Characteristics of tilt-to-length coupling coefficients for different time-delay interferometry combinations for LISA

Tilt-to-Length (TTL) noise is one of the dominant noise sources in space-based gravitational wave (GW) detection. Methods such as the least squares estimator and the instrumental variables estimator can be employed to subtract TTL noise. A prerequisite for practical subtraction is the accurate estimation of the TTL coupling coefficients, whose characteristics depend on the performance of the specific time-delay interferometry (TDI) combinations. For instance, the Michelson-type TDI combinations allow the precise estimation of twelve TTL coefficients, while the Monitor-type and Relay-type combinations enable the estimation of sixteen TTL coefficients. This study systematically investigates the TTL coupling characteristics across forty-five geometric TDI combinations. We establish an exhaustive classification framework identifying each combination's estimable TTL coefficient forms. Our findings reveal that among the combinations studied, only the Michelson-type combinations [X]¹⁶₁ and [X]¹⁶₂ present two TTL coefficients that are indistinguishable from one another. In contrast, we demonstrate that fully symmetric Sagnac combinations facilitate the estimation of all twenty-four TTL coefficients. Moreover, simulation results indicate that applying the least squares method subtracts TTL noise effectively, meeting the requirements of space-based GW detection.