Correcting for the ionosphere in the uv-plane

TL;DR

This paper explores a method to correct ionospheric effects directly in the uv-plane in radio astronomy, aiming to reduce computational load by analyzing mathematical formulations, expansions, and potential efficiency techniques.

Contribution

It introduces a novel approach to ionospheric correction in the uv-plane, including mathematical analysis, expansion methods, and computational efficiency strategies.

Findings

Analytic solutions are limited to specific ionospheric perturbation expansions.

Optimal Taylor expansion order is identified for sinusoidal perturbations.

Proposed techniques offer potential computational savings with trade-offs.

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.