Phase Estimation Using Discrete Chirp-Fourier-Transform-Based Method

Spherical measurement is a relatively important application in optical measurement. The interferogram obtained in spherical inspection usually consists of closed fringe patterns. Obtaining high-precision phases from interferograms containing closed fringes remains challenging. An improved discrete chirp Fourier transform (DCFT) method is proposed to directly estimate parameters such as the radius of curvature, ring center, and displacement, and in turn, the spherical phase can be reconstructed from these parameters. In this study, a Michelson interferometer was employed to conduct 100 repeated experiments, capturing $256\times 256$ pixels fringe patterns of a spherical standard component with a curvature radius of 10.02 mm. The results demonstrated that the proposed method achieved an average phase demodulation accuracy of less than 0.07 rad (root-mean-square (rms) error) in these 100 experiments, showcasing exceptional noise robustness and estimation efficiency. This method provides a practical approach for analyzing spherical phases and offers insights into the measurement of related physical parameters.