Focusing Nonparabolic Mirrors by Using Phase‐Corrected Multiple‐Beam Sources

Abstract

The author describes and analyzes a method for correcting the aberration of nonparabolic mirrors by using a phase-corrected multiple-beam source consisting of an array of radiating elements fed through a Butler matrix. This source, which is identical to a phase-modulated point source, is shown to be able to correct any mirror profile, the only limitation being the dimension of the source. The case of a plane mirror is examined first. An experimental mockup that uses an offset, illuminated plane mirror is measured. This mockup shows clear focusing of the mirror and magnification of the directivity of the source. The case of a mirror of circular profile is then analyzed theoretically, and the possibilities of correction as a function of the geometrical parameters are computed, taking into account the accepted phase error and the obstruction ratio obtained.