In this chapter we turn our attention to scattering from non-penetrable objects, or “surface scattering,” and “diffraction” from planar apertures. As was mentioned in the introduction to the previous chapter, the interaction of an incident wave with a non-penetrable scatterer occurs over the surface of the scattering obstacle and is thus defined by some type of boundary condition over this surface. In a similar vein diffraction of an incident wave from apertures cut into non-penetrable surfaces is also defined by some type of boundary condition over the aperture plus surface and thus can, in a certain sense, be considered to be a type of surface scattering. The formal solution to both types of problems is thus obtained in an identical fashion by converting the problem into a boundary-value problem, which is then easily solved using the theory developed in Chapter 2.

The above prescription for “solving” surface scattering and aperture diffraction problems has one missing ingredient: determination of the boundary values required in the solution of the scattering or diffraction problem. This is the ingredient that distinguishes a scattering or diffraction problem from the purely mathematical boundary-value problem. In this chapter we will restrict our attention to non-penetrable objects over which the total field (incident plus scattered) satisfies homogeneous Dirichlet or Neumann conditions. By invoking this condition it is possible to represent the scattered field in terms of either the value of the normal derivative of the total field (the homogeneous Dirichlet case) or the total field itself (the homogeneous Neumann case) over the scatterer surface.