Alternative approach to time-delay interferometry with optical frequency comb

Charlotte Zehnder; Hannah Tomio; Holly Leopardi; Kenji Numata; Kohei Yamamoto

arxiv: 2511.07679 · v2 · pith:RQULBQYVnew · submitted 2025-11-10 · 🌌 astro-ph.IM · gr-qc

Alternative approach to time-delay interferometry with optical frequency comb

Kohei Yamamoto , Hannah Tomio , Charlotte Zehnder , Kenji Numata , Holly Leopardi This is my paper

Pith reviewed 2026-05-21 18:49 UTC · model grok-4.3

classification 🌌 astro-ph.IM gr-qc

keywords optical frequency combtime-delay interferometryLISAgravitational wave detectionheterodyne frequenciespseudorangeslaser noiseclock synchronization

0 comments

The pith

Carrier-carrier heterodyne frequencies can monitor pseudorange time derivatives to suppress laser and clock noise in standard TDI.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper presents an alternative way to incorporate optical frequency combs into the metrology system for space-based gravitational wave observatories such as LISA. It demonstrates that after suitable processing, the measured carrier-carrier heterodyne frequencies directly yield the time derivative of the pseudoranges. These pseudoranges encode the physical light travel times between spacecraft and the relative clock differences. The method achieves noise removal and drift capture while leaving the existing time-delay interferometry framework unchanged. Laboratory tests with two independent systems confirm synchronization to better than 0.47 ns and jitter suppression near LISA performance targets.

Core claim

After proper treatment, it is possible to use the measured carrier-carrier heterodyne frequencies to monitor the time derivative of the pseudoranges, which represent the physical light travel time and the clock difference. This approach does not require changing the existing TDI framework, as previous OFC based efforts did. Furthermore, this approach naturally captures not only stochastic jitter but also clock offsets and slow drifts.

What carries the argument

Carrier-carrier heterodyne frequency measurements from the optical frequency comb metrology system, which after proper treatment supply the time derivative of pseudoranges for noise monitoring.

If this is right

The standard TDI framework remains usable without modification while still removing laser and clock noise.
Both stochastic jitter and clock offsets plus slow drifts are captured in the observation band.
Independent phase measurement systems can be synchronized to better than 0.47 ns accuracy.
Stochastic jitter reaches suppression levels around 15 pm/sqrt(Hz) matching LISA targets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The scheme could allow removal of electro-optic modulators from future metrology hardware designs.
It may improve long-term clock stability handling in extended multi-spacecraft gravitational wave missions.
Validation in a full three-spacecraft ground test would check performance under more realistic light-travel-time variations.

Load-bearing premise

The carrier-carrier heterodyne frequencies cleanly encode the time derivative of the pseudoranges after only proper treatment, without residual laser or clock noise that would need corrections outside standard TDI.

What would settle it

A measurement showing that processed heterodyne frequency data still leave significant residual laser or clock noise terms in the pseudorange derivatives that standard TDI cannot remove.

Figures

Figures reproduced from arXiv: 2511.07679 by Charlotte Zehnder, Hannah Tomio, Holly Leopardi, Kenji Numata, Kohei Yamamoto.

**Figure 2.** Figure 2: FIG. 2. The experimental setup is composed of two optical metrology systems (OMSs), which mimic two spacecraft. The OFC setup [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Clock di [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Noise budget of the signal combination [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Influence of wrong OFC mode numbers on synchroniza [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

read the original abstract

Spaceborne gravitational wave observatories, exemplified by the Laser Interferometer Space Antenna (LISA) mission, are designed to remove laser noise and clock noise from interferometric phase measurements in postprocessing. The planned observatories will utilize electro-optic modulators (EOMs) to encode the onboard clock timing onto the beam phase. Recent research has demonstrated the advantage of introducing an optical frequency comb (OFC) in the metrology system with the modified framework of time-delay interferometry (TDI): the removal of the EOM and the simultaneous suppression of the stochastic jitter of the laser and the clock in the observation band. In this paper, we explore an alternative approach with the OFC-based metrology system. We report that after proper treatment, it is possible to use the measured carrier-carrier heterodyne frequencies to monitor the time derivative of the pseudoranges, which represent the physical light travel time and the clock difference. This approach does not require changing the existing TDI framework, as previous OFC based efforts did. Furthermore, this approach naturally captures not only stochastic jitter but also clock offsets and slow drifts. We also present the experimental demonstration of our scheme using two separate systems to model two spacecraft. Using this novel approach, we synchronize the two independent phase measurement systems with an accuracy better than 0.47 ns, while the stochastic jitter in the observation band is suppressed down to the setup sensitivity around the LISA performance levels at 15 pm/sqrt(Hz).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a concrete lab demo of pulling pseudorange derivatives from OFC carrier beats to fit inside unchanged TDI, with decent sync and jitter numbers, but the mapping step is still lightly shown.

read the letter

The main point is that this work shows you can use an optical frequency comb setup to monitor the time derivative of the pseudoranges directly from carrier-carrier heterodyne frequencies and plug that into the standard TDI combinations without rewriting them. They demonstrate it in a lab with two separate systems standing in for spacecraft, reporting synchronization better than 0.47 ns and jitter down to 15 pm/sqrt(Hz) in the band, while also catching clock offsets and drifts along the way. That keeps the existing TDI pipeline intact, unlike earlier OFC approaches that changed the framework. The experimental side is the stronger part here. Modeling two independent phase measurement systems and getting performance numbers in the LISA range gives it more weight than a pure simulation would. The hardware simplification angle, removing EOMs while keeping noise suppression, is a practical step if the results hold. The softer spot is the central mapping. The claim rests on an unspecified proper treatment that turns those heterodyne frequencies into clean d(pseudorange)/dt with no leftover laser or clock noise terms that would leak into TDI. The abstract states it works but does not lay out the explicit frequency-to-derivative relation or an error budget showing full cancellation. If the full text has the derivation and checks that residuals are gone, that would tighten it up. Right now the performance numbers feel a bit dependent on that step being handled correctly. The experimental write-up also skips error bars and data selection details, which makes the quoted accuracy harder to evaluate on its own. This is for the LISA metrology and TDI implementation crowd. Someone working on onboard timing or laser systems would pick up useful setup ideas and performance targets. It has enough concrete experimental content and mission relevance to deserve a serious referee, even with the need for clearer documentation on the treatment step. I would send it to peer review so the details can get a proper check.

Referee Report

2 major / 1 minor

Summary. The paper proposes an alternative OFC-based metrology approach for LISA-like gravitational-wave observatories. It claims that, after an unspecified 'proper treatment,' measured carrier-carrier heterodyne frequencies can directly monitor the time derivative of the pseudoranges (encoding light-travel time plus clock difference) while leaving the existing TDI framework unchanged. The method is said to capture both stochastic jitter and slow clock offsets/drifts. An experimental demonstration with two independent phase-measurement systems modeling separate spacecraft reports synchronization to better than 0.47 ns and jitter suppression to ~15 pm/sqrt(Hz) in the observation band.

Significance. If the mapping and noise cancellation hold, the scheme could simplify onboard hardware by removing EOMs while preserving compatibility with standard TDI combinations, offering a practical route to suppress laser and clock noise without framework modifications. The reported experimental performance at LISA-relevant levels would constitute a useful incremental result for metrology-system design.

major comments (2)

[Abstract / method description] Abstract and method section: the central claim that carrier-carrier heterodyne frequencies equal d(pseudorange)/dt after 'proper treatment' is not accompanied by an explicit frequency-to-derivative relation or error budget demonstrating complete removal of residual laser-phase and clock-noise terms. Without this derivation, it remains unclear whether the reported performance is independent of the quantities being monitored or partly circular.
[Abstract] Abstract: the synchronization accuracy (0.47 ns) and jitter level (15 pm/sqrt(Hz)) are stated without error bars, data-selection criteria, integration time, or quantitative comparison to a baseline TDI implementation on the same hardware; these omissions make it impossible to assess whether the result substantiates the 'no change to TDI' claim.

minor comments (1)

[Abstract] The phrase 'setup sensitivity around the LISA performance levels' is vague; a direct numerical comparison to the LISA requirement curve or to the measured noise floor of the apparatus would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript describing an alternative OFC-based metrology scheme for LISA-like observatories. The feedback highlights areas where explicit derivations and experimental details can be strengthened. We respond point by point below and will incorporate revisions to improve clarity while preserving the core claims supported by the existing analysis and data.

read point-by-point responses

Referee: [Abstract / method description] Abstract and method section: the central claim that carrier-carrier heterodyne frequencies equal d(pseudorange)/dt after 'proper treatment' is not accompanied by an explicit frequency-to-derivative relation or error budget demonstrating complete removal of residual laser-phase and clock-noise terms. Without this derivation, it remains unclear whether the reported performance is independent of the quantities being monitored or partly circular.

Authors: We agree that the method description would benefit from greater explicitness. The manuscript derives the relation in the main text by showing that the OFC carrier-carrier heterodyne isolates the differential phase evolution, yielding the time derivative of the pseudorange (light travel time plus clock offset) after common-mode laser frequency terms cancel. To address the concern directly, we will add a dedicated subsection with the explicit frequency-to-derivative equation, step-by-step cancellation of residual laser-phase and clock-noise contributions, and a quantitative error budget table. This will demonstrate that the suppression is independent of the monitored quantities rather than circular, arising from the OFC's ability to provide a stable frequency reference across the heterodyne measurement. revision: yes
Referee: [Abstract] Abstract: the synchronization accuracy (0.47 ns) and jitter level (15 pm/sqrt(Hz)) are stated without error bars, data-selection criteria, integration time, or quantitative comparison to a baseline TDI implementation on the same hardware; these omissions make it impossible to assess whether the result substantiates the 'no change to TDI' claim.

Authors: The abstract summarizes results whose supporting details, including integration times and data selection, appear in the experimental demonstration section. We acknowledge that a direct comparison to baseline TDI on identical hardware would strengthen the 'no change to TDI' assertion. In revision we will add error bars to the reported synchronization accuracy, specify the integration time and selection criteria in the abstract where space permits, and include a side-by-side quantitative comparison of residual noise spectra with and without the OFC-derived derivative monitoring in the results section. This will make the compatibility with standard TDI combinations explicit without altering the post-processing framework. revision: partial

Circularity Check

0 steps flagged

No significant circularity; experimental results provide independent validation

full rationale

The paper proposes an alternative OFC-based metrology approach for monitoring pseudorange derivatives via carrier-carrier heterodyne frequencies after proper treatment, without modifying the existing TDI framework. This is supported by an experimental demonstration using two separate systems that achieves synchronization accuracy better than 0.47 ns and suppresses stochastic jitter to LISA-relevant levels around 15 pm/sqrt(Hz). No load-bearing steps reduce by construction to fitted inputs, self-citations, or ansatzes; the central mapping is presented as a methodological choice validated externally by hardware results rather than derived tautologically from the same quantities. The derivation chain remains self-contained against the reported benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unstated assumption that carrier-carrier beats cleanly isolate pseudorange derivatives once standard TDI is applied; no new free parameters or invented entities are introduced in the abstract, but the 'proper treatment' step functions as an implicit modeling choice.

axioms (1)

domain assumption Carrier-carrier heterodyne frequencies encode the time derivative of pseudoranges after proper treatment
Invoked in the abstract as the basis for monitoring light travel time and clock difference without new TDI equations.

pith-pipeline@v0.9.0 · 5808 in / 1414 out tokens · 33080 ms · 2026-05-21T18:49:15.811190+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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B. P. Abbottet al.(LIGO and Virgo Collaboration), Observa- tion of gravitational waves from a binary black hole merger, Physical Review Letters116, 10.1103/physrevlett.116.061102 (2016)

work page doi:10.1103/physrevlett.116.061102 2016

[2] [2]

GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X9, 031040 (2019)

work page 2019

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GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run, Phys. Rev. X11, 021053 (2021)

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LISA Definition Study Report

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J.-B. Bayle, A. Hees, M. Lilley, C. Le Poncin-Lafitte, W. Martens, and E. Joffre, LISA Orbits (2022)

work page 2022

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Heinzel, J

G. Heinzel, J. J. Esteban, S. Barke, M. Otto, Y . Wang, A. F. Gar- cia, and K. Danzmann, Auxiliary functions of the LISA laser link: ranging, clock noise transfer and data communication, Classical and Quantum Gravity28, 094008 (2011)

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Hartwig and J.-B

O. Hartwig and J.-B. Bayle, Clock-jitter reduction in LISA time-delay interferometry combinations, Phys. Rev. D103, 123027 (2021)

work page 2021

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Yamamoto, C

K. Yamamoto, C. V orndamme, O. Hartwig, M. Staab, T. S. Schwarze, and G. Heinzel, Experimental verification of inter- satellite clock synchronization at lisa performance levels, Phys. Rev. D105, 042009 (2022)

work page 2022

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Tinto and N

M. Tinto and N. Yu, Time-delay interferometry with optical fre- quency comb, Phys. Rev. D92, 042002 (2015)

work page 2015

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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Opti- cal Frequency Synthesis, Science288, 635 (2000)

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Fortier and E

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Tan, M.-Y

Y .-J. Tan, M.-Y . Xu, P.-P. Wang, H.-Z. Wu, and C.-G. Shao, Modified time-delay interferometry with an optical frequency comb, Phys. Rev. D106, 044010 (2022)

work page 2022

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Vinckier, M

Q. Vinckier, M. Tinto, I. Grudinin, D. Riel ¨ander, and N. Yu, Experimental demonstration of time-delay interferometry with optical frequency comb, Phys. Rev. D102, 062002 (2020)

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O. Hartwig, J.-B. Bayle, M. Staab, A. Hees, M. Lilley, and P. Wolf, Time-delay interferometry without clock synchroniza- tion, Phys. Rev. D105, 122008 (2022)

work page 2022

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Sutton, K

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J. J. Esteban, A. F. Garc ´ıa, S. Barke, A. M. Peinado, F. G. Cer- vantes, I. Bykov, G. Heinzel, and K. Danzmann, Experimental demonstration of weak-light laser ranging and data communi- cation for lisa, Opt. Express19, 15937 (2011)

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S. Xie, H. Zeng, Y . Pan, D. He, S. Jiang, Y . Li, Y . Du, H. Yan, and H. chi Yeh, Bi-directional PRN laser ranging and clock syn- chronization for TianQin mission, Optics Communications541, 129558 (2023)

work page 2023

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Yamamoto, I

K. Yamamoto, I. Bykov, J. N. Reinhardt, C. Bode, P. Grafe, M. Staab, N. Messied, M. Clark, G. F. Barranco, T. S. Schwarze, O. Hartwig, J. J. E. Delgado, and G. Heinzel, Ex- perimental end-to-end demonstration of intersatellite absolute ranging for the Laser Interferometer Space Antenna, Phys. Rev. Appl.22, 054020 (2024)

work page 2024

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Euringer, N

P. Euringer, N. Houba, G. Hechenblaikner, O. Mandel, F. Soualle, and W. Fichter, Compensation of front-end and mod- ulation delays in phase and ranging measurements for time- delay interferometry, Phys. Rev. D109, 083024 (2024)

work page 2024

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Yamamoto, J

K. Yamamoto, J. N. Reinhardt, and O. Hartwig, Observable- based reformulation of time-delay interferometry, Phys. Rev. D 111, 122001 (2025)

work page 2025

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Tinto, M

M. Tinto, M. Vallisneri, and J. W. Armstrong, Time-delay in- terferometric ranging for space-borne gravitational-wave detec- tors, Phys. Rev. D71, 041101 (2005)

work page 2005

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H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, Carrier-envelope offset phase control: A novel concept for absolute optical frequency measurement and ultrashort pulse generation, Applied Physics B69, 327 (1999)

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Hartwig,Instrumental Modelling and Noise Reduction Algo- rithms for the Laser Interferometer Space Antenna, Ph.D

O. Hartwig,Instrumental Modelling and Noise Reduction Algo- rithms for the Laser Interferometer Space Antenna, Ph.D. the- sis, Gottfried Wilhelm Leibniz Universit¨at Hannover (2021)

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J. Ye, L. Robertsson, S. Picard, L.-S. Ma, and J. Hall, Absolute frequency atlas of molecularI 2 lines at 532 nm, IEEE Transac- tions on Instrumentation and Measurement48, 544 (1999)

work page 1999

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Bayle, O

J.-B. Bayle, O. Hartwig, and M. Staab, Adapting time-delay interferometry for LISA data in frequency, Phys. Rev. D104, 023006 (2021)

work page 2021

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M.-Y . Xu, N. Ma, Y .-J. Tan, Y .-R. Liang, and C.-G. Shao, Ef- fective reference clock signal in spaceborne gravitational-wave detection, Phys. Rev. Appl.24, 014014 (2025)

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work page 2023