Analytical solution to the phase-diversity problem for real-time wavefront sensing.

High-resolution optical systems require a very accurate control of the optical paths. For the measurement of aberrations on extended objects, several iterative phase-diversity algorithms have been developed, based on aberration estimation from focal-plane intensity measurements. Here we present an analytical estimator in the case of small aberrations.

Unambiguous phase retrieval as a cophasing sensor for phased array telescopes.

Cophasing a multiple-aperture optical telescope (MAOT) or optical interferometer requires the knowledge of the tips/tilts and of the differential pistons on its subapertures. In this paper we demonstrate in the case of a point source object that a single focal-plane image is sufficient for MAOT cophasing. Adopting a least-square approach allows us to derive an analytic estimator of the subaperture aberrations, provided that these are small enough (typically for closed-loop operation) and that the pupil is diluted noncentrosymmetric.