Mathematical Relationship of an Isotropic Point Source and the Spherically Distributed Antenna Array

This work investigates beam pattern behavior of an isotropic point source and a collection of sources distributed amongst a spherical volume. Pattern behavior is compared to the tapering of a plane wave expansion of spherical waves demonstrating self-adjoint characteristics. Beampatterns of atomic like orbitals and Zernike polynomials are provided as connections to common applications.