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Data products from high spectral resolution astronomical polarimeters are often limited by fringes. Fringes can skew derived magnetic field properties from spectropolarimetric data. Fringe removal algorithms can also corrupt the data if the fringes and object signals are too similar. For some narrow-band imaging polarimeters, fringes change the calibration retarder properties and dominate the calibration errors. Systems-level engineering tools for polarimetric instrumentation require accurate predictions of fringe amplitudes, periods for transmission, diattenuation, and retardance. The relevant instabilities caused by environmental, thermal, and optical properties can be modeled and mitigation tools developed. We create spectral polarization fringe amplitude and temporal instability predictions by applying the Berreman calculus and simple interferometric calculations to optics in beams of varying F/ number. We then apply the formalism to superachromatic six-crystal retarders in converging beams under beam thermal loading in outdoor environmental conditions for two of the world’s largest observatories: the 10-m Keck telescope and the Daniel K. Inouye Solar Telescope (DKIST). DKIST will produce a 300-W optical beam, which has imposed stringent requirements on the large diameter six-crystal retarders, dichroic beamsplitters, and internal optics. DKIST retarders are used in a converging beam with F/ ratios between 8 and 62. The fringe spectral periods, amplitudes, and thermal models of retarder behavior assisted DKIST optical designs and calibration plans with future application to many astronomical spectropolarimeters. The Low Resolution Imaging Spectrograph with polarimetry instrument at Keck also uses six-crystal retarders in a converging F / 13 beam in a Cassegrain focus exposed to summit environmental conditions providing observational verification of our predictions.
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