Phase Maps Retrieval from Sequences of Phase Shifted Images with Unknown Phase Steps Using Generalized N-Dimensional Lissajous Figures—Principles and Applications

This article presents an alternative approach for retrieving phase information from a sequence of images with unknown phase shifts. A sequence of five or more discrete interferograms with unknown and different phase shifts are used to determine the parameters of N-dimensional Lissajous figures. A set of N-dimensional discrete points are used to calculate the relative phase shifts. Once zthe phase shifts are determined, the phase values for each image pixel are determined from a generalized phase calculation equation for irregular phase shifts. The article presents the physical and mathematical basis of the developed approach and discusses some results obtained from simulated data and real data from controlled experiments.