title: Second-order robust regularization cost function for detecting and reconstructing phase discontinuities.
abstract: We propose a robust method for computing discontinuous phase maps from a fringe pattern with carrier frequency. Our algorithm is based on the minimization of an edge-preserving regularized cost function, specifically, on a robust regularized potential that uses a paradigm called the plate with adaptive rest condition, i.e., a second-order edge-preserving potential. Given that the proposed cost function is not convex, our method uses as its initial point an overly smoothed phase computed with a standard fringe analysis method and then reconstructs the phase discontinuities. Although the method is general purpose, it is introduced in the context of interferometric gauge-block calibration. The performance of the algorithm is demonstrated by numerical experiments with both synthetic and real data.
authors.affiliation: Centro Nacional de Metrologia Apartado Postal 1-100 Centro, Queretaro, Queretaro, Mexico 76000. cgalvan@cenam.mx
authors.forename: Carlos
authors.initials: C
authors.lastname: Galvan
authors.forename: Mariano
authors.initials: M
authors.lastname: Rivera