The extension of a spectroscopic ellipsometer that consists of a fixed polarizer, a rotating polarizer, a sample, and a fixed analyzer ~PRPSE! to generalized ellipsometry to determining the generalized ellipsometric angles and the optical functions of an anisotropic medium is reported. The PRPSE configuration eliminates the polarization sensitivity of the light source. A general numerical technique has been derived to characterize the optical properties of the anisotropic material without intermediate generalized ellipsometric angles. The proposed method is experimentally verified for uniaxial mercuric iodide. The ordinary and the extraordinary refractive and absorption indices, respectively, No 5 no 2 iko and Ne 5 ne 2 ike, can be extracted directly from the Fourier coefficients measured by the PRPSE on a HgI2 crystal face that contains the optical axis. The orientations of the optical axis with respect to the plane of incidence were also determined by direct analysis of the measured Fourier coefficients. Measurements were made of reflection across a spectral range of 1.5–4.13 eV at one angle of incidence ~F 5 70°! for several azimuths w of the optical axis with respect to the plane of incidence. The generalized ellipsometric angles were obtained from numerical inversion by changes of both polarizer and analyzer azimuth angles P and A.