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An approach to the exterior Dirichlet problem in ℝ2 with applications to wave scattering

The study of phenomena arising from the scattering of waves from rough surfaces is of interest in many fields of physics and engineering. For instance, one of the most promising application in optics seems to be the employment of a laser beam scattering for non-destructive inspection of topography and optical quality of surfaces. In dealing with scattering from rough surfaces, approximate methods, such as perturbation techniques [1] or the Kirchhoff approximation [2], have gained ground. Unfortunately, the validity of these methods proves insufficient to handle interaction with resonance roughnesses, as well as grazing incidence geometries. For this reason a large amount of research, reported in the last 15 years, has been devoted to rigorous methods based, in particular, on boundary integral equations. (A review may be found in [3].)