A fast algorithm for the computation of focal fields of reflector antennas for a range of incidence angles and frequencies is proposed. The algorithm is based on the physical optics approximation. It uses a hierarchical domain decomposition of the reflector surface. For the smallest subdomains the received fields are computed over a coarse grid of angles, frequencies, and observation points. The fields for all incidence angles, frequencies, and focal plane points are obtained by a multilevel aggregation of the fields received by neighboring subdomains while employing interpolation and phase correction.