Improved 3D displacement measurements method and calibration of a combined fringe projection and 2D-DIC system

An improved measurement method and an automatic calibration procedure are proposed for a combined 2D Digital Image Correlation and Fringe Projection system that allows measuring in- and out-of-plane displacement maps with only one image at each deformation stage of a specimen. The proposed method increases the accuracy and range of the out-of-plane displacements by taking into account the divergences of both the projected fringes (uncollimated) and the camera (with non-zero FOV). The calibration is performed automatically by acquiring a sequence of images of a reference plane by displacing perpendicular to it the camera and fringe projector with a motorized translation stage. The acquired images are then used to obtain a fringe function for each pixel and the necessary parameters required for the correction of the in-plane displacements. Furthermore, a closed form expression is obtained that relates the out-of-plane displacements with the shifted phase at each pixel for a given experimental set-up. This expression is in good agreement with the fringe function obtained by fitting a simple 2nd order polynomial to the experimental obtained calibration data. Finally, the polynomial approach is proposed as a fringe function because it avoids the errors in the determination of the required parameters of the theoretical expression as well as some small misalignment or aberration effects.