Global approach for fitting 2D interferometric data

The present paper describes a fitting procedure capable of providing a smooth approximation of experimental data distributed on a bi-dimensional domain, e. g. the typical output of an interferometric technique. The procedure is based on the optimization of an analytical model defined on the whole domain by the B-spline formulation. In the paper rectangular, circular and polygonal convex domains are considered in details, but, according to the need of the operating conditions, the procedure can be extended to domains of different shapes. The proposed procedure was initially calibrated by an analytical case study: a thin square plate simply supported along the edges and loaded by a uniform pressure. Subsequently, by the operative parameters defined by the analyses carried out on the analytic data, the fitting procedure was applied on experimental data obtained by phase shifting speckle interferometry.