The design of rounded-edge optical waveguide lenses is presented. The lenses constructed by this method are aberration-free, rotationally symmetric geodesic lenses, where the radius and the focal length are arbitrarily given initial parameters. The rounding section of these lenses is a part of the lens; that is, without the rounding, the lens would not be aberration free. The design involves conversion of uniform refractive index rounding sections of depression lenses into outer annuli of generalized Luneberg lenses. The inner part of each generalized Luneberg lens is constructed with a technique called the annulus technique. Finally, these generalized Luneberg lenses are converted into uniform index depression lenses. The profiles of lenses so constructed are at least one-time continuously differentiable.
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