  We show that, under the right conditions, one can make highly accurate
polarization-based measurements without knowing the absolute polarization state
of the probing light field. It is shown that light, passed through a randomly
varying birefringent material has a well-defined orbit on the Poincare sphere,
which we term a generalized polarization state, that is preserved. Changes to
the generalized polarization state can then be used in place of the absolute
polarization states that make up the generalized state, to measure the change
in polarization due to a sample under investigation. We illustrate the
usefulness of this analysis approach by demonstrating fiber-based ellipsometry,
where the polarization state of the probe light is unknown, and, yet, the
ellipsometric angles of the investigated sample ($\Psi$ and $\Delta$) are
obtained with an accuracy comparable to that of conventional ellipsometry
instruments by measuring changes to the generalized polarization state.
