###### Abstract  
Space-based gravitational wave detection programs, such as the Laser Interferometer Space Antenna (LISA) or Taiji program, obtain gravitational wave signals by measuring the change in the distance between three satellites by laser. The telescope is an important part of the measurement system, and its function is to transmit and receive laser signals. Due to changes in the space environment, the telescope will inevitably introduce additional dynamic aberrations, which will bring optical path errors to the inversion of gravitational wave signals. Taking LISA as an example, to achieve pm-level measurement accuracy at the detection frequency of 0.1 mHz-1 Hz, the stability requirements of the telescope are less than 1 pm/Hz\({}^{1/2}\). This paper theoretically deduces the aberration types that affect the telescope's stability and conducts simulation analysis according to the actual phase demodulation method, which verifies the theory's correctness. In addition, using this theory, it can be concluded that under the condition that the total size of the telescope aberration is determined to be stable, reducing the ratio of rotationally symmetric aberrations such as \"spherical aberration\" and \"defocusing\" among common aberrations can significantly improve the stability of the telescope. The conclusion guides the optical system design of LISA or Taiji. wavefront aberration; telescope stability; gravitational waves; Taiji 2022122697. 202222122697. 2022221222122212  
the coupling relationship between wave aberration and phase has a guiding significance for the design of the telescope wavefront index and aberration control. [PERSON] and [PERSON] et al. analyzed and studied the phase noise of the far-field wavefront caused by primary aberrations [5; 6; 7; 8]. [PERSON] analyzed the effect of the wavefront error on the received beam phase noise of distant spacecraft through numerical and ray tracing [9; 10; 11]. However, in the optical-mechanical-thermal integration analysis, the aberrations are often complex; high-level aberrations exist, and the dynamic changes of the aberrations will also have a greater impact on the phase. [PERSON] et al. made a more detailed analysis of the influence of the tilt jitter error in the interference process of a double beam (far-field beam and local Gaussian beam) on phase demodulation. At the same time, the relationship between the aberration and the phase brought by the telescope system was briefly analyzed, and it was pointed out that when the telescope aberration is within \(\lambda/20\), the demodulation effect on the phase information can be maintained at 25 pm/nrad. However, there was no quantitative analysis of specific aberrations [12; 13; 14]. Therefore, a more complex and comprehensive analysis of the effects of aberrations and their dynamic changes on the phase is necessary to explore the influencing factors of telescope stability. In this paper, the theoretical algorithm of phase demodulation of two-beam interference is firstly constructed, the aberration is fitted by the Zernike polynomial, and the influence of the wavefront aberration on the phase signal is deduced: after ignoring the higher-order terms, it can be concluded that the effect of non-rotationally symmetric aberrations (NRSAs) is negligible on an ideal detector; however, rotationally symmetric aberrations (RSA) such as spherical aberration and defocusing have great influences that cannot be ignored. At the end of the manuscript, the relationship between the dynamic aberration of the gravitational wave telescope and the laser phase demodulation on the quadrant photodiode (QPD) is simulated, which is consistent with the theoretical situation. Therefore, this conclusion shows that different aberrations have different effects on the detection of gravitational waves in practical engineering. When designing telescopes, not only is the wavefront index required, but the consideration of specific aberration allocation is also necessary.