Spherical shell and volume arrays

By applying appropriate phase weights, an array of omnidirectional elements on a spherical shell can be made to scan the main beam over 4π steradians. Although the general analytic solution for the radiation pattern appears to be intractable, the result when the elements are uniformly weighted in amplitude is a sinc function. This result is applied to derive the radiation pattern from a fully or partially filled spherical array with uniform amplitude weighting throughout. The established optimal aperture distributions used with linear arrays are adapted to obtain volume distributions to apply to the elementary shells in a fully filled sphere to obtain the corresponding radiation pattern characteristics