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. Soc. Am. 57, 1105-1114 (1967)] is used to describe the specular reflection of rough surfaces. We compare this model with the BRDF measurements of four manmade surfaces with different roughnesses. The model can be used to describe the basic features of the measured BRDFs. We found that the width of the specular peak perpendicular to the principal 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 theta(i), and the deviations are determined by the roughness of the surface. This relationship is accompanied by an increase in reflectance in the specular direction in the principal plane that is 1/cos theta(i) stronger than the increase for a perfectly smooth surface.