The physical optics of focused scatterers using source multipole expansions

A multipole-expansion technique is developed which permits the two-dimensional scattering integral for reflector antennas to be replaced by a finite sum of simple algebraic terms. The series, which accurately represents the radiated field over the main antenna beam and first few sidelobes, converges rapidly because the source dimensions are small. It is demonstrated that the reciprocity theorem is satisfied by the boresight physical-optics field of a paraboloid illuminated by a generalized linear electric current feed centered at the focus.