Luneberg lens design: optimization using effective medium theories

A procedure for minimizing the weight of a Luneberg lens composed of a composite made from a low dielectric foam and a spherical pigment is presented. The spherical pigment is distributed radially to obtain the Luneberg distribution of the permittivity. The lens considered here is greater than 2 ft in diameter, and therefore minimization of weight is a priority. Effective medium theories are used with measured permittivities and densities of pigments and foams to derive a function which minimizes weight while maximizing the Luneberg electromagnetic design. A Maxwell-Garnet (1904) mixture theory is used to obtain closed-form solutions.<>