Optimization in physical optics analysis.

Abstract

The application of optimization techniques to the design and analysis of physical optics systems is studied. Optimization techniques such as the method of least squares are commonly applied during design and analysis of geometrical or ray-based optical systems. Many optical systems, such as simple laser oscillator cavities have properties well described by geometrical optics. However, a more general class of optical systems exists where geometric properties do not sufficiently describe the system. For example, ray-based optical descriptions are adequate only in regions away from focal points. In simple laser oscillators, ABCD matrices provide an adequate description, however, when complex apertures or gain media are introduced, the system is no longer adequately described by these geometric properties. These more general optical systems fall under the category of physical optics. Optimization has found widespread use in geometrical optics design. Physical optics design using optimization techniques adapted from geometrical optimization techniques is the primary focus of this research. The key issues were: identification of differences between geometrical and physical optics optimization, development of a suitable optimization algorithm, determination of solutions for dealing with noisy derivatives and singular systems, identification of classes of problems which benefit from optimization techniques, and testing of the algorithm through representative examples. This dissertation discusses aspects of optimization techniques applied to physical optics modeling problems. The method of singular value decomposition is discussed as it applies to the solution of singular least squares matrices. The computational difficulty with noisy derivatives is discussed, and a solution proposed. Physical optics modeling and optimization is described, and several example cases are studied at length.