Polarization Modeling and Predictions for DKIST Part 2: Application of the Berreman Calculus to Spectral Polarization Fringes of Beamsplitters and Crystal Retarders

We outline polarization fringe predictions derived from a new application of the Berreman calculus for the Daniel K. Inouye Solar Telescope (DKIST) retarder optics. The DKIST retarder baseline design used 6 crystals, single-layer anti-reflection coatings, thick cover windows and oil between all optical interfaces. This new tool estimates polarization fringes and optic Mueller matrices as functions of all optical design choices. The amplitude and period of polarized fringes under design changes, manufacturing errors, tolerances and several physical factors can now be estimated. This tool compares well with observations of fringes for data collected with the SPINOR spectropolarimeter at the Dunn Solar Telescope using bi-crystalline achromatic retarders as well as laboratory tests. With this new tool, we show impacts of design decisions on polarization fringes as impacted by anti-reflection coatings, oil refractive indices, cover window presence and part thicknesses. This tool helped DKIST decide to remove retarder cover windows and also recommends reconsideration of coating strategies for DKIST. We anticipate this tool to be essential in designing future retarders for mitigation of polarization and intensity fringe errors in other high spectral resolution astronomical systems.