Ionospheric Power-Spectrum Tomography in Radio Interferometry

TL;DR

This paper introduces a tomographic method to determine the three-dimensional power-spectrum of ionospheric electron-density fluctuations from radio interferometry data, improving calibration accuracy for wide-field, low-frequency observations.

Contribution

It derives an exact mathematical expression linking the 3D power-spectrum to observed scattered and incident intensity fields, extending phase-screen models to full 3D ionospheric structures.

Findings

The method accurately retrieves the 3D power-spectrum from radio data.

It shows the limitations of single phase-screen approximation for thick ionospheres.

Residual speckle may limit the dynamic range in long-exposure radio images.

Abstract

A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to first-order Born approximation and might be applicable to correct observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that not the ionospheric electron density distribution is the primary structure to model in interferometry, but its autocorrelation function or equivalent its power-spectrum. An exact mathematical expression is derived that provides the three dimensional power-spectrum of the ionospheric electron-density fluctuations directly from a rescaled scattered intensity field and an incident intensity field convolved with a complex unit phasor that depends on the w-term and is defined on the full sky pupil plane. In the limit of a small field of view, the method reduces to the single phase screen approximation. Tomographic self-calibration can become important in high-dynamic range observations at low radio frequencies with wide-field antenna interferometers, because a three-dimensional ionosphere causes a spatially varying convolution of the sky, whereas a single phase screen results in a spatially invariant convolution. A thick ionosphere can therefore not be approximated by a single phase screen without introducing errors in the calibration process. By applying a Radon projection and the Fourier projection-slice theorem, it is shown that the phase-screen approach in three dimensions is identical to the tomographic method. Finally we suggest that residual speckle can cause a diffuse intensity halo around sources, due to uncorrectable ionospheric phase fluctuations in the short integrations, which could pose a fundamental limit on the dynamic range in long-integration images.