ON THE THEORY OF SPECKLE SHEARING INTERFEROMETRY WITH DIFFRACTION GRATINGS AS SHEARING COMPONENTS

The use of double-frequency diffraction gratings as a means of shearing optical images in speckle shearing interferometry is investigated. Fresnel approximations to the scalar field theory are employed to derive the film-plane intensity patterns for the sheared images. The Fourier filtering technique used to post-process the transmission function of the film is analyzed. The case of linear strain is analyzed in closed form using simplifying assumptions. Numerical solutions for more realistic situations are presented. Results show that double-frequency gratings are effective shearing components for use in speckle shearing interferometry. In contrast to other shearing components, the diffraction gratings are both adaptable and simple to use. The numerical work suggests that optimization of the Fourier filtering system is feasible.