Taking into account the radiation pattern of a practical feed for a Luneberg lens

A method of taking into account the real feed radiation pattern for a Luneberg lens is proposed. According to this, the field of a feed with the given radiation pattern is expanded into series in spherical harmonics. Using this approach, it is possible to introduce the radiation patterns of real feeds into strict electrodynamic solution for a Luneberg lens, thus significantly refining a mathematical model of the antenna.