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Luneberg-lens reflectors, which provide passive wideband and wide-angle radar-signature augmentation, have been widely used in small military target drones, decoys, and marine vessels. Due to the difficulty of fabricating inhomogeneous dielectrics with a continuously varying index, Luneberg lenses are usually constructed with multilayered step-index dielectrics. This paper presents a quantitative study of a practical design of a three-layer Luneberg-lens reflector for C- and X-band operations. Extensive wideband and wide-angle measurements were carried out for this lens with three different cap reflectors, as well as for the lens alone without any reflector. A comprehensive numerical analysis, using the finite-element method combined with boundary integral equations, was also conducted. This was done to support the measured data and to provide additional insight for a better understanding of the performance and the limitations of the Luneberg-lens reflector than could be achieved with the traditional ray-optics method. The effect of reflector size is discussed, and the limitation of three-layer design is demonstrated. It has also been shown that very accurate material parameters must be ascertained so as to achieve the level of accuracy commonly desired in the computational electromagnetic codes applied to inhomogeneous dielectrics. The excellent agreement between the numerical and measured data indicates that this full-wave Maxwell solver can be used to explore the design limits and optimize designs for this type of lens reflector.