Phase retrieval for chromatic aberrations and wide-field detectors

Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2017. "Chapter 3 was co-authored with Alden Jurling, who wrote the introduction as well as Sections 3.2 and 3.3, except for subsections 3.2.5 and 3.3.3"--Page xiii.We present a series of advancements to the state of the art in computational optics, in particular by enabling new areas of application for image-based wavefront sensing via phase retrieval. This includes demonstration of a parameterized model for chromatic aberrations which can improve diagnostics in dispersive optical systems. Potential sign ambiguities are identified and strategies to avoid or remove them are prescribed. The algorithm is also tested in a real-world laboratory environment, with results in good agreement with expected values. As a prerequisite to this advance, we also evaluate a collection of less frequently utilized discrete Fourier transform (DFT) algorithms that have an advantage over the fast Fourier transform in that they allow for an arbitrary scaling factor between the input and output domains. The trade-off in terms of computation speed is demonstrated using timing benchmarks for a variety of physical optics modeling scenarios, and multiple cases are found where the arbitrarily-scaled DFTs are preferable. In addition, we address issues with image-based wavefront sensing that arise from the unusually-large detector plane of a wide-field space telescope, where large chief ray angles at the edges of the field violate the small angle assumption of the usual Fresnel propagationintegral. By starting from an exact expression and adapting an approximation approach previously derived for digital holography with non-parallel planes, we find an algorithm that is both computationally efficient and sufficiently accurate. Finally, we present a computational optical system with an extended depth of field that was achieved by inducing field-independent coma intrinsic to the geometrical optics design via optimized decentration of the lens elements. This is a departure from the more common approach that requires a phase mask to control the wavefront