Analysis of Coherent Gradient Sensing (CGS) by Fourier optics

A coherent laser beam reflected or transmitted from a deforming plate specimen acquires an optical path difference (phase change) which is related to the deformation and stress field. The optical method of Coherent Gradient Sensing (CGS) uses two parallel grating plates to displace (shear) and recombine the distorted light beam emerging from the specimen. Fringes are produced on the image plane by the interference of the shifted and unshifted beams. The fringe pattern is related to the spatial difference of the phase in the shearing direction. If the shearing distance is small enough, the spatial difference of the phase approximates to its gradient. Each fringe in the image represents a locus of equal gradient component of the phase in the shearing direction. The technique is interpreted by means of wave optics, using the Fraunhofer approximation and the paraxial theory of lenses. The assumptions made in earlier analyses have been removed here. A more precise analysis based on Fourier optics is presented. The simplicity of the optical setup and variable resolution of the technique have led to its frequent use in the area of solid mechanics, including fracture mechanics. Some examples are discussed in the second half of this paper.