Direct Solution of the Inverse Problem for Rough Surface Scattering

We consider the inverse scattering problem for a scalar wave field incident on a perfectly conducting one-dimensional rough surface. The Dirichlet Green function for the upper half-plane is introduced, in place of the free-space Green function, as the fundamental solution to the Helmholtz equation. Based on this half-plane Green function, two reasonable approximate operations are performed, and an integral equation is formulated to approximate the total field in the two-dimensional space, then to determine the profile of the rough surface as a minimum of the total field. Reconstructions of sinusoidal, non-sinusoidal and random rough surface are performed using numerical techniques. Good agreement of these results demonstrates that the inverse scattering method is reliable.