Impact of phase signal formulations on tilt-to-length coupling noise in the LISA test mass interferometer

TL;DR

This study compares different phase signal formulations in the LISA test mass interferometer to determine their impact on tilt-to-length coupling noise, finding that the averaged phase generally reduces noise and non-linear effects are negligible.

Contribution

The paper evaluates the influence of phase signal formulations on TTL coupling noise in LISA, demonstrating the advantages of the averaged phase method through simulations.

Findings

Averaged phase reduces TTL coupling noise in most cases.

Non-linear TTL contributions are negligible across tested scenarios.

Three simulation methods yielded consistent results.

Abstract

Tilt-to-length (TTL) coupling in the Laser Interferometer Space Antenna (LISA) can generate spurious displacement noise that potentially affects the measurement of gravitational wave signals. In each test mass interferometer, the coupling of misalignments with spacecraft angular jitter produces noise in the longitudinal pathlength signal. This signal comes from the phase readout combinations of an interfering measurement beam and a local reference beam at a quadrant photodetector, but various formulations exist for its calculation. Selection of this pathlength signal formulation affects the TTL coupling noise. We therefore simulated two pathlength signal candidates, the complex sum and the averaged phase, and evaluated their performance in the LISA test mass interferometer under the assumption of static alignment imperfections. All simulations were performed using three different methods with cross-checked results. We find with all three methods that the averaged phase is the choice with equal or less TTL coupling noise in four out of the five test cases. Finally, we show that the non-linear TTL contributions in the test mass interferometer to be negligible in all our test-cases, no matter which formulation of pathlength signal is chosen.