The images recorded by optical telescopes are often degraded by aberrations that induce phase variations in the pupil plane. Several wavefront sensing techniques have been proposed to estimate aberrated phases. One of them is phase diversity, for which the joint least-square approach introduced by Gonsalves et al. is a reference method to estimate phase coefficients from the recorded images. In this paper, we rely on the asymptotic theory of Toeplitz matrices to show that Gonsalves' technique provides a consistent phase estimator as the size of the images grows. No comparable result is yielded by the classical joint maximum likelihood interpretation (e.g., as found in the work by Paxman et al.). Finally, our theoretical analysis is illustrated through simulated problems.

The on-orbit calibration of the transfer function (TF) of a spaceborne optical telescope is of paramount importance for the restoration of its recorded images. The authors propose a novel method based on a physical modeling of the TF and on the automatic extraction from the image of sub-images containing appropriate patterns such as step functions. A least-square criterion is computed with all the extracted subimages, and is minimized as a function of the unknowns, which are the TF parameters and the step parameters. The simulation results validate the method and show a precise estimation of the full 2D TF.