Robust three-frame random phase-shifting interferometry based on dynamic mode decomposition method

Dynamic mode decomposition has shown promise in phase demodulation. However, existing strategies usually require at least four interferogram frames with equal phase-shift steps. This paper proposes a three-frame random phase-shifting algorithm based on dynamic mode decomposition. The algorithm begins by eliminating background patterns through differencing and normalization, and subsequently constructs what we believe to be a new sequence of phase-shifted interferograms by algebraic operations on the processed frames, which is then used for phase extraction based on the dynamic mode decomposition. This new procedure not only reduces the minimum frame requirement from four to three, but also enables phase demodulation of the randomly phase-shifted interferograms. Compared with several representative three-frame algorithms, the proposed method achieves high phase estimation accuracy and demonstrates strong robustness to noise, variations in fringe numbers, and fluctuations in background intensity and modulation amplitude.