On discretizing continuous aperture distributions

A method for applying continuous-aperture design results to discrete antenna arrays is described. Instead of sampling the continuous aperture distribution, one requires that the pattern zeroes found in the continuous case also occur in the starting pattern for the discrete case. If the resulting pattern does not meet the design goal, a perturbation procedure is applied to the discrete distribution in order to bring the final pattern within specification. The approach is illustrated by two examples: (1) a 20-dB Taylor pattern, modified so that the innermost three sidelobes on one side of the main beam are down 30 dB and (2) a pattern in which the innermost seven sidelobes on one side of the main beam are at -25 dB, while on the other side they cascade in 5-dB steps from -45 dB next to the main beam to -15 dB for the seventh sidelobe.