Fundamentals of the Physical Theory of Diffraction, 2nd Edition

12 Focusing of Multiple Edge Waves Diffracted at a Disk

The theory presented in this chapter is based on papers by Ufimtsev (1989, 1991). It represents an extension of Chapter 11 to the disk diffraction problem, where it is necessary to take into account the edge waves propagating along both faces of a disk (Fig. 12.1). This problem is complicated by the fact that the wave traveling along one face of the disk generates (due to diffraction at the edge) higher-order waves not only on the same face but also on the other face. However, its solution can be lightened if we utilize the symmetry of the scattered field. Let us consider scattering at an arbitrary plate located in the plane z = 0. It follows from Equation (1.10) that

(12.1)

Figure 12.1 Disk projection on the plane y0z (bold solid lines) and edge waves (dashed lines). The angles φ and ψ = 2π − φ (measured from the left and right faces of the disk) determine the directions to the observation point P.

Here, the first equality is obvious and the second is caused by the factor

(12.2)

where . The geometry of the problem ...