Fundamentals of the Physical Theory of Diffraction, 2nd Edition

10 Diffraction Interaction of Neighboring Edges on a Ruled Surface

The following relationships exist between acoustic and electromagnetic diffracted waves:

Here is tangent to the edge and is the normal to the face at the diffraction point ζ. These relationships, together with Equation (7.159), allow one to determine all components of the electromagnetic diffracted wave.

Consider a diffraction interaction of two edges with a common face. If this face is bent, the edge wave already undergoes diffraction on its way along the face to another edge. This problem is not amenable to theoretical treatment in a general case. However, the disturbing effect of the face can be neglected in a particular case illustrated in Figure 10.1. The common face S of edges L₁ and L is a ruled surface whose generatrices coincide with the edge-diffracted rays arising at edge L₁ and propagating to edge L. It is assumed that a plane tangential to the face does not change its orientation along the generatrix. Notice that a planar facet can be considered as a limiting case of a ruled surface. Therefore, the theory developed here is applicable in this case as well.

Figure 10.1 Element of a ruled surface ...