Scattering losses in a large luneberg lens due to random dielectric inhomogeneities

An approximate theoretical calculation is made of the scattering losses due to random inhomogeneities in a large Luneberg lens made of dielectric blocks. A simple model is used in which the average index of refraction of each block may differ slightly from the value called for by the lens design, and the index may vary linearly with position inside a given block. The losses are described by attributing an effective scattering loss tangent to the lens medium. Tables and curves are given to facilitate the computation of total scattering loss as a function of block size, mean-square deviation of average index, and mean-square index gradient within the blocks. Manufacturing processes for foam dielectric blocks are monitored by testing the blocks in various orientations in an oversize resonant cavity. An approximate relationship is derived between the results of cavity resonator measurements and the parameters of the theoretical model; but it is pointed out that the assumption of linear index variation across a single block can be quite unrealistic in practice. Numerical results derived from the present theory are most likely to be meaningful if the dimensions of the individual blocks are less than one wavelength.