The Effect of Small Phase Errors Upon Transmission Between Confocal Apertures

The use of beam waveguide 1 systems for the transmission of information, 2 or for the transmission of power,3 necessitates the design of lenses (or cylindrical reflectors4) as focusing elements. In the design of these elements, it is desirable to estimate the degradation in performance caused by surface profile errors. Such degradation results in transmission loss and, in a communications system, will contribute to interference. Typically, the profile errors are associated with machining operations and, for lenses with circular symmetry, these errors are frequently circularly symmetric. The principal effect of the errors is to impart small, circularly symmetric phase perturbations to the field distribution adjacent to the lenses. The purpose of this paper is to calculate the reduction in transmission, caused by phase errors of this type, in a simple system comprising two coaxial, circular apertures as shown in Fig. 1. The field distributions on the apertures may represent the fields in the aperture planes of two antennas or the fields on adjacent lenses in a beam waveguide system. In the absence of phase errors the transmission between coaxial apertures has been extensively studied by Kay, 5 Borgiotti, 6 Heurtley, 7 and others, with the principal objective of determining that aperture 783