ABSTRACT
Knowledge of an optical system’s retardance provides important information on the polarization dependence of the exiting wavefronts. This chapter develops an algorithm for the calculation of retardance, a subtle topic. Retardance is typically described as an optical path difference between two orthogonal polarization states. However, when a system has more than two interfering beams, other conceptual issues arise; issues which complicate measuring and interpreting the properties of birefringent films for displays.
It would be desirable, even expected, to have an algorithm that takes a polarization ray tracing matrix P as an input, along with the associated input and output propagation vectors, and returns the magnitude of the retardance and the fast and slow axes. The actual situation is not so easy since the calculation of retardance for a ray path through an optical system depends on the entire sequence of propagation vectors transiting the optical system.
When describing rays propagating through optical systems, the effects of coordinate system changes on refraction can masquerade as circular retardance. Similarly, local coordinate system changes on reflection can masquerade as a half wave of linear retardance. These two effects need to be calculated and corrected to obtain a correct retardance calculation. This chapter’s objectives are the following: (1) critically consider several different definitions of retardance with the objective of finding a sufficiently robust definition generally applicable for optical design, (2) explore the local coordinate transformation associated with parallel transport of transverse vectors along ray paths through optical systems, and (3) present an algorithm for the calculation of proper retardance in polarization ray tracing using the three-by-three polarization ray tracing calculus. This algorithm will separate the part of the polarization ray tracing matrix that describes proper retardance from the part that describes non-polarizing rotations, the geometrical transformation. The collection of geometrical transformations across a wavefront is the skew aberration, the subject of the next chapter.
