Direction-dependent Correction Research Articles

Direction-dependent Corrections in Polarimetric Radio Imaging. III. A-to-Z Solver—Modeling the Full Jones Antenna Aperture Illumination Pattern

Abstract In this third paper of a series describing direction-dependent corrections for polarimetric radio imaging, we present the the A-to-Z solver methodology to model the full Jones antenna aperture illumination pattern (AIP) using Zernike polynomials. In order to achieve accurate, thermal noise-limited imaging with modern radio interferometers, it is necessary to correct for the instrumental effects of the antenna primary beam (PB) as a function of time, frequency, and polarization. The algorithm employs the orthonormal, circular Zernike polynomial basis to model the full Jones AIP response, which is obtained by a Fourier transform of corresponding antenna holography measurements. These full Jones models are then used to reconstruct the full Mueller AIP response of an antenna, in principle accounting for all the off-axis frequency-dependent leakage effects of the PB. The A-to-Z solver is general enough to accommodate any interferometer for which holographic measurements exist, and we have successfully modeled the AIP of the VLA, MeerKAT, and ALMA as a demonstration of its versatility. We show that our models capture the PB morphology to high accuracy within the first two side lobes, and show the viability of full Mueller gridding and deconvolution for any telescope given high-quality holographic measurements.

Direction-dependent Corrections in Polarimetric Radio Imaging. II. A-solver Methodology: A Low-order Solver for the A-term of the A-projection Algorithm

Abstract The effects of the antenna far-field power pattern limits the imaging performance of modern wide-bandwidth, high-sensitivity interferometric radio telescopes. Given a model for the aperture illumination pattern (AIP) of the antenna, referred to as the A-term, the wide-band (WB) A-Projection algorithm corrects for the effects of its time, frequency, and polarization structure. The level to which this correction is possible depends on how accurately the A-term represents the true AIP. In this paper, we describe the A-Solver methodology that combines physical modeling with optimization to holographic measurements to build an accurate model for the AIP. Using a parametrized ray-tracing code as the predictor, we solve for the frequency dependence of the antenna optics and show that the resulting low-order model for the Karl G. Jansky Very Large Array antenna captures the dominant frequency-dependent terms. The A-Solver methodology described here is generic and can be adapted for other types of antennas as well. The parameterization is based on the physical characteristics of the antenna structure and optics and is therefore arguably a compact representation (minimized degrees of freedom) of the frequency-dependent structure of the antenna A-term. In this paper, we also show that the parameters derived from A-Solver methodology are expected to improve sensitivity and imaging performance out to the first side-lobe of the antenna.

Direction-dependent Corrections in Polarimetric Radio Imaging. I. Characterizing the Effects of the Primary Beam on Full-Stokes Imaging

Abstract Next generation radio telescope arrays are being designed and commissioned to accurately measure polarized intensity and rotation measures (RMs) across the entire sky through deep, wide-field radio interferometric surveys. Radio interferometer dish antenna arrays are affected by direction-dependent (DD) gains due to both instrumental and atmospheric effects. In this paper, we demonstrate the effect of DD errors of the parabolic dish antenna array on the measured polarized intensities of radio sources in interferometric images. We characterize the extent of polarimetric image degradation due to the DD gains through wide-band VLA simulations of representative point-source simulations of the radio sky at L band (1–2 GHz). We show that at the 0.5 gain level of the primary beam there is significant flux leakage from Stokes I to Q, U amounting to 10% of the total intensity. We further demonstrate that while the instrumental response averages down for observations over large parallactic angle intervals, full-polarization DD correction is required to remove the effects of DD leakage. We also explore the effect of the DD beam on the RM signals and show that while the instrumental effect is primarily centered around 0 rad-m−2, the effect is significant over a broad range of RM requiring full polarization DD correction to accurately reconstruct the RM synthesis signal.

DIRECTION-DEPENDENT POLARIZED PRIMARY BEAMS IN WIDE-FIELD SYNTHESIS IMAGING

The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionization experiments. These experiments seek to detect weak signatures from redshifted 21 cm emission in deep residual datasets, after suppression and subtraction of foreground emission. Many subtraction algorithms benefit from low side-lobes and polarization leakage at the outset, and both of these are intimately linked to how the polarized primary beams are handled. Building on previous contributions from a number of authors, in which direction-dependent corrections are incorporated into visibility gridding kernels, we consider the special characteristics of arrays of fixed dipole antennas operating around 100–200 MHz, looking towards instruments such as the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Arrays (HERA). We show that integrating snapshots in the image domain can help to produce compact gridding kernels, and also reduce the need to make complicated polarized leakage corrections during gridding. We also investigate an alternative form for the gridding kernel that can suppress variations in the direction-dependent weighting of gridded visibilities by 10 s of dB, while maintaining compact support.