Novel estimator for the aberrations of a space telescope by phase diversity

In this communication, we propose a novel method for estimating the aberrations of a space telescope from phase diversity data. The images recorded by such a telescope can be degraded by optical aberrations due to design, fabrication or misalignments. Phase diversity is a technique that allows the estimation of aberrations. The only estimator found in the relevant literature is based on a joint estimation of the aberrated phase and the observed object. By means of simulations, we study the behavior of this estimator. We propose a novel marginal estimator of the sole phase by Maximum Likelihood. It is obtained by integrating the observed object out of the problem; indeed, this object is a nuisance parameter in our problem. This reduces drastically the number of unknown and provides better asymptotic properties. This estimator is implemented and its properties are validated by simulation. Its performance is equal or even better than that of the joint estimator for the same computing cost.