AN EXTENSION TO THE ANALYSIS OF THE SHIFT-AND-ADD METHOD: THEORY AND SIMULATION (SPECKLE, ATMOSPHERIC TURBULENCE, IMAGE RESTORATION).

Abstract

The turbulent atmosphere degrades images of objects viewed through it by introducing random amplitude and phase errors into the optical wavefront. Various methods have been devised to obtain true images of such objects, including the shift-and-add method, which is examined in detail in this work. It is shown theoretically that shift-and-add processing may preserve diffraction-limited information in the resulting image, both in the point source and extended object cases, and the probability of ghost peaks in the case of an object consisting of two point sources is discussed. Also, a convergence rate for the shift-and-add algorithm is established and simulation results are presented. The combination of shift-and-add processing and Wiener filtering is shown to provide excellent image restorations.