Deconvolution of lateral shear interferograms.

This dissertation develops and presents an existing but little known method to provide an exact solution to the Wavefront Difference Equation routinely encountered in the reduction of Lateral Shear Interferograms (LSI). The method first suggested by Dr. Roland Shack treats LSI as a convolution of the wavefront with an odd impulse pair. This representation casts the Lateral Shear problem in terms of Fourier optics operators and filters with a simplified treatment of the reduction of the LSI possible. This work extends the original proposal applied to line scans of wavefronts to full two-dimensional recovery of the wavefront along with developing the associated mathematical theory and computer code to efficiently execute the wavefront reduction. Further, a number of applications of the wavefront reduction technique presented here are developed. The applications of the filtering technique developed here include optical imaging systems exhibiting the primary aberrations, a model of residual tool marks after fabrication and propagation of an optical probe through atmospheric turbulence. The computer program developed in this work resides on a PC and produces accurate results to a 1/500 wave when compared to ray traced input wavefronts. The combination of the relatively simple concept providing the basis of the reduction technique with the highly accurate results over a wide range of input wavefronts makes this a timely effort. Finally, the reduction technique can be applied to the accurate testing of aspheric optical components