By assuming that a linearly polarized plane wave was incident obliquely onto a small F number lens, ray tracing and Stratton Chu diffraction formula were used to calculate the vectorial diffracted field in the focal space of the lens. Phase distribution of the field over the exit surface of the lens, which determined the pattern of the diffracted field, was illustrated. The power distributions of the diffracted field in the focal plane of a hyperbolic lens were calculated for different incident angles, which agreed well with the experiments. The vectorial characteristics of the diffracted field were examined. Calculation and experiments were carried out in millimeter wavelength range.