Optimal Sharpness Function for SAR Autofocus

Phase-error correction through the optimization of an image-domain sharpness function provides one method for the auto-focus of synthetic aperture radar (SAR) imagery. Several ad-hoc sharpness functions have been proposed, implemented, and analyzed, but none of these has been motivated as the solution to a well-defined statistical estimation problem. In this letter, a SAR sharpness function is derived that induces the solution to maximum-likelihood and maximum-posterior estimation for idealized SAR data. Furthermore, a limiting form of the optimal sharpness function is shown to be the popular intensity-squared sharpness