Laboratory development of a heterodyne interferometric system for translation and tilt measurement of the proof mass in the space gravitational wave detection

Laser heterodyne interferometry plays a key role in the proof mass's monitor and control by measuring its multiple degrees of freedom motions in the Space Gravitational Wave Detection. Laboratory development of polarization-multiplexing heterodyne interferometer (PMHI) using quadrant photodetectors (QPD) is presented in this paper, intended for measuring the translation and tilt of a proof mass. The system is of symmetric design, which can expand to five degrees of freedom measurements based on polarization-multiplexing and differential wavefront sensing (DWS). The ground-simulated experimental results demonstrate that a measurement noise of 3 pm/Hz$^{1/2}$ and 2 nrad/Hz$^{1/2}$ at 1 Hz have been achieved respectively. The tilt-to-length error is dominated by geometric misalignment for the current system, the coupling of which is at micrometer level within a tilt range of 1000 {\mu}rad.