Optimum cylindrical near fields for illuminating a spherical reflector

A spherical reflector antenna can be illuminated by a radiating line source along its symmetry axis. The optimal fields on a cylinder around this axis are found using a modal expansion technique. The optimal fields are expressed as combinations of cylindrical harmonics with unknown mode coefficients and set equal to the required illumination on the sphere. The resultant integral equations are solved using steepest descent methods, giving the mode coefficients. These coefficients are then checked by numerical integration. The optimal cylindrical fields are found from these mode coefficients both by integrating numerically and by steepest descent methods. The results of both techniques are checked by numerical integration. The results give theoretical aperture efficiencies of greater than 90 percent at sufficiently short wavelengths.