Reconstruction of roughness profile of fractal surface from scattering measurement at grazing incidence

As a scalar wave is incident upon a rough surface at grazing angle, the Helmholtz wave equation can be approximated by the parabolic equation. Inverse scattering has been formulated in the form of a pair of coupled integral equations in two unknown functions, i.e., surface current and surface roughness. The aim of this article is to implement this approach for profile reconstruction of complex fractal rough surface. The fractal rough surfaces described by a band-limited Weieztrass–Mandelbrot function are numerically realized using the Monte Carlo method. As the scattering fields along a line parallel to the mean surface are measured or solved with a scalar wave incidence at low grazing angle, the rough surface profile is progressively inverted. Numerical examples show that the reconstructed profile and its parameters such as the fractal dimension, roughness variance, and correlation length are well matched with the simulated surfaces.