An Optimal Procedure for the Design of Discrete Constrained Lens Antennas with Minimized Optical Aberrations. Part I: Two-Dimensional Architectures

Abstract

Despite to the significant literature available on the design and applications of two-dimensional constrained lens antennas, and in particular on the Rotman–Turner lens, a rigorous study focused on the minimization of optical aberrations does not seem to be available. A general procedure for the design of two-dimensional bootlace lens antennas with a flat front profile is proposed in this paper. For the 3-foci lens, the best performance is achievable when, in addition to the three nominal focal points, two additional symmetric quasi foci are present. For the 4-foci lens the best performance is obtained when the presence of one additional quasi focus on the lens axis is guaranteed. Both the 3- and 4-foci lenses, when optimized, converge to the same configuration which exhibits aberrations following a Chebyshev-like behavior and guarantees quasi 5 foci. The optimized lens architecture is such that, for every scanning angle, the aberrations in the two extreme points are the most significant and exhibit opposite values. Any variation from this optimal condition implies increased aberrations. Although a 5-foci lens with flat front profile cannot be derived, one quasi-5-foci lens is derived asymptotically starting from two completely different lens architectures. A maximization of the number of foci combined with a rigorous derivation of the focal curve turned to be the key driver to identify an optimal two-dimensional bootlace lens. The quasi 5-foci lens presented can be considered the optimum Rotman–Turner lens in terms of optical aberrations allowing to reduce the optical aberrations by about one order of magnitude as compared to the best results available in the literature.