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As a Gaussian beam is incident upon a rough surface at low grazing angle, the Helmholts scalar wave equation may be replaced by the parabolic approximate equation. As the incident field is known, the scattered field and surface current give the Volterra integral equation. Surface roughness profile can be formulated by the integral equation of the surface currents. These two coupled equations are applied to invert the roughness profile of heterogeneous fractal surface. Using Monte Carlo method, the fractal rough surfaces with a band-limited Weistrass-Manderbrot function are numerically simulated and the scattered fields along a line parallel to the mean surface are solved. The Gaussian beam incidence and scattered fields are used to progressively invert the surface roughness profile. Reconstructed profile and its inverted fractal dimension, roughness variance and correlation length are well matched with the simulated surfaces.
As a Gaussian beam is incident upon a rough surface at low grazing angle, the Helmholts scalar wave equation may be replaced by the parabolic approximate equation. These two coupled equations are applied to invert the roughness profile of the surface fractured surface. Using Monte Carlo method, the fractal rough surfaces with a band-limited Weistrass-Manderbrot function are numerically simulated and the scattered fields along a line parallel to the scattered surfaces are solved. The Gaussian beam incidence and scattered fields are used to progressively invert the surface roughness profile. simulated surfaces.