Applying full polarization A-Projection to very wide field of view instruments: An imager for LOFAR

The required high sensitivities and large fields of view of the new generation of radio interferometers impose high dynamic ranges, e. g., similar to 1:10(6) to 1:10(8) for the Square Kilometre Array (SKA). The main problem for achieving these high ranges is the calibration and correction of direction dependent effects (DDE) that can affect the electro-magnetic field (antenna beams, ionosphere, Faraday rotation, etc.). It has already been shown that the A-Projection is a fast and accurate algorithm that can potentially correct for any given DDE in the imaging step. With its very wide field of view, low operating frequency (similar to 30-250 MHz), long baselines, and complex station-dependent beam patterns, the LOw Frequency ARray (LOFAR) is certainly the most complex SKA pathfinder instrument. In this paper we present a few implementations of the A-Projection in LOFAR which can deal nondiagonal Mueller matrices. The algorithm is designed to correct for all DDE, including individual antennas, projection of the dipoles on the sky, beam forming, and ionospheric effects. We describe a few important algorithmic optimizations related to LOFAR's architecture that allowed us to build a fast imager. Based on simulated datasets we show that A-Projection can dramatically improve the dynamic range for both phased array beams and ionospheric effects. However, certain problems associated with the calibration of DDE remain (especially ionospheric effects), and the effect of the algorithm on real LOFAR survey data still needs to be demonstrated. We will be able to use this algorithm to construct the deepest extragalactic surveys, comprising hundreds of days of integration.