Intrinsic Cross-Polarization Ratio of Dual-Linearly Polarized Antennas for Low-Frequency Radio Astronomy

This note discusses the intrinsic cross-polarization ratio (IXR) from an antenna engineering perspective in that we seek to identify an a priori (coordinate) system where IXR is well approximated by the raw cross-polarization numbers. We begin by establishing a special case where IXR is identical to the raw cross-polarization ratios for in-phase dual-linearly-polarized antennas when the Jones matrix is expressed using circular polarization bases. This insight allows physical interpretation of IXR which may be useful in antenna design and system calculations. In addition, we discuss comparisons between direct IXR calculations and circular polarization approximations for more realistic cases involving dual-polarized Murchison widefield array (MWA) bow-tie antennas.