Design of circular apertures for narrow beamwidth and asymmetric low sidelobes

Taylor's earlier work on circular apertures is enlarged to include a class of radiation patterns consisting of a narrow central beam and asymmetric sidelobes. A synthesis technique applicable to such problems, and using Taylor patterns as building blocks, is formulated. One special case is treated in detail: a sidelobe topography which is 25 dB down in the
\phi = 0
half-plane, smoothly rising to 15 dB down in the
\phi= \pi/2
half-plane, remaining at that level until the
\phi = 3\pi/2
half-plane is reached, and then smoothly subsiding to 25 dB again as
\phi
increases from
3\pi/2
to
2\pi
. The complex aperture distribution is derived generally, and exhibited specifically for this case.