A new numerical method, Fourier-Bessel series techniques, has been developed to investigate the far-field pattern and focal region distribution of reflector antennas under wide-angle scanning. In this Fourier-Bessel series technique, the current on the reflector surface is first expanded in terms of elementary sinusoidal functions via the well established fast Fourier transform (FFT) algorithm and the surface integration involved in physical optics integration is then carried out analytically. The derivation of Fourier-Bessel series and its convergence as applied to parabolic reflectors are described. The secondary patterns and focal region distributions of a parabolic reflector with

and scanning up to 48 beamwidths are presented.