ABSTRACT
This chapter summarizes the main results on the geometric characterization of Mueller matrices, some of which have been obtained. Due to the power of graphic and visual codes for the interpretation and analysis of polarimetric measurements, the study of geometric representations of Mueller matrices constitutes a way to geometrize the polarization algebra, as well as to get better insight into the physical behavior of the measured sample. Geometric and visual representations can provide useful tools for the study and analysis of experimental Mueller matrices, with potential applications to several fields of significant practical interest, such as imaging of biological tissues, remote sensing, and scattering by turbid media. A natural geometric view of a Mueller matrix (M) is given by the corresponding Poincare sphere mapping, that is, by the specific way a given M maps the totally polarized states lying on the surface of the sphere.
