A Method for Image Restoration and Wavefront Sensing by Using Phase Diversity

Cleaning the distortions of an unknown image due to an unknown spatially invariant point spread function (PSF) is a problem of particular interest for optical systems, like telescopes, wherein the radiation from the object passes trough a medium in turbulent motion. The aim of this paper is to present a stable method, based on the approach presented in [1] for the case of coherent radiation, which is able to estimate both the optical path disturbance (OPD) and the unknown object from noisy and incoherent multiple images, in absence of a reference source. The presented technique, at variance of other existing methods, [2-3], is able to take explicitly into account the measurement errors and noise without requiring any hypothesis on their statistical nature. The stability of the method is ensured by exploiting both a physical constraint on the OPD and a stabilizing functional.