As light passes through a optical system the reflections and refractions will in general change the polarization state of the light. If we assume that all of the materials in the thin film coatings and substrate are isotropic and homogeneous then calculating the amount of "instrumental" polarization is a relatively straight forward task. In the following sections we will present a of the steps required to perform a 'polarization ray trace' calculation for a single ray and monochromatic and hence polarized light. The thin film portion of the calculation is also shown. The reason for explicitly showing the thin film equations is that there are sign conventions imposed on the boundary value equations by the orientation and handedness of the various coordinate frames which are attached to the geometric rays. The attenuation of light through a optical system, is relatively simple, and requires at the very least a lens (average) reflectivity or transmissivity. Determining the polarization sensitivity of a optical system is still relatively straight forward requiring at least a knowledge of the behavior of the "s" and "p" components at each interface for the chief ray. Determining the thin film induced aberrations of a optical system are somewhat more demanding. Questions about the arithmetic sign of the phase factors and how this relates to the overall "OPD" of a ray are ubiquitous. Many rays are required to construct a wavefront. Thin film codes which modify the OPD's of rays are a requirement for this last mentioned computation. This requires a consistent scheme of coordinate frames and sign conventions and is probably the most demanding task of a polarization ray trace. Only the electric field will used in the discussion. This is not a restriction as the Stokes parameters are functions of the electric field. The following does not attempt to explain, but only to present all of the required concepts and formulas.
