Analysis of tilt-to-length coupling suppression based on the ray transfer matrix in space-based gravitational wave detection

In space-based gravitational wave detection, tilt-to-length (TTL) coupling induced by test mass (TM) or spacecraft jitter is one of the major noise sources limiting displacement measurement sensitivity. To analyze this effect, this work develops a second-order analytical model of TTL coupling in Gaussian beam optical systems. The model uses the ray transfer matrix (ABCD matrix) to describe paraxial transmission between the TM surface and the photodetector and introduces a Padé approximation to treat the error function term, thereby yielding an explicit second-order analytical expression for the total TTL coupling. The analysis reveals how the ABCD matrix governs the transmission of geometric and non-geometric contributions to TTL. Based on this model, a targeted suppression strategy is obtained: under the average phase definition of a quadrant photodetector (QPD), second-order TTL coupling can be suppressed by optimizing the ABCD parameters through an imaging system, while the residual first-order term can be compensated by laterally shifting the QPD. Numerical simulations verify the analytical results. This work studies imaging system based TTL suppression by considering not only geometric equal optical path effects but also non-geometric phase effects. These results provide analytical guidance for TTL noise suppression in high-precision laser interferometry for future space-based gravitational wave missions.