Reconstruction of roughness profile of fractal surface with a Gaussian beam incidence at low grazing angle

As a Gaussian beam is incident upon a rough surface at low grazing angle (LGA), the Helmholtz scalar wave equation can be approximated by the parabolic equation. The scattered field and surface current, with a known incident field, give the Volterra integral equation. The rough surface profile can be described by the integral equation of the surface currents. These two integral equations are applied to reconstruction of the roughness profile of complex fractal surface. The fractal rough surfaces described by the band-limited Weistrass-Manderbrot function are numerically realized by using the Monte Carlo method. As the scattered fields along a line parallel to the mean surface are solved with the Gaussian beam incidence, the rough surface profile are then progressively inverted. Our numerical examples show that the reconstructed profiles and its parameters such as the fractal dimension, roughness variance and correlation length are well matched with the simulated surfaces.