Abstract
This paper explores a multi-directional (multiple directional) shearing synchronous polarization phase-shifting interferometer that utilizes a birefringent crystal displacer. This design effectively mitigates nonlinear issues and environmental influences commonly encountered in synchronous phase-shifting interferometry. Additionally, it enables the acquisition of shear wavefront information from multiple directions. By solving for the coefficients of the measured wavefront using multi-directional differential wavefront data, the system performs coefficient fitting to reconstruct the wavefront. The characteristics of crystal birefringence beam modulation, phase grating diffraction, and the polarization phase-shifting array for synchronous phase-shifting interferometry are investigated, based on the specific implementation methods of multi-directional shearing and synchronous polarization phase-shifting. The preprocessing method for the multi-directional shearing phase-shifting interferogram is then presented, followed by a detailed explanation of the spatial position registration technique for the shearing interferogram and the calculation method for the shear amount. The interferometer's construction system was experimentally tested using a spherical optical component, and the results were compared with those obtained from ZYGO to verify its accuracy and testing reliability.