IONOSPHERIC POWER-SPECTRUM TOMOGRAPHY IN RADIO INTERFEROMETRY

A tomographic method is described to quantify the three-dimensional power spectrum of the ionospheric electrondensity fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid for the first-order Born approximation and might be applicable in correcting observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that the ionospheric electron-density distribution is not the primary structure to model in interferometry, but rather its autocorrelation function or equivalently 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.