The discovery and study of Earth-like planets orbiting stars other than our own sun requires the use of direct imaging techniques. Aside from having the capabilities to suppress the starlight before the image plane, a mission designed to image such targets must be equipped with a high-quality wavefront control system including multiple deformable mirrors in order to compensate for errors in the telescope optics.

The most mature wavefront correction algorithms to-date use an estimate of the full, complex electric field in the image plane in order to determine the voltage commands to send to the actuators of the deformable mirrors. The focus of this thesis is the study of previously developed electric field estimation algorithms and the development of new methods. There is an in-depth study of the diversity-based estimation algorithm including both its strengths and weaknesses. The two-camera estimation algorithm, a new estimation algorithm that takes advantage of a second detector located at the pupil plane, is developed and demonstrated both in simulation and in laboratory experiments.

Using the stroke-minization correction algorithm together with each of the estimation algorithms, laboratory results from the high-contrast imaging laboratory at Princeton University are presented. A single deformable mirror is used to create both small and large dark holes on one side of the image, and two sequential deformable mirrors are used to create symmetric dark holes. The best results that have been achieved on the Princeton testbed are presented in this thesis, as well as results from simulating a full, high-fidelity model of the lab. By comparing the simulation results to the experimental results, we are able to discuss the limiting factors and steps that can be taken to overcome them.

The high-contrast imaging system is discussed from a controls system point of view, and we study filtering techniques such as the Kalman filter in order to develop faster, more efficient wavefront estimation algorithms. This study is done in order to begin the development of an optimal estimation algorithm for high-contrast imaging.