Scattering Losses in a Large Luneberg Lens Due to Random Dielectric Inhomogeneities

In recent years, large Luneberg lenses have been used as antennas for long-range radars.1 Such lenses have been built of cubical blocks of very low density polystyrene foam, loaded with varying amounts of aluminum slivers2 in order to approximate the desired variation of refractive index between the surface of the lens and the center. In theory each block is perfectly homogeneous and isotropic and has a specified permittivity; in practice, however, the blocks are not perfectly homogeneous or isotropic, and the average permittivity of a block generally differs more or less from the value called for by the designer. If the tolerances on the 679 092 T H E B E L L SYSTEM TECHNICAL JOURNAL, MARCH 19(34 blocks are too loose, excessive power will be lost from the lens by scattering from the "misfits"; in extreme cases, scattering may also lead to unacceptable antenna patterns. On the other hand, if the tolerances are too tight the yield of acceptable blocks by any reasonable manufacturing process will be reduced, and the cost of the lens correspondingly increased. Considerable importance attaches, therefore, to setting the proper tolerances. This paper treats the problem of scattering losses in a large Luneberg lens, due to random dielectric inhomogeneities, on the basis of a simple mathematical model which is described in Section I I . According to the present analysis, the effect of dielectric scattering can be described by attributing to the material of the lens an effective loss tangent given by (1) of Section I I .