title: Analytical solution to the phase-diversity problem for real-time wavefront sensing.
abstract: 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. Under this assumption, a quadratic criterion is derived that allows us to express the solution (phase and object) under a simple analytical form. We also compare the performance of our algorithm with the iterative phase diversity, demonstrating that the analytic estimator is appropriate for closed-loop operation.
authors.affiliation: Office National d'Etudes et de Recherche Aérospatiales, Optics Department, BP 72, 92322 Châtillon Cedex, France. mocoeur_astro@orange.fr
authors.forename: Isabelle
authors.initials: I
authors.lastname: Mocoeur
authors.forename: Laurent M
authors.initials: LM
authors.lastname: Mugnier
authors.forename: Frédéric
authors.initials: F
authors.lastname: Cassaing