- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Design of dedicated tilt-to-length calibration maneuvers for LISA

Henry Wegener*, Sarah Paczkowski, Marie-Sophie Hartig, Martin Hewitson, Gerhard Heinzel, and Gudrun Wanner†

  • *Contact author: henry.wegener@aei.mpg.de
  • †Contact author: gudrun.wanner@aei.mpg.de
PDF

Phys. Rev. D 112, 023006 – Published 7 July, 2025

DOI: https://doi.org/10.1103/ndwh-vr2y

Abstract

Tilts of certain elements within a laser interferometer can undesirably couple into measurements as a form of noise, known as tilt-to-length (TTL) coupling. This TTL coupling is anticipated to be one of the primary noise sources in the Laser Interferometer Space Antenna mission, after time delay interferometry is applied. Despite the careful interferometer design and calibration on the ground, TTL is likely to require in-flight mitigation through postprocessing subtraction to achieve the necessary sensitivity. Past research has demonstrated TTL subtraction in simulations through the estimation of 24 linear coupling coefficients using a noise minimization approach. This paper investigates an approach based on performing rotation maneuvers for estimating coupling coefficients with low uncertainties. In this study, we evaluate the feasibility and optimal configurations of such maneuvers to identify the most efficient solutions. We assess the efficacy of TTL calibration maneuvers by modulating either the spacecraft attitude or the moving optical subassembly yaw angle. We found that sinusoidal signals with amplitudes of around 30 nrad and frequencies near 43 mHz are practical and nearly optimal choices for such modulations. Employing different frequencies generates uncorrelated signals, allowing for multiple maneuvers to be executed simultaneously. Our simulations enable us to estimate the TTL coefficients with precision below 15  μm/rad (1−σ, in free space) after a total maneuver time of 20 min. The results are compared to the estimation uncertainties that can be achieved without using maneuvers.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (23)

  1. M. Colpi et al., LISA definition study report, arXiv:2402.07571.
  2. M. Tinto and S. V. Dhurandhar, Time-delay interferometry, Living Rev. Relativity 24, 1 (2020).
  3. M. Armano et al., Tilt-to-length coupling in LISA Pathfinder: A data analysis, Phys. Rev. D 108, 102003 (2023).
  4. G. Heinzel, M. Hewitson, M. Born, N. Karnesis, L. Wissel, B. Kaune, G. Wanner, K. Danzmann, S. Paczkowski, A. Wittchen, M.-S. Hartig, H. Audley, and J. Reiche, LISA Pathfinder mission extension report for the German contribution, Technical Report, Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Teilinstitut Hannover, 2020, 10.2314/KXP:1692401564.
  5. H. Wegener, Analysis of tilt-to-length coupling in the GRACE follow-on laser ranging interferometer, Ph.D. thesis, Leibniz Universität Hannover, 2022, 10.15488/11984.
  6. H. Wegener, V. Müller, G. Heinzel, and M. Misfeldt, Tilt-to-length coupling in the GRACE follow-on laser ranging interferometer, J. Spacecr. Rockets 57, 1362 (2020).
  7. G. Wanner, S. Shah, M. Staab, H. Wegener, and S. Paczkowski, In-depth modeling of tilt-to-length coupling in LISA’s interferometers and TDI Michelson observables, Phys. Rev. D 110, 022003 (2024).
  8. S. Paczkowski, R. Giusteri, M. Hewitson, N. Karnesis, E. D. Fitzsimons, G. Wanner, and G. Heinzel, Postprocessing subtraction of tilt-to-length noise in LISA, Phys. Rev. D 106, 042005 (2022).
  9. S. Paczkowski et al., Update on TTL coefficient estimation for LISA using noise minimisation (to be published).
  10. D. George, J. Sanjuan, P. Fulda, and G. Mueller, Calculating the precision of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information, Phys. Rev. D 107, 022005 (2023).
  11. N. Houba, S. Delchambre, T. Ziegler, and W. Fichter, Optimal estimation of tilt-to-length noise for spaceborne gravitational-wave observatories, J. Guid. Control Dyn. 45, 1078 (2022).
  12. N. Houba, S. Delchambre, T. Ziegler, G. Hechenblaikner, and W. Fichter, LISA spacecraft maneuver design to estimate tilt-to-length noise during gravitational wave events, Phys. Rev. D 106, 022004 (2022).
  13. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Automatic alignment of optical interferometers, Appl. Opt. 33, 5041 (1994).
  14. J.-B. Bayle, Simulation and data analysis for LISA, Ph.D. thesis, Université de Paris, 2019, https://hal.archives-ouvertes.fr/tel-03120731/document.
  15. M. Otto, Time-delay interferometry simulations for the Laser Interferometer Space Antenna, Ph.D. thesis, Leibniz Universität Hannover, Germany, 2015, 10.15488/8545.
  16. M. Hewitson et al., lisasim: An open-loop LISA simulator in matlab, Report No. LISA-LCST-INST-DD-003, Albert Einstein Institute, 2021.
  17. M. Armano et al. (LISA Pathfinder Collaboration), LISA Pathfinder micronewton cold gas thrusters: In-flight characterization, Phys. Rev. D 99, 122003 (2019).
  18. TEB, LISA—Optical assembly tracking mechanism development, Report No. ESA-SCI-F-ESTEC-SOW-2019-028, European Space Agency, 2021, Programme Reference: C215-137FT.
  19. M. Hewitson et al., LISA performance model, Report No. LISA-LCST-INST-TN-003 i2.1, Albert Einstein Institute, 2021.
  20. S. Paczkowski, M. Hartig, and R. Giusteri, Post-processing subtraction of tilt-to-length noise in LISA—Phase B1 investigations, Report No. LISA-LCST-INST-TN-017 i1.0, Albert Einstein Institute, 2023.
  21. M. Chwalla et al., Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer, Phys. Rev. Appl. 14, 014030 (2020).
  22. M.-S. Hartig, J. Marmor, D. George, S. Paczkowski, and J. Sanjuan, Tilt-to-length coupling in LISA—uncertainty and biases, Classical Quantum Gravity 42, 045004 (2025).
  23. J. L. Crassidis and J. L. Junkins, Optimal Estimation of Dynamic Systems (CRC Press LLC, Boca Raton, Florida, USA, 2004).

Outline

Information

Phys. Rev. D 112, 023006– Published 7 July, 2025
  • Received 22 November 2024
  • Accepted 23 May 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation