The optimum radiation of a lens antenna with an array feed of

elements is desired, which will exhibit maximum gain in a number (

) of specified directions and nulls in other (

) specified directions. This optimum is not derived; however, a condition for the optimum is shown to be some superposition of just (

) individual radiation patterns where each individual pattern is obtained by a separate excitation set of all

feed elements such that the gain is maximized in each of the (

) directions. (The feed array excitation set for each of the (

) maximum gain individual patterns is derived.) Thus the number of unknown feed excitation coefficients is reduced from

to (

).