Differential geometry of normalized Stokes vector trajectories in anisotropic media.

Trajectory of the normalized Stokes vector on the Poincaré sphere corresponding to light propagation in anisotropic tissues with birefringence and biattenuance is derived. Analytic expressions are determined from the Serret-Frenet formulas and derivatives of arc length for five quantities including the tangent, normal, and binormal vectors with curvature and torsion. Depth variation of curvature and torsion of normalized Stokes vector trajectories corresponding to light propagating in rodent tail tendon are given. Use of analytic expressions for depth variation of curvature and torsion of the normalized Stokes vector trajectories on the Poincaré sphere is discussed for analysis of polarization-sensitive optical coherence tomography data recorded from anisotropic biological tissues with birefringence and biattenuance.