Optimal electric field estimation and control for coronagraphy

Detecting and characterizing extrasolar planets has become a very relevant field in Astrophysics. There are several methods to achieve this, but by far the most difficult and potentially most rewarding approach is direct imaging of the planets. Coronagraphs can be used to image the area surrounding a star with sufficient contrast to detect orbiting planets. However, coronagraphs exhibit an extreme sensitivity to optical aberrations which causes starlight to leak into the search area. To solve this problem we use deformable mirrors to correct the field, recovering a small search area of high contrast (commonly referred to as a "dark hole") where we can once again search for planets.;These coronagraphs 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. Given the large number of images required for estimation, the ideal choice is to use fewer exposures to estimate the electric field. With a more efficient monochromatic estimation in hand, we also seek to apply this correction over as broad a bandwidth as possible. This allows us to spectrally characterize a target without having to repair the field for every wavelength.;This thesis derives and demonstrates 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. With an optimal estimator in place for monochromatic light, we also demonstrate a controller that can suppress the field over a bandwidth when provided with this monochromatic estimate. The challenges, current levels of performance, and future directions of this work are discussed in detail.