  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 interferrometric calculations to optics in beams of varying
F/ number. We then apply the formalism to super-achromatic six crystal
retarders in converging beams under beam thermal loading in outdoor
environmental conditions for two of the worlds largest observatories: the 10m
Keck telescope and the Daniel K. Inouye Solar Telescope (DKIST). DKIST will
produce a 300 Watt 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 beams 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 (LRISp) 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.
