A statistical ray method is developed for deriving reflection models of rough surfaces. Using this method, we derive generic equations of reflection due to single scattering. We have studied an isotropic surface with Gaussian statistics, and the derived bidirectional reflectance distribution function is found with four distinct regimes, namely, mirror reflection, grazing reflection, retroreflection, and normal reflection. An explicit form of self-shadowing for a surface with Gaussian statistics is also derived, and the result agrees well with computer simulation. Our solution is useful to describe the entire reflection of a highly or moderately smooth surface and offers a basis for studying multiple scattering. While focusing on optical reflection, the approach also applies to other waves if the assumptions are satisfied.
© 2007 Optical Society of America
Original Manuscript: May 25, 2006
Revised Manuscript: September 22, 2006
Manuscript Accepted: September 26, 2006
Published: February 14, 2007
Yinlong Sun, "Statistical ray method for deriving reflection models of rough surfaces," J. Opt. Soc. Am. A 24, 724-744 (2007)