Synthesis of two-reflector antennas on the basis of an amplitude pattern

A system of three transcendental equations and one second-order partial differential equation is obtained for the determination of the form of the secondary reflector in the general case. This system is reduced to two transcendental equations and one first-order ordinary differential equation for axisymmetric antennas. The problem of synthesizing an antenna with a fan-like pattern is reduced to a system of three transcendental equations and one second-order integrodifferential equation. An explicit solution is obtained for the transcendental equations in the case when the primary reflector is a second-order surface, while the wave front of the feed is planar, cylindrical, or spherical. As an example, the synthesis of two-reflector antennas with axisymmetric and fan-like patterns is considered.