Correcting for the ionosphere in the uv-plane

Abstract

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.