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A one-parameter circular aperture distribution is developed which provides an optimum compromise between narrow beamwidth, low sidelobes, and low aperture . The pattern is a modified , analogous to the Taylor one-parameter modified sin line source distribution. Sidelobe envelope taper is essentially that of a uniformly excited circular aperture; hence the aperture is low . The aperture distribution which is rotationally symmetric is given by a modified Bessel function of zero order. Like all high efficiency distributions, it has a pedestal. All antenna quantities, sidelobe ratio, beamwidth, aperture efficiency, and edge taper, are uniquely related to the parameter . A table of these quantities is given for sidelobe ratios up to 50 dB. A typical pattern and several distributions are graphed. This new distribution allows tradeoff studies to be made against any design quantity, with all other quantities determined through the one-parameter.