A method for synthesis of optimum directional patterns from nonplanar apertures

The scalar radiation problem is considered for sources lying on a surface of arbitrary shape. An optimum directional pattern is specified and the source distribution which gives rise to the optimum pattern is determined in terms of the Green's function for the surface. The optimum source distribution is found to be proportional to the complex conjugate of the Green's function evaluated at the beam pointing coordinates and to lie in a region enclosed by an equimagnitude curve of this function, Examples are included for sources on planes and spheres.