A non-paraxial scattering theory for specifying and analyzing fabrication errors in optical surfaces

Abstract

There are three fundamental mechanisms in optical systems that contribute to image degradation: aperture diffraction, geometrical aberrations caused by residual design errors, and scattering effects due to optical fabrication errors. Diffraction effects, as well as optical design errors and fabrication errors that are laterally large in nature (generally referred to as figure errors), are accurately modeled using conventional ray trace analysis codes. However, these ray-trace codes fall short of providing a complete picture of image degradation; they routinely ignore fabrication-induced errors with spatial periods that are too small to be considered figure errors. These errors are typically referred to as mid-spatial-frequency (ripple) and high-spatial-frequency (micro-roughness) surface errors. These overlooked, but relevant, fabrication-induced errors affect image quality in different ways. Mid-spatial-frequency errors produce small-angle scatter that tends to widen the diffraction-limited image core (i.e. for a system with a circular exit pupil, this is the central lobe of the Airy pattern), and in doing so, reduces the optical resolution of a system. High-spatial-frequency errors tend to scatter energy out of the image core into a wide-angle halo, causing a reduction in image contrast. Micro-roughness and ripple are inherent aspects of the less conventional, small-tool-based optical fabrication approaches. It is especially important in these cases to specify these errors accurately during the design phase of a project, and deterministically monitor and control them during the fabrication phase of a project. Surprisingly, most current approaches to this issue employ some guessing and "gut feel" based on past experience, because accurate theories and analysis tools are not readily available. This dissertation takes the first step towards solving this problem by describing a Fourier-based approach for classifying and quantifying surface errors that can be present in a fabricated optical surface. Classical scalar diffraction theories and scatter theories are reviewed and their strengths, weaknesses and misuses are discussed. Then, this dissertation focuses on the development of more accurate surface scatter theories. Modified surface scatter theories are presented that do not exhibit the small angle or smooth surface limitations that are inherent in other theories. These improvements are especially critical for surfaces considered rough with respect to the test wavelength or for systems where large scatter and/or incidence angles are present. Predictions from these modified theories are then compared to and shown to be in excellent agreement with experimental measurements.