Bidirectional reflectance distribution function algorithm based on the Poynting vector analysis

We used Maxwell’s partial differential equations of electrodynamics to quantify radiation and scattering on rough surfaces. The electrical field and the magnetic field are the results from the near-field. To find the bidirectional reflectance distribution function (BRDF) of the far-field, we present an algorithm for BRDF based on near-to-far-field projection and Poynting vector analysis. This algorithm accounts for characteristics of the BRDF function, focuses on the Poynting vector of the outgoing radiation, and creates a virtual projection surface to serve for the BRDF. The near-field data are recorded on a rectangular shape, and the far-field data are recorded on a virtual hemispherical surface. The BRDF can be calculated using Green’s theorem for the selected area on the virtual hemispherical surface. The results show that, for RMS 0.1 to 0.5 μm, the incident wavelengths are 400 to 700 nm, the surface roughness ranges from smooth to slightly rough, the simulation agrees with the scattering theory, and the accuracy of the algorithm is significantly higher than that of the Cook–Torrance BRDF model.