Width of the specular peak perpendicular to the principal plane for rough surfaces

The bidirectional reflectance distribution function (BRDF) model developed by Torrance and Sparrow [J. Opt. Sec. Am. 57, 1105-1114 (1967)] is used to describe the specular reflection of rough surfaces. We compare this model w ith the BRDF measurements of four manmade surfaces with different roughness es. The model can be used to describe the basic features of the measured BR DFs, We found that the width of the specular peak perpendicular to the prin cipal plane decreases strongly with an increasing illumination zenith angle in the data as well as in the model. A model analysis shows that the width is approximately proportional to the cosine of the illumination angle thet a (i), and the deviations are determined by the roughness of the surface. T his relationship is accompanied by an increase in reflectance in the specul ar direction in the principal plane that is 1/cos theta (i) stronger than t he increase for a perfectly smooth surface. (C) 2001 Optical Society of Ame rica.