Complex ray interpretation of reflection from concave-convex surfaces

Reflection from a smooth target with inflection points, when investigated by the physical optics method, reveals far-zone contributions arising from real and complex stationary points. The former represent conventional specularly reflected real-ray fields whereas the latter, which are nonspecular in real space, can be interpreted as complex-ray fields reflected specularly from the complex extension of the scatterer surface. To explain the nonspecular contributions, the complex stationary point fields are regarded as specular reflections of complex incident rays from the analytic extension of the boundary into a complex coordinate space. It is verified that this construction using complex geometrical optics is in complete agreement with physical optics asymptotics and that the complex reflection points for far-zone fields lie near the concave-to-convex transitions on the physical contour. Numerical results supporting the validity of this assertion are provided. It is concluded, therefore, that a complete ray theory of reflection from the illuminated portion of a smooth object with inflection points must include specularly reflected real as well as complex rays, with the latter originating from the complex extension of the surface contour