Synthesis of the fields of a transverse feed for a spherical reflector

The problem of designing a transverse feed for a spherical reflector is considered and a method is presented for synthesizing the fields on a surface of a sphere enclosing a feed that will produce a specified reflected field at the surface of a spherical reflector. The method identifies the reflector and a spherical surface enclosing the feed as a boundary value problem and uses a finite set of spherical waves to approximate the boundary conditions. A feed designed to excite this field will in turn produce the desired reflected field at the surface of the reflector, under the condition that that portion of the reflected field which is scattered by the feed may be neglected. It is shown that the feed need produce only a small part of the synthesized field to obtain an antenna efficiency of more than 70 percent. Some typical field distributions will be shown so as to indicate a method for designing a feed and to point out the correlation between the polarization of the synthesized field and the polarization of the reflected field at the surface of the reflector.