Estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection

In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials are used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between the distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show that the pointing jitter is strongly related to the wavefront error. Furthermore, when the jitter decreases 10 times from 100 nrad to 10 nrad, the wavefront error reduces for more than an order of magnitude. In the analysis of multi-parameter minimization, the minimum of wavefront error tends to Z5,3 Zernike in some parameter ranges. Some Zernikes have a strong correlation with the wavefront error of the received beam. When the aperture diameter increases at Z5,3 Zernike, the wavefront error is not monotonic and has oscillation. Nevertheless, the wavefront error almost remains constant with the arm length increasing from 10 ⁻¹ Mkm to 10 ³ Mkm. When the arm length decreases for three orders of magnitude from 10 ⁻¹ Mkm to 10 ⁻⁴ Mkm, the wavefront error has only an order of magnitude increasing. In the range of 10 ⁻⁴ Mkm to 10 ³ Mkm, the lowest limit of the wavefront error is from 0.5 fm to 0.015 fm at Z5,3 Zernike and 10 nrad jitter.