We report the development of a new ellipsometry technique which is especially well suited to the measurement of the dielectric constants of high reflectivity metals. Modulation methods are used to permit the measurement of a differential reflectance parameter which does not decrease in sensitivity in the high reflectivity limit as do the usual reflectance parameters measured with standard techniques. In addition the ellipsometer is faster than previous methods, being capable of recording the relevant data in a few minutes as the wavelength is swept continuously over a range of several thousand angstroms. The precision of the dielectric constants so measured is 1% in most cases. The polarization modulation technique, upon which the ellipsometer is based, is presented in detail, with emphasis on its wider applicability to any problem involving the study of dichroic phenomena.