Figure 1 illustrates the geometry of this problem and the various regions of the analysis. The diagram shows the end of the dipole rod with the two rods located normal to the page. The dipole pattern is omnidirectional in the page with the electric field directed normal to the page. When we trace rays from the dipole to the finite strip, we discover two significant directions on both sides of the strip. The dashed boundaries labeled RB (reflection boundary) are the directions of the last rays reflected from the strip. Similarly, the dashed boundaries labeled SB (shadow boundary) are the last rays of radiation not blocked by the strip. The radiation in region I results from the sum of the direct radiation from the dipole plus the radiation reflected by the strip. Only direction radiation from the dipole occurs in the two parts of region II. Finally, region III is totally blocked from any radiation by a direct or reflected ray. This region receives rays diffracted around the edges.

If we add the direct and reflected rays in an analysis, we obtain the pattern given in Figure 2, which also traces the actual pattern. The pattern, using only the direct and reflected rays, accounts for the phasing between the direct radiation from the dipole and an image dipole located below the strip. If you compare the two traces on Figure 2, you see that the two patterns are similar near  = 0, but the direct plus reflected ray pattern has discontinuities at the SBs and RBs. Figure 3 gives the results for the same analysis, but using a 5λ-wide ground-plane strip. When using the larger strip, the two patterns match to about , and in the second case the simple analysis is correct over most of the forward semicircle. Simple geometric optics gives good results for large objects provided that you realize the patterns will contain discontinuities.

Removing the discontinuities requires extra effort. A discontinuity in the pattern cannot exist because shadow and reflection boundaries occur in free space. It takes a material boundary to produce a discontinuous field. But, for example, the tangential electric field must be continuous across even material boundaries. Edge diffraction solves the discontinuity problem. Figure 4 gives the pattern of the edge diffraction for both edges normalized to the total pattern. The edge diffraction has matching discontinuities to the sum of the direct and reflected rays at the SBs and RBs. The UTD (uniform theory of diffraction) technique calculated these diffractions. When these diffractions are added to the direct and reflected ray radiation, the total pattern given in Figure 2 is obtained. The dipole, its image in the ground plane, and the two edge diffractions form a four-element array where each element has a unique pattern. Adding edge diffractions to the geometric optics fields removes the discontinuities and allows calculation of the pattern behind the strip ground plane.

FIGURE 2 H-plane pattern of a dipole over asymmetrical ground using direct and reflected rays compared only to a full solution for the 1λ ground plane of Figure 1.