In order to eliminate zeroth order effect and to make the phase shifting algorithm insensitive to phase shifting error, an 11-frame phase shifting algorithm is proposed in this paper. The analytical expression of phase-restoration error function is derived. The principle of phase shifting error compensation and the capability of suppressing zeroth order effect are explained, in comparison of existing algorithm. The analytical results show that this algorithm’s phase-restoration error is proportional to sine of double shearing phase and to biquadratic of phase shifting error. Finally, we generate the interference patterns of 11-frame algorithm and existing algorithm, restore the shearing phases and calculate the phase-restoration errors by simulations. The simulation results verify the theoretical analyses.

As one of the key payloads for space-borne gravitational wave detection (SGWD), the phasemeter is primarily responsible for conducting phase measurements of heterodyne signals. A phase extraction precision at the micro-radian level constitutes a crucial performance metric for intersatellite heterodyne interferometry. In this work, an ultra-stable hexagonal optical bench was developed using hydroxide-catalysis bonding technology. Different beat-notes were generated in accordance with the requirements of four experimental stages, which were applied to simulate the main beat-note of the inter-satellite scientific interferometer, thereby verifying the phase measurement performance of the phasemeter for beat-notes. Experimental results demonstrate that the phase extraction precision meets the index requirement of $2\pi \mu \mathrm{rad}/\sqrt{\mathrm{Hz}}$ for SGWD missions. Based on the test environment of the ultra-stable hexagonal optical bench, the feasibility of the phasemeter’s core phase measurement function was verified, laying a solid foundation for subsequent research on its auxiliary functions and extended tests.

In this paper, a calibration method is proposed which eliminates the zeroth order effect in lateral shearing interferometry. An analytical expression of the calibration error function is deduced, and the relationship between the phase-restoration error and calibration error is established. The analytical results show that the phase-restoration error introduced by the calibration error is proportional to the phase shifting error and zeroth order effect. The calibration method is verified using simulations and experiments. The simulation results show that the phase-restoration error is approximately proportional to the phase shift error and zeroth order effect, when the phase shifting error is less than 2° and the zeroth order effect is less than 0.2. The experimental result shows that compared with the conventional method with 9-frame interferograms, the calibration method with 5-frame interferograms achieves nearly the same restoration accuracy.