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Evolution of the transfer function characterization of surface scatter phenomena
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Paper 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.

Paper Details

Date Published: 26 September 2016
PDF: 17 pages
Proc. SPIE 9961, Reflection, Scattering, and Diffraction from Surfaces V, 99610E (26 September 2016); doi: 10.1117/12.2237083
Show Author Affiliations
James E. Harvey, Photon Engineering, LLC (United States)
Richard N. Pfisterer, Photon Engineering, LLC (United States)


Published in SPIE Proceedings Vol. 9961:
Reflection, Scattering, and Diffraction from Surfaces V
Leonard M. Hanssen, Editor(s)

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