Fast and robust two-frame random phase-shifting interferometry without pre-filtering.

To obtain higher phase accuracy with less computation time in phase-shifting interferometry, a random phase-shifting algorithm based on principal component analysis and least squares iteration (PCA&LSI) is proposed. The algorithm does not require pre-filtering, and only requires two-frame phase-shifted interferograms and less computation time to obtain a relatively accurate phase distribution. This method can still extract the phase with high precision when there are few fringes in the interferogram. Moreover, it eliminates the limitation that the PCA algorithm needs more than three frames of interferograms with uniform phase shift distribution to accurately extract the phase. Numerical simulations and experiments confirm that the method is suitable for complex situations with different fluctuations in background intensity and modulation amplitude. And it can still achieve accurate phase extraction compared with other methods under different noise conditions.