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

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 (TMIs), 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 TMI 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 TMI to be negligible in all our test-cases, no matter which formulation of pathlength signal is chosen.