The distribution of cross polarization across the main beam and near sidelobes of a reflector antenna is calculated. Results are expressed in terms relevant to imaging in radio astronomy, using Stokes parameters, as plots of instrumental polarization Q/I, U/I, and V/I, showing conversion of total intensity of a signal which is unpolarized into apparent linear and circular polarization. The calculations use GRASP8, software that is based on physical optics and the physical theory of diffraction. For purposes of calculation, the symmetrical paraboloidal reflector (diameter ~40 wavelengths) is fed at the prime focus with a linearly polarized signal. Computed radiation patterns at a number of feed orientations are averaged to establish the antenna response to an unpolarized radio astronomy signal. The results of the computations are consistent with measurements of instrumental polarization of the Dominion Radio Astrophysical Observatory Synthesis Telescope at 1420 MHz made using unpolarized radio sources. For this telescope, the dominant source of instrumental polarization across the field is the cross polarization of the feed. The next most significant effect is scattering by the feed struts; both three-strut and four-strut configurations are examined. Struts affect performance in linear polarization but also introduce some instrumental circular polarization. The contribution to instrumental polarization from the reflector itself is comparatively small. Roughness of the reflector surface has relatively little effect in the main beam in Q and U but introduces V and also randomizes the polarization of the sidelobes. In all cases considered, the computations show that the first and subsequent sidelobes are highly polarized, with levels of instrumental polarization up to 50%.