By applying appropriate phase weights, an array of omnidirectional ele
ments on a spherical shell can be made to scan the main beam over 4 pi
steradians. Although the general analytic solution for the radiation
pattern appears to be intractable, the result when the elements are un
iformly weighted in amplitude is a sine function. This result is appli
ed to derive the radiation pattern from a fully or partially filled sp
herical array with uniform amplitude weighting throughout. The establi
shed optimal aperture distributions used with linear arrays are adapte
d to obtain volume distributions to apply to the elementary shells in
a fully filled sphere to obtain the corresponding radiation pattern ch
aracteristics.