Designing an optimal estimator for more efficient wavefront correction

Space-based coronagraphs for future earth-like planet detection will require focal plane wavefront control techniques to achieve the necessary contrast levels. These correction algorithms are iterative and the control methods require an estimate of the electric field at the science camera, which requires nearly all of the images taken for the correction. In order to maximize science time the amount of time required for correction must be minimized, which means reducing the number of exposures required for correction. This means reducing both the number of iterations and the number of exposures per iteration required to achieve a targeted contrast. Given the large number of images required for estimation, the ideal choice is to use fewer exposures to estimate the electric field. Here we demonstrate an optimal estimator that uses prior knowledge to create the estimate of the electric field. In this way we can optimally estimate the electric field by minimizing the number of exposures required to estimate under an error constraint. The performance of this method is compared to a pairwise estimator which is designed to give the least-squares minimal error. This allows us to evaluate the number of images necessary to achieve a contrast target and is the first step towards generating an adaptive algorithm which combines estimation and control to optimize the entire correction problem.