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The authors demonstrate the method of generic curve series to obtain the profiles of dielectric antennas, with design conditions either for the specification of the aperture-amplitude distribution from a given source distribution, or for agreement with the Abbe sine condition. The method has already proved successful in the design of dual reflector antennas, and the extension to refractive media is shown to be straightforward. The method involves obtaining two equivalent expressions for a fundamental parameter from the usual optical equations and internal geometry of the lens, and obtaining agreement between them by a computational optimisation procedure using the series of curves. The parameter used is the internal segment of the ray within the lens. The method applies equally well to lenses with other a priori conditions such as afocal linear magnification or off-axis bifocality.