Optimization of aperture distributions for difference patterns

A design method previously developed to give distributions with a minimal edge brightening for sum patterns with arbitrary sidelobe topography is shown to be applicable to difference patterns as well. The method is based on obtaining some null-filling in the desired pattern that provides a multiplicity of solutions, some of which may be smoother than that corresponding to the pattern with deep nulls. The improvement in the aperture distributions, for linear and planar array synthesis, is found to be very good with the resulting loss in directivity being small.