Far-field optical path noise coupled with the pointing jitter in the space measurement of gravitational waves

Space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna or the Taiji program, aim to detect gravitational waves in space with interferometric arms of millions of kilometers. In the process of far-field propagation, the exit wavefront error of the transmitting telescope will couple with the unavoidable pointing between two spacecraft to generate an optical path noise. In this paper, we firstly build a comprehensive theoretical model concerning the effect of 3rd ∼ 7 t h aberrations on this coupling and compare the coupling coefficients of different aberrations. Then, we use this model to analyze the far-field optical path noise of the exit wavefront of a built prototype telescope for the Taiji program. Finally, we take advantage of the Monte Carlo algorithm of the model for investigating the effect of the different wavefront qualities on optical path noise. The results can provide meaningful guidance for the construction of the subsequent telescope.