Method for designing space gravitational-wave telescopes based on wavefront aberration regulation and...

In space-based gravitational-wave observatories, tilt-to-length (TTL)-coupled noise represents a critical limitation, ranking as the second-largest noise contribution after shot noise. Suppressing this noise in large-aperture telescopes, which typically exhibit high TTL coupling coefficients, remains a significant challenge due to the absence of a generalized suppression methodology. This work introduces a comprehensive design strategy to directly mitigate TTL-coupled noise in such systems. A wavefront aberration contribution model based on Zernike coefficients is established, and a hierarchical optimization strategy is introduced, in which lower-order aberrations are controlled based on their contribution to the total root mean square, whereas adaptive weights are assigned to higher-order aberrations. An optimization metric centered on the TTL-coupled noise coefficient is formulated, establishing a direct link between optical performance and noise suppression. The method is applied to design an off-axis four-mirror optical system. Aberration contribution ratios are quantified, hierarchical optimization weights assigned, and 24 sampling zones defined to compute the TTL noise coefficient. This coefficient guides optimization via a custom evaluation function implemented in Zemax. Simulations confirm the method's efficacy: under identical disturbance conditions, the TTL-coupled noise coefficient is reduced from 50.9519 pm/µrad to 0.0441 pm/µrad-a suppression exceeding 99%. This approach markedly enhances detection sensitivity and offers a generalizable framework for the design of high-precision space gravitational-wave telescopes.