Comprehensive optimization approach for telescope optical parameters targeting minimal tilt-to-length coupling coefficient with required wavefront aberration in intersatellite laser interferometer for gravitational wave detection

Telescope is one key optical unit for ensuring pico-meter level measurement sensitivity in intersatellite laser interferometer (ILI) in space-based gravitational wave detection. It needs to meet critical requirement of tilt-to-length (TTL) coupling coefficient less than 0.6 pm/nrad with wavefront aberration less than λ/40. This study employs Gaussian beam decomposition method to calculate the combined geometric and non-geometric TTL coupling noise of telescope with high computational efficiency and accuracy, which is superior to existing diffraction integral methods or ray-tracing methods. Then a comprehensive optimization approach is proposed to simultaneously minimize the combined TTL coupling noise while maintaining wavefront aberration below λ/40, addressing a critical gap in existing methods that focus only on single performance metrics. The approach innovatively integrates Bayesian algorithm with Zemax software for high-efficient multi-parameter global optimization of the telescope, while the former is aiming to minimize the combined TTL coupling noise and the latter is further used for wavefront control. Results demonstrate a TTL coupling coefficient of 0.134 pm/nrad, which is significantly below the 0.6 pm/nrad requirement, with wavefront aberration below λ/40, outperforming prior designs. The method effectively balances TTL noise suppression and wavefront quality, fulfilling stringent demands for ILI in missions like LISA/Taiji/TianQin.