Displacement measurement using Talbot effect

Linear gratings and circular gratings are most commonly used in the applications of Talbot effect, due to their simple patterns and ease of analysis of Moire fringes. In the present paper, we demonstrate a scheme to measure the displacement of a deformed object which based on the Talbot effect. We designed a hologram of a two-dimensional square-hole grating. For the test, we used a computer-controlled liquid crystal spatial light modulator (LC-SLM) and the computer-generated Talbot array hologram. The Talbot array hologram is displayed on the LC-SLM screen. The beam diffracted by the grating is transmitted to the surface of an object. By adjusting the distance between the LC-SLM and the object, a clear image is formed on the surface of the object. A speckled pattern of the object surface is captured by a CCD camera. Two speckle patterns before and after the deformation is recorded. The information about the displacement is codified in the intensity pattern. The displacement can be obtained by digital image correlation (DIC). The DIC obtains the displacement components by comparing the gray intensity changes between the digital images of an object surface before and after the deformation. This method is simple and easy, and can be used as an alternative method to measure in-plane and out-of-plane displacements. Theoretical and experimental results are presented.