Three-dimensional polarization ray tracing, retardance

The retardance associated with a three-by-three polarization ray tracing matrix is analyzed. The retardance of the polarization ray tracing matrix contains both a geometrical transformation and the polarization properties of diattenuation and retardance associated with a ray path through the optical and polarization elements. A method using parallel transport of transverse vectors is able to separate the geometrical transformation from the "physical" retardance, allowing the retardance to be calculated. A non-polarizing ray tracing matrix provides proper local coordinates to calculate the physical retardance without the geometrical transformation.