Rank-based optimization techniques for estimation problems in optics

Aberrations in optical systems, such as telescopes and microscopes, degrade the quality of the images that can be produced by these systems. For example, an object that is positioned out of focus produces a blurred image on a camera sensor and the turbulent air in the earth’s atmosphere reduces the imaging performance of telescopes. In this thesis we only consider wavefront aberrations. AO can be used to compensate for these wavefront aberrations. The working principle of AO is to quantify by measuring or estimation the wavefront aberration and to dynamically adjust wavefront modulating devices, such as Deformable Mirrors (DMs), to counteract the aberration and thereby improving the optical performance. The estimation of the wavefront aberration based on images of a point source is called phase retrieval, which is a highly nonlinear estimation problem. The success of the estimation usually depends on the (type of) algorithm, the available information on the aberration that is incorporated in the estimate, and the degree to which the model of the optical system corresponds to reality. In this thesis we propose a convex optimization-based method for phase retrieval. The method allows for easy inclusion of many types of prior information on the aberration. Furthermore, we develop an efficient implementation of the optimization. The robustness of the approach against measurement noise is investigated and compared with several other state of the art algorithms. Experimental validation shows the algorithmis well able to estimate aberrations in real-life circumstances. A new type of prior information is introduced to estimate dynamic wavefront aberrations. In literature and in practice, the optical path is split between either a wavefront sensor and a camera, or between multiple cameras in order to reliable estimate an aberration. The inherent problem is that between the sensor and cameras the aberration can differ (Non-Common Path (NCP) errors), and a wrong estimate is used in the compensation by the AO system. We propose a method to estimate the aberration from measurements by a single camera, by assuming that the aberration evolves according to (non-specific) model, i.e. the dynamics are contained in a model-set. At the same time that we estimate the aberration, we also identify the dynamics according to which the aberration evolves over time. The estimation of the wavefront aberration based on images of an unknown object is called blind deconvolution if both the aberration and object are estimated. Like phase retrieval, this too is a highly nonlinear estimation problem. We propose the first convexoptimization based estimation method for blind deconvolution problems that estimate aberration and object when the images are acquired using coherent illumination. The method allows for the inclusion of many existing types of prior information on the object and/or aberration. Finally, we analyze controllers for segmented mirrors in large ground-based telescopes. These mirrors consist of many interconnected hexagonal segments. This distributed nature of the system warrants the investigation into whether the controller that keeps the segments aligned can be designed in such a way that it can be distributed over the segments as well, essentially resulting in a distributed controller where local controllers communicate with each other. What complicates the analysis is that the dynamics across segments are not necessarily decoupled: the wind load can be correlated and the flexibility in the supporting structure of the segments can cause dynamic coupling. We investigate the design of a distributed controller that incorporates these global dynamics. Furthermore, we investigate the performance of the distributed controller and howit relates to the communication and interconnection pattern of the local controllers.