Reconstruction of two-dimensional randomly rough surfaces based on bidirectional reflectance distribution function

This article presents an inverse method for reconstructing two-dimensional randomly rough surfaces based on the available (experimental or given) data of the bidirectional reflectance distribution function (BRDF). The Maxwell's equations of electromagnetic waves are applied to describe the light scattering process of rough surfaces by accounting for the near-field effect. Such a forward problem is numerically solved with the finite-difference time-domain algorithm. The inverse scattering problem of reconstructing the surface profile is handled by means of an optimization technique - the particle swarm optimizer algorithm. As an example, reconstruction of a Gaussian rough surface is conducted based on the experimental data of BRDFs. The retrieved results of the surface profile are compared with those measured by atomic force microscopy from the samples, which shows that the reconstruction algorithm can provide the credible prediction of surface profiles. The reconstruction approach studied in this study can make reliable predictions of the actual or required surface profiles.