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

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.