it is reflected parallel to the axis to arrive at a point A on the imaginary aperture plane. Equation 9.49, where F is the focal length, describes the surface. r2=4F(F-z) (9.49) At the edge of the reflector, of diameter D, equation 9.50 applies. -1-cot(2) (9.50) Reflective Antenna Types Fig. 9.10 Geometry of a reflector antenna. The depth of the paraboloid is usually specified by its F/D ratio. Common sizes are between F/D = 0.25 (O0 = 90°) to F/D = 0.4. Aperture Fields and Radiation Patterns Ray optics indicate that the path length from F to P to A is equal to twice the focal length. Hence the phase across the aperture is constant. The amplitude across the aperture plane will peak at the center and taper toward the edge for two reasons: First, the feed will have a tapered radiation pattern and, second, the action of a parabola in transforming a spherical wave from the feed into a plane wave across the aperture introduces a path loss, which is a function of angle O. The aperture electric field is then given by equation 9.51, where F(0, Q) is the pattern of the feed. (9.51) Feeds suitable for reflector antennas are discussed in a later section, but it is often con- venient in initial design to take the feed pattern as being given by equation 9.52. F(0,0)=cos9(0) (9.52) Experience has shown that good-quality feeds approximate well to this function. The radiation patterns can be predicted from the aperture fields using the Fourier trans- form relations described in the Radiation from Apertures section. This works well for large reflectors, but for detailed design of small to medium reflectors, it is necessary to take account of the precise form of the currents on the reflector surface and the diffraction that occurs at its edges. The former can be accomplished with physical optics theory (Rusch & Potter, 1970; Rusch, Ludwig, & Wong, 1986) and is good for predicting the main beam and near-in sidelobes. The diffracted fields influence the far-out sidelobes and can be predicted using the Geometrical Theory of Diffracti