A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

An interpretation of Moiré interferometry from wavefront interference theory

The primary output from several full-field deformation measurement techniques, e.g., Digital Image Correlation (DIC), is the displacement vector at a dense grid of points covering the area of interest. Since such displacement data inherently contain noise, they are usually smoothed first and then differentiated to obtain strains. Another common approach is to use finite-element shape functions for the strains and compute them by treating the measured displacements as nodal displacements. In this paper, we propose a novel method for strain calculation from full-field data, based on the multivariate analysis technique of Principal Component Analysis (PCA) using which we first obtain the singular values and singular vectors for each component of the displacement field. By choosing only the dominant singular values and their corresponding singular vectors, we show that the dimensionality of the displacement data is sharply reduced and a significant portion of the noise is eliminated. Moreover, the shapes of the dominant singular vectors offer physical insight into dominant deformation patterns. We demonstrate the accuracy of the proposed technique by applying it to two cases each of homogeneous and inhomogeneous strain fields and show that in all cases the proposed method yields excellent results.

Computation of Full-field Strains Using Principal Component Analysis

The concept of conjugate lateral shear interferometry is introduced It involves producing two lateral shear interferograms with carrier fringes identically distorted in opposite directions The moire fringes formed by overlapping such interferograms display information proportional to the sum of the derivatives of the functions encoded in the interferograms A simple method for generating conjugate interferograms by using a Ronchi test configuration and the self-imaging phenomenon is described In the case of large phase gradients and shears, a spatial-filtering operation is required The principles derived are verified by an experiment The application of the technique is proposed

Conjugate lateral shear interferometry and its implementation

A new method of obtaining the spatial derivative of out-of-plane displacements in a moire interferometry setup is presented. It is based on the recently developed concept of conjugate lateral shear interferometry applied to the diffracted beams generated by the specimen grating. The moire fringes produced by overlapping the two interferograms give the desired information using either the uniform or finite fringe detection method. Simulation experiments using specially prepared transmission-type distorted gratings are given to verify the principles.

Generation of the derivative of out-of-plane displacements using conjugate shear and moire interferometry

New methods of optical differentiation of fringe patterns obtained by the moire interferometry method are presented. They provide spatial derivatives of in-plane and out-of-plane displacements of the specimen under load in the form of moire or two-beam interference fringes. Either the uniform or finite fringe detection mode can be used. Simulation experiments using specially prepared transmission-type gratings are given to verify the principles.

Matgorzata Kujawinska

Papers

Optical differentiation of displacement patterns using moire interferometry.