Stochastic model for quantifying effect of surface roughness on light reflection by diffuse reflectance standards

Diffuse reflectance standards of known hemispherical reflectance Rh are widely used in optical and imaging studies. We have developed a stochastic surface model to investigate light reflection and roughness dependence. Through Monte Carlo simulations, the angle-resolved distributions of reflected light have been modeled as the results of local surface reflection with a constant reflectance Rs representing the overall ability of a reflectance standard. The surface was modeled by an ensemble of random Gaussian surface profiles parameterized by a mean surface height δ and transverse correlation length a. By decreasing δ / a, the calculated reflected light distributions were found to transit from Lambertian to specular reflection regime. Reflected light distributions were measured with three standards by nominal reflectance Rh valued at 10%, 80%, and 99%. The calculated results agree well with the measured data in their angular distributions at different incident angles by setting Rs = Rh and δ = a = 3.5 μm.