A Fundamental Figure of Merit for Radio Polarimeters

Many modern radio applications, such as astronomy and remote sensing, require high-precision polarimetry. These applications put exacting demands on radio polarimeters (antenna systems that can measure the state of polarization of radio sources), and in order to assess their polarimetric performance, a figure of merit (FoM) would be desirable. Unfortunately, we find that the parameter commonly used for this purpose, the cross-polarization ratio, is not suitable as a polarimetry FoM unless it is given in an appropriate coordinate system. This is because although the cross-polarization ratio is relevant for raw, uncalibrated polarimetry, in general it is not relevant to the quality of the polarimetry after polarimetric calibration. However, a cross-polarization ratio can be constructed from invariants of the Jones matrix (the matrix that describes the polarimetric response of a polarimeter) that quantifies polarimetric performance even after calibration. We call this cross-polarization ratio the intrinsic cross-polarization ratio (IXR) and conclude that it is a fundamental FoM for polarimeters. We then extend the IXR concept from the Jones calculus to the Mueller calculus and also to interferometers, and we give numerical examples of these parameters applied to the Parkes radio telescope, the Westerbork synthesis radio telescope, and the Effelsberg telescope.