Reconstruction of a heterogeneous fractal surface profile from scattering measurements at low grazing incidence

Scattering from rough surfaces has been extensively studied in electromagnetics, optics, acoustics, etc. However, the associated problems of inverse scattering from rough surface, i.e., inversion of surface characteristic parameters and reconstruction of surface profile, have received little progress. In recent years, fractal geometry has been introduced to the study of rough surfaces (Jaggard, D.L. and Sun, X., J Appl. Phys., vol.68, p.5456, 1990). The paper develops a numerical approach to reconstruct the roughness profile of complex fractal surfaces. Using the Monte Carlo method, the fractal rough surfaces with a band-limited Weistrass-Mandelbrot function are numerically realized. The incident field used is a Gaussian beam at low grazing angle. The scattering fields and surface currents can be solved and employed to invert the rough surface profile progressively. The reconstructed profile and its parameters, such as the fractal dimension, roughness variance and correlation length, are well matched with simulated surfaces.