Specification and modeling of mid-spatial frequency errors in optical systems

Recent advancements in manufacturing and post-processing of optics with sub-aperture methods have enabled greater degrees of freedom to realize complex optical surfaces. Introduction of residual mid-spatial frequency (MSF) surface errors is a consequence of sub-aperture manufacturing. MSF errors have spatial frequencies between ‘low frequency’ form and ‘high frequency’ roughness with ambiguous bounds and with distributions that range from nearly random to highly deterministic and complex, depending on manufacturing method and conditions. MSF errors degrade optical performance and present significant challenges for both specification and optical performance predictions. The lack of specifications that directly connect to optical performance and the lack of widely available capabilities and procedures for modeling of generalized MSF errors are significant impediments to understanding their impacts in imaging systems.
The primary goals of this dissertation are (1) to explore and expand the connections between MSF specifications and optical performance for complex MSF error distributions, and (2) to demonstrate the implementation of these concepts within commercial software packages to enable the exploration of generalized MSF errors in optical systems. Results are addressed through three articles. The first article addresses the mathematical development and benefits of pupil-difference probability distribution (PDPD) moments to specify MSF errors and connect them to optical performance. The second article builds from this work to provide modeling procedures and explores their application to both random and deterministic MSF errors. The third article demonstrates the integration of these new concepts and methods into MATLAB™ and CODE V™, and their use on sample refractive and reflective imaging systems.