  The separation of cosmological signal from astrophysical foregrounds is a
fundamental challenge for any effort to probe the evolution of neutral hydrogen
during the Cosmic Dawn and epoch of reionization (EoR) using the 21 cm
hyperfine transition. Foreground separation is made possible by their intrinsic
spectral smoothness, making them distinguishable from spectrally complex
cosmological signal even though they are ~5 orders of magnitude brighter.
Precisely calibrated radio interferometers are essential to maintaining the
smoothness and thus separability of the foregrounds. One powerful calibration
strategy is to use redundant measurements between pairs of antennas with the
same physical separation in order to solve for each antenna's spectral response
without reference to a sky model. This strategy is being employed by the
Hydrogen Epoch of Reionization Array (HERA), a large radio telescope in South
Africa that is now observing while being built out to 350 14-m dishes. However,
the deviations from perfect redundancy inherent in any real radio telescope
complicate the calibration problem. Using simulations of HERA, we show how
calibration with antenna-to-antenna variations in dish construction and
placement generally lead to spectral structure in otherwise smooth foregrounds
that significantly reduces the number of cosmological modes available to a 21
cm measurement. However, we also show that this effect can be largely
eliminated by a modified redundant-baseline calibration strategy that relies
predominantly on short baselines.
