The impact of telescope aberrations on the magnitude of tilt to length coupling noise in space based gravitational wave detectors

Tilt-to-length (TTL) coupling noise is one of the main noise sources that affect space gravitational wave detection, and the Tianqin project requires that the internal TTL coupling noise of the telescope used be less than 0.4 pm/Hz1/2 within the frequency band from 0.1 mHz to 1 Hz. In order to design a telescope that meets the requirements of TTL coupling noise and carry out preliminary error allocation research, it is necessary to analyze and calculate the TTL coupling noise, and then guide the design and optimization of the telescope system. This paper establishes a computational analysis model for the non-geometric TTL coupling noise inside the telescope using the first 36-order edge Zernike polynomials. A method was proposed to reduce the internal TTL coupling noise of the telescope by reducing the proportion of sensitive aberrations caused by non-geometric TTL coupling noise. Simulation results show that, with the RMS value of wavefront aberration at the telescope exit pupil unchanged, reducing the proportion of sensitive aberrations at the telescope exit pupil can effectively reduce the internal TTL coupling noise of the telescope. By optimizing the telescope optical system to reduce the proportion of noise-sensitive aberrations, the non-geometric TTL coupling noise inside the telescope has been reduced from 0.34 pm/Hz1/2 @ 0.1 mHz similar to 1 Hz to 0.25 pm/Hz1/2. This result can provide some guidance for the design of telescope optics based on the suppression of internal TTL coupling noise in the telescope.