Phase demodulation of interferograms with open or closed fringes

Analysis of fringe patterns with partial--field and/or closed fringes is still a challenging problem that requires the development of robust methods. This paper presents a method for fringe pattern analysis with those characteristics. The method is initially introduced as a phase refinement process for computed coarse phases, as those obtained from partial--field patterns with a full-field method for open fringes analysis. Based on the phase refinement method, it is proposed a propagative scheme for phase retrieval from closed-fringe interferograms. 1. PHASE REFINEMENT METHOD The phase refinement method assumes that there are available approximations of contrast, b, and phase, \psi , in the domain of interest, R (we assume in this point that R=T, but in general R \subseteq T). Such approximations can be computed using standard fringe analysis methods, for instance, the Discrete Fourier Transform based method [1]. As it is well known, such methods introduce artefacts at the borders of the image or along phase discontinuities. So that, in order to compute the true phase, f=\psi +\phi, we need to estimate a residual phase, \phi. Now, we suppose that \psi is close enough to f such that the first order Taylor series approximates very well the model, i.e. (1) Therefore, we propose to compute the residual phase, \phi , and an outlier detector field, w, as the minimizers of the regularized half-quadratic [4] cost function: