Global approach for fitting 2D interferometric data

Abstract

The present paper describes a fitting procedure capable of providing a smooth approximation of experimental data distributed on a bidimensional 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.

Low-cost speckle interferometry for measuring 3D deformation fields: Hardware and software

“…[25]. After the unwrapping, the phase variation of each map (a matrix of 500 Â 500 elements) was described analytically by 25 (5 Â 5) parabolic blending function according to the B-spline formulation.…”

“…The first one concerns with the smoothness of the measured quantities. The differentiation amplifies the noise usually high when speckle interferometry is applied for measuring deformations, hence filtering [24] or fitting [25] the experimental data is mandatory for obtaining consistent results. Secondly, if the investigated area is not planar the strain evaluation could be difficult, because the shape of the surface must be taken into account in the analytical formulation.…”

Compensation method for obtaining accurate, sub-micrometer displacement measurements of immersed specimens using electronic speckle interferometry

“…The strategy used to build the B-spline system is conceptually based on the formulation proposed in [20], where a set of functions based on the B-spline formulation are linearly combined to define the entire fitted domain. The fitting system reported in [20] is directly applicable to a rectangular domain and it works well in a rectangular reference system.…”

Sequential-Digital Image Correlation for Mapping Human Posterior Sclera and Optic Nerve Head Deformation

“…[31]. Noisy strain data can be eventually smoothed in a 3D computer-aided design environment by using nonuniform rationale B-splines (NURBS) that, with a proper control of surface span and stiffness, can easily remove outliers without altering the local fluctuation of the parameter of interest (deformation or strain) [18,30,31,39]. Given the complex shape of the calibration target, we express the results of the null strain test in terms of a coordinate-free measure, the first invariant of E defined as /i = tr(E) (Fig.…”