Ionospheric Power-Spectrum Tomography in Radio Interferometry

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.

8 pages; Accepted for publication in ApJ

References in corpus (3)

• Ionospheric Calibration of Low Frequency Radio Interferometric Observations using the Peeling Scheme: I. Method Description and First Results
• A generalised Measurement Equation and van Cittert-Zernike theorem for wide-field radio astronomical interferometry
• Probing Fine-Scale Ionospheric Structure with the Very Large Array Radio Telescope

Cited by in corpus (21)

• Reionization and the Cosmic Dawn with the Square Kilometre Array
• Improved upper limits on the 21-cm signal power spectrum of neutral hydrogen at $\mathbf{z}\approx 9.1$ from LOFAR
• Initial deep LOFAR observations of Epoch of Reionization windows: I. The North Celestial Pole
• Probing Ionospheric Structures using the LOFAR radio telescope
• Statistical 21-cm Signal Separation via Gaussian Process Regression Analysis
• Systematic biases in low frequency radio interferometric data due to calibration: the LOFAR EoR case
• Scintillation noise in widefield radio interferometry
• The AARTFAAC Cosmic Explorer: observations of the 21-cm power spectrum in the EDGES absorption trough
• Wide-field LOFAR-LBA power-spectra analyses: Impact of calibration, polarization leakage and ionosphere
• Foreground modelling via Gaussian process regression: an application to HERA data
• Deeper multi-redshift upper limits on the Epoch of Reionization 21-cm signal power spectrum from LOFAR between z=8.3 and z=10.1
• Quantifying ionospheric effects on time-domain astrophysics with the Murchison Widefield Array
• Statistical analysis of the causes of excess variance in the 21 cm signal power spectra obtained with the Low-Frequency Array
• A probabilistic approach to direction-dependent ionospheric calibration
• Ionospheric contributions to the excess power in high-redshift 21-cm power-spectrum observations with LOFAR
• First upper limits on the 21-cm signal power spectrum of neutral hydrogen at $z=9.16$ from the LOFAR 3C196 field
• A new angle for probing field-aligned irregularities with the Murchison Widefield Array
• Robust direction-dependent gain-calibration of beam-modelling errors far from the target field
• Simulations of ionospheric refraction on radio interferometric data
• The impact of lunar topography on the 21-cm power spectrum for grid-based arrays : Insights for the Dark-ages EXplorer (DEX)
• Robust Foregrounds Removal for 21-cm Experiments