We describe a new imaging polarimeter that is based on a modified Sagnac interferometer and allows full polarimetric description of complex random electromagnetic beams from only two images as compared with the four images needed in conventional polarimetry. The procedure is analyzed in terms of the interference laws of Fresnel and Arago, and very good agreement with standard Stokes polarimetry is demonstrated. In certain cases the new technique provides the degree of polarization and the retardance from only one image.