Diagram illustrating a typical polarization ray tracing interaction in reflection with the q-th surface in the optical system. The wave vector before the surface k_q−1 is incident on the surface with a linear polarization shown in purple. The angle of reflection is determined by the angle of incidence with respect to the surface normal η_q, which points into the surface to maintain a right-handed coordinate system. Next, the polarization state is transformed by the surfaces PRT matrix P_q and propagated along the existent wave vector k_q. Here P_q is a partial retarder, so the polarization state becomes elliptical.