- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

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

Impact of missing data on the construction of LISA time-delay-interferometry Michelson variables

Ollie Burke1,*, Martina Muratore2,†, and Graham Woan1

  • *Contact author: ollie.burke@glasgow.ac.uk
  • †Contact author: martina.muratore@aei.mpg.de
PDF

Phys. Rev. Applied 25, 034041 – Published 12 March, 2026

DOI: https://doi.org/10.1103/xpvf-syrw

Abstract

We investigate the impact of missing input data on the construction of second-generation time-delay-interferometry (TDI) variables, which enable data analysis for the Laser Interferometer Space Antenna (LISA). TDI relies on the introduction of precise time delays into the raw interferometric data streams before they are combined to suppress otherwise dominant laser phase noise. We show that a single missing sample, corresponding to 0.25 s of data, will result in an effective data gap of approximately 90 s in the second-generation TDI output if further measures are not taken. This additional gap is largely independent of the initial gap duration, but it increases linearly with the order of the fractional-delay filter used for the computations. For a realistic gap scenario, incorporating both planned and unplanned data interruptions consistent with a target duty cycle of approximately 84%, we find that frequent, short-duration gaps (e.g., a total of 1000 per year, each of which has a duration of approximately 100 s) could result in an additional loss in the TDI variables of about one day per year, corresponding to a reduction of approximately 0.3% in duty cycle. This amounts to a loss of approximately one day of LISA data suitable for the global fit per year.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (67)

  1. Monica Colpi, Karsten Danzmann, Martin Hewitson, Kelly Holley-Bockelmann, Philippe Jetzer, Gijs Nelemans, Antoine Petiteau, David Shoemaker, Carlos Sopuerta, Robin Stebbins, et al., LISA definition study report, arXiv:2402.07571.
  2. Monica Colpi, Kelly Holley-Bockelmann, Tamara Bogdanovic, Priya Natarajan, Jillian Bellovary, Alberto Sesana, Michael Tremmel, Jeremy Schnittman, Julia Comerford, Enrico Barausse, et al., Astro2020 science white paper: The gravitational wave view of massive black holes, arXiv:1903.06867.
  3. Christopher P. L. Berry, Scott A. Hughes, Carlos F. Sopuerta, Alvin J. K. Chua, Anna Heffernan, Kelly Holley-Bockelmann, Deyan P. Mihaylov, M. Coleman Miller, and A. Sesana, The unique potential of extreme mass-ratio inspirals for gravitational-wave astronomy, arXiv:1903.03686.
  4. Massimo Tinto and Sanjeev V. Dhurandhar, Time-delay interferometry, Living Rev. Relativ. 17, 6 (2014).
  5. J. Aasi, et al., LIGO Scientific Collaboration, Advanced LIGO, Class. Quantum Grav. 32, 074001 (2015).
  6. B. P. Abbott, et al., LIGO Scientific, and Virgo Collaborations, Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016).
  7. Pau Amaro-Seoane, Heather Audley, Stanislav Babak, John Baker, Enrico Barausse, Peter Bender, Emanuele Berti, Pierre Binetruy, Michael Born, Daniele Bortoluzzi, et al., Laser interferometer space antenna, arXiv:1702.00786.
  8. Martin Staab, Marc Lilley, Jean-Baptiste Bayle, and Olaf Hartwig, Laser noise residuals in LISA from onboard processing and time-delay interferometry, arXiv:2306.11774.
  9. Jan Niklas Reinhardt, Philipp Euringer, Olaf Hartwig, Kohei Yamamoto, and Karsten Danzmann, Time-delay interferometry with onboard optical delays, Phys. Rev. D 110, 082005 (2024).
  10. Jean-Baptiste Bayle, Antoine Petiteau, and Hubert Halloin, Effect of filters on the time-delay interferometry residual laser noise for LISA, Phys. Rev. D 99, 084023 (2019).
  11. Massimo Tinto, Glenn de Vine, Jeffrey C. Livas, Kirk McKenzie, and Daniel A. Shaddock, Extended time-delay interferometry for LISA, Phys. Rev. D 102, 022003 (2020).
  12. Martina Muratore, Time delay interferometry for LISA science and instrument characterization. PhD thesis, Trento U., 2021.
  13. Marie-Sophie Hartig, Sönke Schuster, and Gudrun Wanner, Geometric tilt-to-length coupling in precision interferometry: Mechanisms and analytical descriptions, J. Opt. 24, 065601 (2022).
  14. 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).
  15. M.-S. Hartig, S. Paczkowski, M. Hewitson, G. Heinzel, and G. Wanner, Postprocessing subtraction of tilt-to-length noise in LISA in the presence of gravitational wave signals, Phys. Rev. D 111, 043048 (2025).
  16. Jean-Baptiste Bayle and Olaf Hartwig, Unified model for the LISA measurements and instrument simulations, Phys. Rev. D 107, 083019 (2023).
  17. European Space Agency (ESA. Science performance requirements document for LISA, 2022. LISA Science Requirements Document (SciRD).
  18. Eleonora Castelli, Quentin Baghi, John G. Baker, Jacob Slutsky, Jérôme Bobin, Nikolaos Karnesis, Antoine Petiteau, Orion Sauter, Peter Wass, and William J. Weber, Extracting gravitational wave signals from LISA data in the presence of artifacts, Class. Quantum Gravity 42, 065018 (2025).
  19. Ollie Burke, Sylvain Marsat, Jonathan R. Gair, and Michael L. Katz, Addressing data gaps and assessing noise mismodeling in LISA, Phys. Rev. D 111, 124053 (2025).
  20. Ruiting Mao, Jeong Eun Lee, and Matthew C. Edwards, Novel stacked hybrid autoencoder for imputing LISA data gaps, Phys. Rev. D 111, 024067 (2025).
  21. Kallol Dey, Nikolaos Karnesis, Alexandre Toubiana, Enrico Barausse, Natalia Korsakova, Quentin Baghi, and Soumen Basak, Effect of data gaps on the detectability and parameter estimation of massive black hole binaries with LISA, Phys. Rev. D 104, 044035 (2021).
  22. Quentin Baghi, Ira Thorpe, Jacob Slutsky, John Baker, Tito Dal Canton, Natalia Korsakova, and Nikos Karnesis, Gravitational-wave parameter estimation with gaps in LISA: A Bayesian data augmentation method, Phys. Rev. D 100, 022003 (2019).
  23. Jerome Carre and Edward K. Porter, The effect of data gaps on LISA galactic binary parameter estimation, arXiv:1010.1641.
  24. Lu Wang, Hong-Yu Chen, Xiangyu Lyu, En-Kun Li, and Yi-Ming Hu, Dealing with data gaps for TianQin with massive black hole binary signal, Eur. Phys. J. C 85, 120 (2025).
  25. Tyson B. Littenberg and Neil J. Cornish, Prototype global analysis of LISA data with multiple source types, Phys. Rev. D 107, 063004 (2023).
  26. Michael L. Katz, Nikolaos Karnesis, Natalia Korsakova, Jonathan R. Gair, and Nikolaos Stergioulas, Efficient GPU-accelerated multisource global fit pipeline for LISA data analysis, Phys. Rev. D 111, 024060 (2025).
  27. Senwen Deng, Stanislav Babak, Maude Le Jeune, Sylvain Marsat, Éric Plagnol, and Andrea Sartirana, Modular global-fit pipeline for LISA data analysis, Phys. Rev. D 111, 103014 (2025).
  28. Stefan H. Strub, Luigi Ferraioli, Cédric Schmelzbach, Simon C. Stähler, and Domenico Giardini, Global analysis of LISA data with galactic binaries and massive black hole binaries, Phys. Rev. D 110, 024005 (2024).
  29. P. Whittle, Curve and periodogram smoothing, J. R. Stat. Soc. Ser. B (Stat. Methodol.) 19, 38 (1957).
  30. Colm Talbot, Eric Thrane, Sylvia Biscoveanu, and Rory Smith, Inference with finite time series: Observing the gravitational Universe through windows, Phys. Rev. Res. 3, 043049 (2021).
  31. Oliver Edy, Andrew Lundgren, and Laura K. Nuttall, Issues of mismodeling gravitational-wave data for parameter estimation, Phys. Rev. D 103, 124061 (2021).
  32. Jean-Baptiste Bayle, Oskar Hartwig, and Markus Staab, LISA Instrument, Zenodo, 2023.
  33. M. Staab, J.-B. Bayle, and O. Hartwig, PyTDI (1.2.1). Zenodo (2022), https://doi.org/10.5281/zenodo.6867012.
  34. Marie-Sophie Hartig, Sönke Schuster, and Gudrun Wanner, Geometric tilt-to-length coupling in precision interferometry: Mechanisms and analytical descriptions, J. Opt. 24, 065601 (2022).
  35. M. Chwalla, K. Danzmann, M. Dovale Álvarez, J. J. Esteban Delgado, G. Fernández Barranco, E. Fitzsimons, O. Gerberding, G. Heinzel, C. J. Killow, M. Lieser, et al., Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer, Phys. Rev. Appl. 14, 014030 (2020).
  36. Olaf Hartwig and Jean-Baptiste Bayle, Clock-jitter reduction in LISA time-delay interferometry combinations, Phys. Rev. D 103, 123027 (2021).
  37. Dam Quang Nam, Yves Lemiere, Antoine Petiteau, Jean-Baptiste Bayle, Olaf Hartwig, Joseph Martino, and Martin Staab, TDI noises transfer functions for LISA, arXiv:2211.02539.
  38. Olaf Hartwig, Jean-Baptiste Bayle, Martin Staab, Aurélien Hees, Marc Lilley, and Peter Wolf, Time-delay interferometry without clock synchronization, Phys. Rev. D 105, 122008 (2022).
  39. Jean-Baptiste Bayle, Olaf Hartwig, and Martin Staab, Adapting time-delay interferometry for LISA data in frequency, Phys. Rev. D 104, 023006 (2021).
  40. Massimo Tinto, F. B. Estabrook, and J. W. Armstrong, Time-delay interferometry for LISA, Phys. Rev. D 65, 082003 (2002).
  41. Massimo Tinto and Sanjeev V. Dhurandhar, Time-delay interferometry, Living Rev. Rel. 17, 6 (2014).
  42. Martina Muratore, Daniele Vetrugno, and Stefano Vitale, Revisitation of time delay interferometry combinations that suppress laser noise in LISA, Class. Quantum Gravity 37, 185019 (2020).
  43. Michele Vallisneri, Geometric time delay interferometry, Phys. Rev. D 72, 042003 (2005). [Erratum: Phys. Rev. D 76, 109903 (2007)]
  44. Maude Le Jeune and Stanislav Babak, LISA Data Challenge Sangria (LDC2a) (Version v2) [Data set]. Zenodo (2022), https://doi.org/10.5281/zenodo.7132178.
  45. Martin Staab, Marc Lilley, Jean-Baptiste Bayle, and Olaf Hartwig, Laser noise residuals in LISA from on-board processing and time-delay interferometry, Phys. Rev. D 109, 043040 (2024).
  46. D. A. Shaddock, B. Ware, R. E. Spero, and M. Vallisneri, Postprocessed time-delay interferometry for LISA, Phys. Rev. D 70, 081101 (2004).
  47. Martin Staab, Jean-Baptiste Bayle, Olaf Hartwig, Aurélien Hees, Marc Lilley, Graham Woan, and Peter Wolf, Optimal design of interpolation methods for time-delay interferometry, Class. Quantum Gravity 42, 115002 (2025).
  48. Olaf Hartwig, Instrumental modelling and noise reduction algorithms for the Laser Interferometer Space Antenna. PhD thesis, Leibniz U., Hannover, 2021.
  49. Markus Otto, Time-delay interferometry simulations for the laser interferometer space antenna. PhD thesis, Leibniz University Hannover, 2015. Doctoral thesis.
  50. M. Abernathy, A. Amato, A. Ananyeva, S. Angelova, B. Baloukas, R. Bassiri, G. Billingsley, R. Birney, G. Cagnoli, M. Canepa, et al., Exploration of co-sputtered Ta2O5–ZrO2 thin films for gravitational-wave detectors, Class. Quantum Gravity 38, 195021 (2021).
  51. Olaf Hartwig, Jean-Baptiste Bayle, Martin Staab, Aurélien Hees, Marc Lilley, and Peter Wolf, Time-delay interferometry without clock synchronization, Phys. Rev. D 105, 122008 (2022).
  52. Waldemar Martens and Eric Joffre, Trajectory design for the ESA LISA mission, J. Astro. Sci. 68, 402 (2021).
  53. Strictly speaking, missing data of this form are represented by “quiet” NaNs: missing data that do not cause code to fail execution on detection of a NaN. As such, these quiet NaNs can be propagated through noise-mitigation pipelines with the idea of understanding how many extra quiet NaNs are detected downstream.
  54. Within the gravitational-wave literature, the quantity S is standard for representing the power spectral density of a stochastic process. Here, we choose S to represent a set of indices of a discrete random process defining the indices of missing data.
  55. Martin Staab, Jean-Baptiste Bayle, Olaf Hartwig, Aurélien Hees, Marc Lilley, Graham Woan, and Peter Wolf, Optimal design of interpolation methods for time-delay interferometry, Class. Quantum Gravity 42, 115002 (2025).
  56. Jean-Baptiste Bayle, Ollie Burke, Eleonora Castelli, and Natalia Korsakova, LISA glitch, 2022.
  57. Jean-Baptiste Bayle, Marc Lilley, Antoine Petiteau, and Hubert Halloin, Effect of filters on the time-delay interferometry residual laser noise for LISA, Phys. Rev. D 99, 084023 (2019).
  58. Note that short-duration, high-rate gaps may be contained in long-duration, low-rate gaps, as extensively demonstrated in Appendix pp1 and Appendix pp2.
  59. Monica Colpi and et al, LISA Definition Study Report, 2 2024.
  60. Neil J. Cornish, Time-frequency analysis of gravitational wave data, Phys. Rev. D 102, 124038 (2020).
  61. Noah Pearson and Neil J. Cornish, Handling data gaps for the next generation of gravitational-wave observatories, arXiv:2509.05479.
  62. Martina Muratore, Daniele Vetrugno, Stefano Vitale, and Olaf Hartwig, Time delay interferometry combinations as instrument noise monitors for LISA, Phys. Rev. D 105, 023009 (2022).
  63. Olaf Hartwig, Jean-Baptiste Bayle, Martin Staab, Aurélien Hees, Marc Lilley, and Peter Wolf, Time-delay interferometry without clock synchronization, Phys. Rev. D 105, 122008 (2022).
  64. Niklas Houba, Jean-Baptiste Bayle, and Michele Vallisneri, Robust Bayesian inference with gapped LISA data using all-in-one TDI-∞, Class. Quantum Gravity 42, 145007 (2025).
  65. Jean-Baptiste Bayle, Martin Staab, Samuel P. Francis, Emily Rose Rees, Robert Spero, and Gerhard Heinzel, Modulation-assisted time-delay interferometric ranging for LISA, Class. Quantum Gravity 42, 155009 (2025).
  66. Jan Niklas Reinhardt, Martin Staab, Kohei Yamamoto, Jean-Baptiste Bayle, Aurélien Hees, Olaf Hartwig, Karsten Wiesner, Sweta Shah, and Gerhard Heinzel, Ranging sensor fusion in LISA data processing: Treatment of ambiguities, noise, and onboard delays in LISA ranging observables, Phys. Rev. D 109, 022004 (2024).
  67. Mar_Mur and Ollie Burke, OllieBurke/gaps_tdi: Impact of gaps on time delay interferometric calculations (1.0.1). Zenodo (2025), https://doi.org/10.5281/zenodo.17977637.

Outline

Information

Phys. Rev. Applied 25, 034041– Published 12 March, 2026
  • Received 4 November 2025
  • Revised 21 December 2025
  • Accepted 13 January 2026
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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation