Aspherical Surface Measurement With Multi-Directional Lateral Shearing Phase-Shifting Interferometry

Lateral shearing interferometry is an effective method for directly measuring the depth gradient of aspherical surfaces. To address the low phase reconstruction accuracy resulting from the fact that lateral shear interferometers typically obtain only two sets of wavefront data in a single orthogonal direction, which leads to fewer sampling points, this paper presents an aspherical surface measurement method based on birefringent crystals and multi-directional lateral shearing phase-shifting interferometry. This method overcomes nonlinear issues and environmental influences during phase-shifting interferometry, captures shear wavefront data in multiple directions, and reconstructs the surface by solving for the wavefront coefficients using multi-directional differential wavefront information. It also reduces system random errors, improving surface reconstruction accuracy. We propose a multi-directional lateral shearing synchronous phase-shifting interferometry technique for measuring aspherical surfaces. The methodology includes multi-directional shearing, synchronous phase-shifting, crystal birefringence modulation, phase grating diffraction, and polarization phase-shifting arrays. An experimental system was built to test aspherical surface samples, and aspherical surface measurements were conducted on a surface with a 90 mm diameter, 606 mm vertex curvature radius, and a quadratic conic coefficient of −1. The deviation of the measured aspherical surface from the optimal spherical surface was obtained, and the initial deviation of the ideal aspherical surface from the optimal spherical surface was calculated using the ray tracing method. The repeated measurement results were consistent with those from the ZYGO interferometer’s self-collimation method, with an RMS deviation better than λ/100. The experiment demonstrated the effectiveness, repeatability and measurement stability of the multi-directional lateral shearing interferometry system for measuring aspherical surfaces.