Sign ambiguity resolution for phase demodulation in interferometry with application to prelens tear film analysis

We present a novel method to solve sign ambiguity for phase demodulation from a single interferometric image that possibly contains closed fringes. The problem is formulated in a binary pairwise energy minimization framework based on phase gradient orientation continuity. The objective function is non-submodular and therefore its minimization is an NP-hard problem, for which we devise a multigrid hierarchy of quadratic pseudoboolean optimization problems that can be improved iteratively to approximate the optimal solutions. Compared with traditional path-following phase demodulation methods, the new approach does not require any heuristic scanning strategy, it is not subject to the propagation of error, and the extension to three dimensional fringe patterns is straightforward. A set of experiments with synthetic data and real prelens tear film interferometric images of the human eye demonstrate the effectiveness and robustness of the proposed algorithm in comparison with existing state-of-the-art phase demodulation methods.