Belenguer T. Phase-shifting interferometry based on principal component analysis. Opt Lett 2011;36(8):1326–8

An asynchronous phase-shifting method based on principal component analysis (PCA) is presented. No restrictions about the background, modulation, and phase shifts are necessary. The presentedmethod is very fast and needs very low computational requirements, so it can be used with very large images and/or very large image sets. The method is based on obtaining two quadrature signals by the PCA algorithm. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results. © 2011 Optical Society of America OCIS codes: 100.5070, 100.2650. Phase-shifting interferometry (PSI) is a useful technique in optical metrology for measuring the modulating phase of interferograms [1]. In standard PSI, a sequence of N interferograms is obtained having known phase shifts be-tween them so the acquisition is synchronous. Usually a minimum of three phase-shifted interferograms are need to retrieve the phase. Other phase-shifting algorithms, named self-calibrating, allow the determination of the modulating phase without any prior knowledge about the phase steps (asynchronous detection) [2–5]. All these methods are iterative and require considerable computa-tion to converge to a solution. Therefore, these methods are not practical when we use large images or a big number of interferograms. Additionally, these methods require the background and the modulation terms to be approximately spatially constant. In this Letter, we present an asynchronous phase-shifting method based on the principal component analysis (PCA) algorithm that is very fast and easy to im-plement. Additionally, it does not use any nonlinear mini-mization or optimization process, so it is not expensive from a computational point of view. In PSI, an interfer-ogram sequence can be described using the following expression