From Event: SPIE Optical Engineering + Applications, 2016
The scalar-based GHSSmooth surface scatter theory results in an expression for the BRDF in terms of the surface
PSD that is very similar to that provided by the rigorous Rayleigh-Rice (RR) vector perturbation theory. However
it contains correction factors for two extreme situations not shared by the RR theory: (i) large incident or scattered
angles that result in some portion of the scattered radiance distribution falling outside of the unit circle in direction
cosine space, and (ii) the situation where the relevant rms surface roughness, σrel, is less than the total intrinsic rms
roughness of the scattering surface. Also, the RR obliquity factor has been discovered to be an approximation of
the more general GHSSmooth obliquity factor due to a little-known (or long-forgotten) implicit assumption in the RR
theory that the surface autocovariance length is longer than the wavelength of the scattered radiation. This
assumption allowed retaining only quadratic terms and lower in the series expansion for the cosine function, and
results in reducing the validity of RR predictions for scattering angles greater than 60°. This inaccurate obliquity
factor in the RR theory is also the cause of a complementary unrealistic “hook” at the high spatial frequency end of
the predicted surface PSD when performing the inverse scattering problem. Furthermore, if we empirically
substitute the polarization reflectance, Q, from the RR expression for the scalar reflectance, R, in the GHSSmooth
expression, it inherits all of the polarization capabilities of the rigorous RR vector perturbation theory.
James E. Harvey and Richard N. Pfisterer, "Comparison of the GHS Smooth and the Rayleigh-Rice surface scatter theories," Proc. SPIE 9961, Reflection, Scattering, and Diffraction from Surfaces V, 996103 (Presented at SPIE Optical Engineering + Applications: August 28, 2016; Published: 26 September 2016); https://doi.org/10.1117/12.2237081.
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