Direction Dependent Corrections in Polarimetric Radio Imaging I : Characterizing the effects of the primary beam on full Stokes imaging

Next generation radio telescope arrays are being designed and commissioned to accurately measure polarized intensity and rotation measures 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 for 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(1-2GHz). We show that at the 0.5 gain level of the primary beam (PB) 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 Rotation Measure(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 RM synthesis signal.