  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 is 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 distorted Gaussian beam and a reference distortion-free Gaussian beam.
The results show the pointing jitter is strongly related to the wavefront
error. Furthermore, when jitter decreases 10 times from 100 to 10 nrad,
wavefront error reduces for more than an order of magnitude. In the analysis of
multi-parameter minimization, the minimum of wavefront error tends to Z[5,3]
Zernike in some parameter ranges. Some Zernikes have a strong correlation with
wavefront error of the received beam. When the aperture diameter increases at
Z[5,3] Zernike, wavefront error is not monotonic and has oscillation.
Nevertheless, 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, 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 Z[5,3] Zernike and 10 nrad jitter.
