Antenna efficiency is one of the most important figures-of-merit of a radio telescope for observations especially at millimeter wavelengths or shorter wavelengths, even for a multibeam radio telescope. To analyze a system with a beam waveguide, a lossless antenna consisting of two apertures in series is considered in the frame of the scalar wave approximation. We found that the antenna efficiency can be evaluated with the field distribution over the second aperture, and that the antenna efficiency is factorized into three factors: efficiencies of beam coupling, transmission spillover, and reception spillover. The factorization is applicable to general aperture-type antennas with beam waveguides, and can relate the aperture efficiency to the pupil function. We numerically confirmed our factorization with an optical simulation. This evaluation enables us to manage the aberrations and is useful in design of multibeam radio telescopes.
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