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Design equations are presented for three-dimensional (volumetric) multiple-beamforming lenses for planar arrays. The minimum lens size for given array dimensions is derived. Theoretical multiple-beam patterns are predicted for a particular lens configuration, using flared waveguide ports, feeding a 37-element planar array. This lens has been constructed and tested, operating over the frequency band 8Â¿12 GHz, and the results show good agreement with theory in most respects. Mutual coupling between lens ports has a significant influence on the lens insertion loss.