Two-step blind phase-shifting interferometry based on the extreme value of interference and least-squares iterative algorithm

To improve the measuring accuracy in two-step phase-shifting interferometry (PSI), a new approach combining the extreme value of interference (EVI) and the least-squares iterative algorithm (LSIA) is proposed to extract the phase from two-frame blind phase-shifting interferograms. This method first evaluates the phase shift between two interferograms by the EVI algorithm, and then constructs the fitted interferogram by the addition of two interferograms after filtering the corresponding background intensities, so the phase with high precision can be retrieved by combining two real interferograms and this fitted interferogram using the LSIA method. The proposed algorithm expands the flexibility of the LSIA method and has the high-precision performance compared with the existing algorithms in two-step PSI. Simulation and experiment are performed to verify the feasibility of the proposed algorithm.