Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without
  Adding Spectral Structure
  21 cm cosmology is a promising new probe of the evolution of visible matter
in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch
of Reionization. However, in order to separate the 21 cm signal from bright
astrophysical foregrounds, we need an exquisite understanding of our telescopes
so as to avoid adding spectral structure to spectrally-smooth foregrounds. One
powerful calibration method relies on repeated simultaneous measurements of the
same interferometric baseline to solve for the sky signal and for instrumental
parameters simultaneously. However, certain degrees of freedom are not
constrained by asserting internal consistency between redundant measurements.
In this paper, we review the origin of these "degeneracies" of
redundant-baseline calibration and demonstrate how they can source unwanted
spectral structure in our measurement and show how to eliminate that
additional, artificial structure. We also generalize redundant calibration to
dual-polarization instruments, derive the degeneracy structure, and explore the
unique challenges to calibration and preserving spectral smoothness presented
by a polarized measurement.
