Nijboer–Zernike approach for far-field propagation simulations in space-based gravitational wave detector

Under construction space-based gravitational wave observatories, such as LISA, Taiji, and TianQin, employ long-baseline laser interferometry to achieve picometer level displacement measurements. Accurate simulation of beam propagation between spacecraft proves crucial for guiding the design and integration of laser transceiver systems within these constellations. This paper presents a numerical model for far-field beam propagation based on the Nijboer-Zernike theory, extending Zernike polynomials to the complex domain to accommodate generalized diffracting source fields. The proposed framework affords well-established physical interpretability in analyzing the coupling between wavefront errors and pointing jitter, thereby directly informing aberration suppression strategies for optical system. Using this approach, we analyze Gaussian beam transfer function characteristics and the impact of typical Zernike aberration modes on far-field distributions, revealing that aberrations with even radial orders contribute more significantly to far-field phase errors. Building on measured aberration coefficient amplitude distributions in practical optical systems, we identify defocus, astigmatism, and spherical aberration as critical modes requiring prioritized suppression. Finally, Monte Carlo methods quantify correlations among RMS wavefront error, critical aberration modes, and pointing accuracy. This research provides theoretical foundations for optimizing optical system design and alignment.