Calculation of Aperture Efficiency of Reflector Antenna with the Measured Far-field Function of its Feed in Ludwig’s Third Definition

Formulas for calculation of aperture efficiency of a primarily-focused parabolic reflector with a rotationally symmetric feed, or so-called Body-of-Revolution (BOR) feed, can be found in literature and many textbooks. Recently, many ultra-wideband (UWB) feeds have been developed for reflectors in radio telescopes, such as the square kilometer array (SKA) project. It has been noticed that all developed UWB feeds are of the non-BOR type. Therefore, it needs to clarify how to calculate the aperture efficiency of a parabolic reflector with the measured far-field function of its feed when the feed is a non-BOR antenna. The purpose of this paper is to derive and document the formulas for calculating aperture efficiency when the far-field function of the non-BOR feed is available by measurements under the Ludwig's third definition. One example of aperture efficiency calculation using the derived formulas based on measurement is presented in this paper.