  Complete polarimeters deliver the full polarization transfer matrix of a
medium that relates input polarization states to output polarization states. In
order to interpret the Mueller matrix of a luminescent medium at the emission
frequency, accountings are required for polarization transformations of the
medium at the excitation frequency, the light scattering event, and the
polarization transformations at the emission frequency. A general framework for
this kind of analysis is presented herein. The fluorescence Mueller matrix is
expressed as a product of Mueller matrices of the medium at the excitation and
emission frequencies and a scattering matrix, integrated over path length. The
Stokes vector for the incident light, evolving according to the Mueller matrix
of the medium at the excitation frequency, is multiplied by the scattering
matrix to give a Stokes vector of the emitted light along the propagation
direction. The scattering matrix is derived from an incoherent orientation
ensemble average over a phenomenological scattering tensor that embodies
intrinsic molecular scattering proprieties, and dynamical processes that occur
during the excited state. The general framework is evaluated for three
anisotropic materials carrying luminescent dye molecules including the
following: a chiral fluid, a stretched polymer film, and a chiral, biaxial
crystal. In the latter case, the most complex, the Mueller matrix was collected
in conoscopic illumination and the fluorescence Mueller matrix, mapped in
k-space, was fully simulated by the strategy outlined above. Luminescence
spectroscopy has typically stood apart from the developments in polarimetry of
the past two generations. This need not be indefinite.
