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Significance Statement
In this paper, a geometric optics (microfacet) class of Bidirectional Reflectance Distribution Function (BRDF) models, which describe realistic optical scattering off surfaces, is compared to a scalar wave optics (modified Beckmann-Kirchhoff) model of the BRDF. Microfacet BRDF models are easy to use, but imprecise since surface reflection is inherently a diffraction (wave optics) problem. On the other hand, a wave optics approach, in the simplest case, results in a BRDF model that is quite cumbersome to calculate. In this paper, the coordinate systems used in the two models are related to each other. Other terms appearing in only one model are also related to their counterparts in the other model. In particular, the microfacet BRDF models include a cross section conversion term and Fresnel reflection, while the scalar wave optics models instead include a polarization factor and an obliquity term. An approximation for these terms is presented in this paper. These novel relationships allow us to better understand what the icrofacet model represents from a diffractive perspective. The physical insight developed in this paper could lead to more accurate, yet still computationally simple, models for the BRDF that could be applied to computer graphics, remote sensing, or scene generation.
Journal Reference
Opt Express. 2015;23(22):29100-12.
Butler SD, Nauyoks SE, Marciniak MA.
Department of Engineering Physics, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433-7765, USA.
Abstract
A popular class of BRDF models is the microfacet models, where geometric optics is assumed. In contrast, more complex physical optics models may more accurately predict the BRDF, but the calculation is more resource intensive. These seemingly disparate approaches are compared in detail for the rough and smooth surface approximations of the modified Beckmann-Kirchhoff BRDF model, assuming Gaussian surface statistics. An approximation relating standard Fresnel reflection with the semi-rough surface polarization term, Q, is presented for unpolarized light. For rough surfaces, the angular dependence of direction cosine space is shown to be identical to the angular dependence in the microfacet distribution function. For polished surfaces, the same comparison shows a breakdown in the microfacet models. Similarities and differences between microfacet BRDF models and the modified Beckmann-Kirchhoff model are identified. The rationale for the original Beckmann-Kirchhoff F(bk)(2) geometric term relative to both microfacet models and generalized Harvey-Shack model is presented. A modification to the geometric F(bk)(2) term in original Beckmann-Kirchhoff BRDF theory is proposed.
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