Comparison of the GHS_(Smooth) and the Rayleigh-Rice surface scatter theories

摘要

The scalar-based GHS_(Smooth) 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, σ_(rel), 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 GHS_(Smooth) 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 GHS_(Smooth) expression, it inherits all of the polarization capabilities of the rigorous RR vector perturbation theory.