Single-shot fringe-pattern analysis algorithm robust against abrupt phase jumps

•Solve phase map using a single fringe pattern.•Recover edge by weighted least-square fitting.•Provide a robust and simple algorithm for phase measurement. Fringe-analysis methods, with fine carrier fringes, allow us to extract phase signals using a single-shot imaging measurement, enabling real-time observation of dynamic phenomena. However, abrupt phase jumps produced by the structural boundaries (or edges) in an object and/or object surfaces occasionally generate significant errors in the resulting images. In this paper, a new algorithm consisting of two steps is proposed to address this problem. In the first step, we computed an approximate phase map by ignoring abrupt phase jumps. In the second step, we solved a weighted least-squares problem to recover the abrupt phase jumps using the approximate phase map. The influence of several factors, such as carrier-fringe frequency and noise, was examined through simulation and experiment, and the effectiveness of the proposed method was demonstrated.