The field of radiometry describes the fundamental radiative processes that are commonly involved in the operation of a passive imaging sensor. Scattering from surfaces is described in radiometry by the bidirectional reflectance distribution function (BRDF) defined by Nicodemus. As it is commonly defined, radiometry does not describe polarization effects in the radiative transfer processes. Vector scattering theories have attempted to describe polarized surface scattering with a 2 X 2 BRDF matrix. Polarimetry suggests that a 4 X 4 Mueller-like matrix is required to describe polarized surface scattering. In this paper, radiometric terms are redefined as polarized, vector quantities in a manner consistent with polarimetry. A full 4 X 4 BRDF matrix is derived from the scattering matrix. (Actually a 3 X 3 BRDF matrix with one row and column of complex values is adopted to simplify the equations and to facilitate relating the BRDF matrix to both the scattering cross section and the 2 X 2 BRDF matrix adopted in vector scattering theories.) A directional reflectance matrix and directional emittance vector are defined and their relationship is given. It is observed that the polarization character of surface reflectances and emittances are commonly not measured completely, and it is recommended that measurement programs be initiated to measure the full polarization character of common materials.