Tilt-to-length noise coupled by wavefront errors in the interfering beams for the space measurement of gravitational waves.

The space-based gravitational wave detection programs, like the Laser Interferometer Space Antenna (LISA) or the Taiji program, aim to detect gravitational waves in space with a triangular constellation of three spacecraft. The unavoidable jitters of the spacecraft and the pointing will couple with the misalignment of the interfering beams into the longitudinal path length readout. This effect is called tilt-to-length (TTL) coupling, which is one of the keys to achieving the required measuring accuracy of 1/. In terms of two phase definitions (the LISA Pathfinder (LPF) signal and the Average Phase (AP) signal), we implement the comprehensive theoretical analysis concerning the effect of aberrations on TTL coupling noise. In addition, we analytically derive that the proper lateral shift of the interfering beams relative to the detector can partly cancel out the TTL noise coupled with aberrations, especially coma and trefoil aberrations for the AP signal. Based on the above results, the meaningful guidance can be provided for the design and construction of the optical system in LISA or Taiji.