A comprehensive review of the principal component analysis applied to the demodulation of phase-shifting interferograms

The use of the Principal Components Analysis (PCA) for recovering the modulating phase, given a sequence of Phase-Shifted Interferograms (PSI), is a very important contribution to the field. However, its verbatim translation from statistics to PSI has limited the view to consider only constant background illuminations. Here, we show that the Singular Value Decomposition (SVD), used in PCA, actually separates the background illumination (constant or not) and the phase modulation terms. We show that the modulating phase can be correctly recovered if the phase-shifts sample full periods uniformly, independently of the spatial distribution of the number of fringes.