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26 September 2016Evolution of the transfer function characterization of surface scatter phenomena
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
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James E. Harvey, 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); https://doi.org/10.1117/12.2237083