Robust weighted principal components analysis demodulation algorithm for phase-shifting interferometry

We present an asynchronous phase-shifting demodulation approach based on the principal component analysis demodulation method that is robust to typical problems as turbulence, vibrations, and temporal instabilities of the optical setup. The method brings together a two-step and a phase-shifting asynchronous demodulation method to share their benefits while reducing their intrinsic limitations. Thus, the proposed approach is based on a two-fold process. First, the modulating phase is estimated from a two-step demodulation approach. Second, this information is used to compute weights to each phase-shifted pattern of the interferogram sequence, which are used in a novel weighted principal component demodulation approach. The proposed technique has been tested with simulated and real interferograms affected by turbulence and vibrations providing very satisfactory results in challenging cases. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement