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This paper describes the application of Bethe's small-aperture theory and leaky-wave antenna theory to the design of planar arrays of rectangular waveguides radiating through small apertures arranged periodically in their broad walls. Such arrays can be designed to have any polarization, including circular, by suitable selection of the shape and orientation of the small apertures. These arrays have narrow beamwidths, and scan with frequency in a plane normal to the broad walls of the waveguides. A circularly polarized array at -band was designed, and a single-wavegnide section of it was built to test the practicality of the design.