The numerical research and optimizing the characteristics of antennas based of double-layer spherical dielectric lenses, taking into account aberration effects, lens refelections, dielectric losses, radiator directivity diagrams and transition layers are carried out. As an optimization criterion, the maximum value of amplifying ratio of the antenna is used. The maximum possible antenna characteristics are determined. The antenna characteristics based on double–layer homogenous sphere and Luneberg lens are compared.