Correcting for the ionosphere in the uv-plane
  In radio astronomy, the correlator measures intensity in visibility space. In
addition, the EoR power spectrum measured by an experiment such as the MWA is
constructed in visibility space. Thus, correcting for the ionosphere in the
uv-plane instead of real space could potentially save computation. In this
paper, we study this technique. The mathematical formula for obtaining the
unperturbed data from the ionospherically reflected data is non-local in the
uv-plane. Moreover, an analytic solution for the unperturbed intensity may only
be obtained for a limited number of expansions of the ionospheric
perturbations. We numerically study one of these expansions (with perturbations
as sinusoidal modes). Obtaining an analytic solution for this expansion
required a Taylor expansion, and we investigate the optimal order of this
expansion. We also propose a number of potential computation saving techniques,
and evaluate their pros and cons.
