We have applied Mueller matrix ellipsometry to assess the change in the state of polarization of a light beam that has double passed the ocular media and is scattered at the fundus of the human eye in vivo. At several positions in the pupil plane, which together cover the area of the dilated pupil, Mueller matrices are assessed. From them the magnitude of the retardation and the orientation of the eigenvector are calculated. The properties of the retardation process are surveyed by measuring the retardation along a horizontal meridian as a function of wavelength, density of visual pigment, and location of retinal fixation. Furthermore, photographs are taken from the polarization patterns on the iris with circularly polarized light. We posit that the cornea behaves as a biaxial crystal with its fastest principal axis normal to its surface and its slowest nasally downward. The retardation of light by a model eye with such a cornea is calculated, and the results are compared with the data.