Scattering by S-shaped surfaces

When an S-shaped surface possesses no derivative discontinuities, techniques such as the geometrical theory of diffraction are not applicable. However, if the radius of curvature is relatively large at every point on the surface, the physical optics approximation may be employed. The authors present a uniform physical optics (UPO) solution which remains valid at caustics occurring when two or more specular points coalesce at the inflection point of the S-shaped surface. The solution is developed by approximating the surface with a localized cubic expansion, leading to exact expressions in terms of Airy integrals. In contrast to other solutions, the one given here requires only a knowledge of the stationary phase points and the first three derivatives of the surface-generating function at those points. A major effort is devoted to the validation of the UPO solution, and this is accomplished with numerical models of the S-shaped surface. It is found that the given UPO solution is quite accurate in the specular and nonspecular regions