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.