Optical design of gravitational wave detection telescope based on suppression of tilt to length coupling noise

Spaceborne telescopes are vital components in space-based gravitational wave (GW) detection observatories, utilized for receiving and emitting laser signals to facilitate heterodyne interferometric displacement measurements. The coupling of wavefront aberrations with tilt-to-length (TTL) noise in space gravitational wave telescopes is a pivotal factor impacting measurement accuracy and warrants thorough attention. This research endeavors to achieve a telescope design with high optical path stability by reducing non-geometric TTL coupling noise, aiming to keep such noise beneath the threshold of 0.025 nm/µrad. We propose a method utilizing tolerance analysis to generate random wavefront samples and have conducted an analysis of the impact of various types of aberrations on TTL coupling noise. Research indicates that constraining the proportion of coma in the telescope's wavefront aberrations can lead to rapid convergence of TTL noise, thereby successfully guiding the improved design of the telescope. When the pointing jitter angle of the telescope is within the range of ±300µrad, the output RMS wavefront error is controlled within λ/300 (λ=1064 nm), and the coupling coefficient has shown a significant decrease compared to the initial design. The method proposed offers a reliable tool for the suppression of TTL noise in space-based GW detection.