26 September 2016 Evolution of the transfer function characterization of surface scatter phenomena
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Abstract
Based upon the empirical observation that BRDF measurements of smooth optical surfaces exhibited shift-invariant behavior when plotted versus    o , the original Harvey-Shack (OHS) surface scatter theory was developed as a scalar linear systems formulation in which scattered light behavior was characterized by a surface transfer function (STF) reminiscent of the optical transfer function (OTF) of modern image formation theory (1976). This shift-invariant behavior combined with the inverse power law behavior when plotting log BRDF versus log   o was quickly incorporated into several optical analysis software packages. Although there was no explicit smooth-surface approximation in the OHS theory, there was a limitation on both the incident and scattering angles. In 1988 the modified Harvey-Shack (MHS) theory removed the limitation on the angle of incidence; however, a moderate-angle scattering limitation remained. Clearly for large incident angles the BRDF was no longer shift-invariant as a different STF was now required for each incident angle. In 2011 the generalized Harvey-Shack (GHS) surface scatter theory, characterized by a two-parameter family of STFs, evolved into a practical modeling tool to calculate BRDFs from optical surface metrology data for situations that violate the smooth surface approximation inherent in the Rayleigh-Rice theory and/or the moderate-angle limitation of the Beckmann-Kirchhoff theory. And finally, the STF can be multiplied by the classical OTF to provide a complete linear systems formulation of image quality as degraded by diffraction, geometrical aberrations and surface scatter effects from residual optical fabrication errors.
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James E. Harvey, James E. Harvey, Richard N. Pfisterer, Richard N. Pfisterer, "Evolution of the transfer function characterization of surface scatter phenomena", Proc. SPIE 9961, Reflection, Scattering, and Diffraction from Surfaces V, 99610E (26 September 2016); doi: 10.1117/12.2237083; https://doi.org/10.1117/12.2237083
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