Simple estimation of all-sky, direction-dependent Jones matrix of primary beams of radio interferometers

The dual-polarized primary beams of imaging radio telescopes are generally not perfectly orthogonal nor have the same gain, the resulting polarimetric images are distorted, in other words, they exhibit instrumental polarization. This is often modeled in radio astronomy using a Jones matrix formalism, and the standard practice is to calibrate (i.e. determine the Jones matrices) using known point source, polarized calibrators. Using point source calibrators on the other hand can be difficult and is ineffective for wide fields-of-view (FoV). Often however, a large portion of the FoV of imaging radio telescopes consists of unpolarized background. In this paper I estimate Jones matrices over the FoV by assuming that most of the background image is unpolarized and then taking the square-root of the brightness matrices. Results from LOFAR LBA data are shown and are consistent with expectation. The usefulness of this particular method, compared to using polarized point source calibrators, is its simplicity and the fact that it can cover most of the FoV.