An aperture antenna may be described in two ways. First, as an area of a surface with a radiating field distribution across it, the field being negligible on the surface outside the area. Second, as an area bounded by edges and excited by a source. Examples are radiating slots, horns and reflectors. These two descriptions characterise the two alternative methods of aperture antenna analysis used in this book. One is based on aperture field radiation, the other on aperture edge diffraction. Both apply strictly to large apertures so slots are generally excluded, but they are also useful for apertures with dimensions comparable to a wavelength. They tend to be complementary in that where one fails the other may succeed.

The Fourier transform relationship between an aperture distribution and its radiation pattern is exact, but its application involves an approximation at once for the field is never known over the entire aperture plane. Usually it is known approximately only within the aperture and is assumed to vanish in the rest of the aperture plane. Suppose a field exists in an aperture S in the plane z = 0 and is negligible outside S. The tangential electric field in S is resolved into appropriate components, usually Cartesian if the aperture shape is rectangular.

The results of this Section are for point measuring probes in the near-field. If the measuring probe directivity is significant axial near-field gain can be specified only for identical antennas. Near-field gain reduction factors for identical circular and square apertures with uniform and tapered distributions have been derived.

The preceding chapters use the approximate Kirchhoff theory of diffraction. As indicated in Sections 2.6 and 6.1 it does not, in general, satisfy the boundary con ditions. This chapter gives a few elementary diffraction solutions for conductors with edges in which boundary conditions are rigorously satisfied. These exact solutions are the basis of the newer approximate method of aperture antenna analysis used in the remaining chapters.

In antenna analysis the geometrical theory of diffraction is particularly useful in obtaining the radiation field at angles well off the beam axis or in the rear direction where the Kirchhoff method either fails or cannot be applied. On or near the beam axis geometrical diffraction theory may fail, as in the case of a paraboloidal reflector. There the Kirchhoff method is both applicable and accurate and should be used. In this sense the two methods are complementary.