Reducing phase noise coupled by wavefront errors in optical telescopes for the space measurement of gravitational...

Space-based gravitational-wave observatories (SGOs) promise to measure pico-meter variations in gigameter separations of a triangular constellation. Telescopes play an essential role in transmitting and receiving laser beams measuring the constellation arms with the heterodyne laser interferometry. The wavefront aberrations of the telescopes are coupled with the unavoidable misalignments caused by jitters and pointing tilts and induce additional phase changes into the heterodyne signal. As a critical aspect of achieving the measuring stability of 1p m/H z, we analytically investigate the above process and determine that by properly controlling the relevant key aberrations in the design of the telescopes, the phase noise can be reduced exponentially, which makes the heterodyne signal insensitive to jitter and reduces the demand for wavefront quality. This method is validated whether the LISA Pathfinder (LPF) signal definition or the Average Phase (AP) signal definition is adopted, underpinning the guidance for the design and manufacturing of the optical telescope in SGOs.