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.
Highlights
Discrete lens antennas are known as bootlace lenses, constrained lenses, or discretized array lenses [1]
The success of the two-dimensional lenses is justified by their design simplicity, their modularity and scalability and other properties they share with three-dimensional discrete lenses
The main benefits associated with this type of discrete lens BFN are associated with the simple implementation in Printed Circuit Board Technology (PCB), the excellent scanning capabilities, the fact that the front aperture is completely flat making the interfaces with other devices and/or antennas easy
Summary
Discrete lens antennas are known as bootlace lenses, constrained lenses, or discretized array lenses [1]. A rigorous and generalized procedure to design two-dimensional constrained discrete lens antennas with a flat front profile is proposed here. Clapp devised a means to use four or six R-2R lenses to feed a full 360◦ aperture, but the hardware design is further complicated by several hybrids for each beam [11] In our opinion, it is the curved profile of the front lens in the R-2R configuration that limits its applicability and its compatibility and integration with other components (like a second block of two-dimensional lenses orthogonal to the first [12,13]). In the paper the dimensions of the radiating elements constituting the focal feeding array, the back array and the front array are never indicated This point does not represent a limitation at all.
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