On the design and performance of feeds for correcting spherical aberration

The maximum power that can be received from the currents in a spherical reflector is obtained with that feed which, when transmitting, produces a tangential electric field, at the surface of a mathematical cylinder that just encloses it, equal to the conjugate of the field that would be produced by the reflector currents if there were a theoretically perfect absorber on the axis. This optimum tangential field is worked out in the form
E_{0} +(\lambda/R)^{1/2}E_{1}+O(\lambda/R) , R
being the radius of the reflector and
\lambda
the wavelength. The results produced by typical feeds designed according to this prescription have been computed for arrays of dipoles spaced along the axis. Typical aperture efficiencies for the Arecibo dish are 90 percent at 100 MHz and within 1 percent of the optical limit at 600 MHz. The optical limit is not 100 percent, however, because of polarization mismatch. More than 98 percent of the power is concentrated onto the dish abbve 300 MHz. Results are available for 30 to 3000 MHz, 0 to
60\deg
scan angle, and various dipole arrangements. Waveguide and dipole feeds for receiving arbitrary polarization, and measurement techniques for designing and testing them, are described.