  The Poincare Equivalence Theorem states that any optical element which
contains no absorbing components can be replaced by an equivalent optical model
which consists of one linear retarder and one rotator only, both of which are
uniquely determined. This has many useful applications in the field of Optics
of Polarized Light. In particular, it arises naturally in attempts to
reconstruct spatially varying refractive tensors or dielectric tensors from
measurements of the change of state of polarization of light beams passing
through the medium, a field which is known as Tensor Tomography. A special case
is Photoelasticity, where the internal stress of a transparent material may be
reconstructed from knowledge of the local optical tensors by using the
stress-optical laws. - We present a rigorous approach to the Poincare
Equivalence Theorem by explicitly proving a matrix decomposition theorem, from
which the Poincare Equivalence Theorem follows as a corollary. To make the
paper self-contained we supplement a brief account of the Jones matrix
formalism, at least as far as linear retarders and rotators are concerned. We
point out the connection between the parameters of the Poincare-equivalent
model to previously introduced notions of the Characteristic Parameters of an
optical model in the engineering literature. Finally, we briefly illustrate how
characteristic parameters and Poincare-equivalent models naturally arise in
Photoelasticity.
