salvo, Ronald Drever, Matt Evans, William Folkner (JPL), William Hamilton (LSU), Mark Kamionkowski, Albert Lazzarini, Lee Lindblom, Sterl Phinney, Mark Scheel, Bonny Schumaker (JPL), Robert Spero (JPL), Alan Weinstein, Phil Willems.