Scattering from Rough Surfaces with Extended Self-Similarity

An extended self-similarity (ESS) model is developed by extending the self-similarity condition in fractional Brownian motion (FBM), then the incremental Fourier synthesis algorithm is introduced to generate ESS rough surfaces, and an estimation algorithm is presented to extract the generalized multiscale Hurst parameter which can also be modified to estimate the Hurst parameter for FBM more accurately. Finally, the scattering coefficient from ESS rough surfaces is calculated with the Scalar Kirchhoff approximation, and its variation with the parameters in the ESS model is obtained. Compared with experimental measurements, it can be concluded that the ESS model provides a good tool to model natural rough surfaces.