N-step self-calibrated generalized amplitude-phase-shifting interferometry

Abstract

We present a precise, efficient, and non-iterative self-calibrated method for complex amplitude retrieval (both amplitude and phase), generalized for an arbitrary number N of phase shifts in phase-shifting interferometry (PSI). In conventional PSI, only the wavefront phase is retrieved, either by performing synchronous detection—using equal phase steps—or asynchronous detection—using unequal but known phase steps. In contrast, the proposed approach enables the simultaneous recovery of the wavefront phase, the reference and probe amplitudes, and the unknown phase steps, without ambiguity and for any number of interferograms, thus allowing a complete reconstruction of the optical field. The technique is first validated through numerical simulations, showing that all optical field parameters can be accurately recovered and that the deviation from the theoretical values is practically zero. Additionally, a comprehensive noise analysis is performed by simulating typical experimental error sources, which are analyzed individually and collectively to emulate real acquisition conditions. The method proves to be robust even under adverse conditions, maintaining high reconstruction accuracy. Experimentally, the method is implemented in a double-aperture common-path interferometer (DACPI) adapted for polarization modulation. Results are presented for up to ten interferograms with arbitrary phase shifts, demonstrating that all parameters can be recovered with high precision and low error. Furthermore, the experimental results show excellent agreement with the numerical noise analysis, validating the reliability and practical applicability of the proposed self-calibrating approach.