Post-processing of tilt-to-length noise due to far-field phase errors

In space-based gravitational wave detection, the interferometer noise caused by angular jitter is referred to as tilt-to-length (TTL) noise. Tilt-to-length noise is a significant obstacle in space-based gravitational wave detection, with tilt-to-length noise due to far-field phase errors being the most difficult to manage. By using Zernike polynomial random aberrations and diffraction calculations, a tilt-to-length noise generation model for far-field phase errors is established. 200 Monte Carlo simulations were performed, in which 87% of the simulation results had TTL noise exceeding $10\text{ }\text{ }\mathrm{pm}/\sqrt{\mathrm{Hz}}$. Based on the characteristics of far-field phase errors, a comparative study was conducted on the post-processing methods using the first-order estimation model and the second-order estimation model. The first-order estimation model post-processing results in an average residual TTL noise of 17.0%, while the second-order estimation model post-processing results in an average residual TTL noise of 8.2%. Further research indicates that spacecraft pointing jitter and noise from differential wave front sensing systems significantly impact post-processing performance.