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This paper describes the analysis and design of a class of antennas which can radiate and receive constant-shape pencil beams with either circular sense, any linear or elliptical polarization by a simple adjustment in the feed circuit. Such radiators are called arbitrarily polarized antennas. The apertures described are located on upper plates of radial waveguides and are composed of annular slots, with each annulus consisting of a discrete number of crossed slots. The annular slots are positioned so that each arm of the crossed slots can couple by a constant factor with the radial or circumferential currents flowing over the aperture plate to produce a common instantaneous direction for the electric field in each slot pair Both standing-wave and traveling-wave array types are employed. The standing-wave array requires only one radial waveguide mode for its operation. The traveling-wave array requires two modes and results in greater bandwidth and greater freedom in arraying many annuli. The methods used to excite the various radial waveguide modes are discussed; theoretical and experimental radiation patterns at band are compared.