Generalization of the Principal Component Analysis algorithm for interferometry

This paper presents a generalization of the Principal Component Analysis (PCA) demodulation method. The accuracy of the traditional method is limited by the number of fringes in the interferograms and it cannot be used when there are one or less interferometric fringes. The Advanced Iterative Algorithm (AIA) is robust in this case, but it suffers when the modulation and/or the background illumination maps are spatially dependant. Additionally, this method requires a starting guess. The results and the performance of the algorithm depend on this starting point. In this paper, we present a generalization of the PCA method that relaxes the PCA and AIA limitations combining both methods. We have applied the proposed method to simulated and experimental interferograms obtaining satisfactory results. A complete MATLAB software package is provided.