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In this paper, we investigate whether and how one can synthesize given far field patterns by acting on the dielectric profile of a lens antenna. In particular, an approach to design a radiating system consisting of a variable dielectric profile and a single or a low number of feeds is proposed and discussed. To properly take into account physical and practical feasibility issues, the proposed method splits the problem into two steps. The first one is aimed to fix design goals (i.e., the nominal field), in such a way to avoid super-directive or physically unfeasible antennas and properly exploits known properties of electromagnetic fields radiated by finite extent sources. The second step, dealing with the dielectric profile synthesis, is based on suitable modifications of inverse scattering techniques and can take into account constraints on the spatial behavior as well as of dielectric characteristics of the profile to be synthesized. To show the interest of the subject, as well as effectiveness of the proposed approach, the synthesis of new dielectric antennas, such as a high directivity source and a lens radiating a steerable degradation-free Chebyshev pattern, is considered in the two dimensional scalar case.