Three-dimensional Displacement and Shape Measurement with a Diffraction-assisted Grid Method

The grid method is a full-field optical technique for computing surface displacements and strains of a material by analyzing the phase of grid lines patterned on the specimen. To date, most experiments using the grid method have measured only two-dimensional in-plane deformations. Here, the grid method is extended to three dimensions by using a crossed grid pattern and a diffraction grating which enables acquiring images from multiple viewing angles on a single camera. In-plane displacements and strains are computed using the conventional grid method, and the corresponding three-dimensional (3D) displacementsincluding out-of-plane displacements or shapesare computed by analyzing the images collected at different viewing angles. The technique is demonstrated by measuring 3D rigid body motion, the 3D displacements of a membrane in a pressure-bulge experiment, and the out-of-plane curvature of a cylindrical specimen.