Figure 1 illustrates the cross section of a horn or, in this case, a two-dimensional approximation to a horn. The waveguide feeds the horn and produces a uniform aperture distribution in the E-plane. In this model the direct GO radiation is a constant wedge signal as shown in Figure 2 ranging between - and + . The reflected pattern combines with the direct radiation and produces the same pattern. Figure 2 also shows the diffraction patterns from the two edges. These peak along the plates and exhibit a discontinuity at the same angle as the GO field. Each diffraction pattern has a discontinuity on one side at   because the mouth of the horn blocks the diffraction from the opposite edge. When we add the diffracted fields to the GO field, the pattern shown in Figure 3 is obtained. By just adding the three components, we obtain an accurate pattern of the horn over most of the angles of the plot. At  we see discontinuities in the pattern caused by not considering enough terms in the GTD calculation. You need to realize that these discontinuities only cause pattern errors at nearby angles. The majority of the pattern is correct.

We need another term to correct the pattern near  . The blockage of the diffraction from one edge by the mouth of the horn causes a secondary diffraction at that edge. We call this double diffraction. Some available programs do not implement double diffraction because the general three-dimensional double diffraction takes considerable calculation due to the extensive ray tracing required. In these cases you must accept the pattern discontinuities. Some programs calculate double diffraction as an option, but turning on this option will slow the calculations. Figure 4 gives the pattern when double diffraction is included. Double diffraction reduces the discontinuity at  , but a small discontinuity remains. Adding triple diffraction would reduce this further, but the pattern area affected by the small discontinuity has shrunk. A new discontinuity near   appeared in the pattern after adding double diffraction at the mouth of the horn. We could continue to add another term to remove this one or just accept it.