A fundamental figure of merit for radio polarimeters

Many modern radio applications, such as astronomy and remote sensing, require high-precision polarimetry. These ap- plications put exacting demands on radio polarimeters (antenna systemsthatcanmeasurethestateofpolarizationofradiosources), 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,isnotsuitableasapolarimetryFoMunlessitisgiveninanap- propriatecoordinatesystem.Thisisbecausealthoughthecross-po- larization ratio is relevant for raw, uncalibrated polarimetry, in general it is not relevant to the quality of the polarimetry after po- larimetric 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 quanti- fies 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 thenextendtheIXRconceptfromtheJonescalculustotheMueller calculus and also to interferometers, and we give numerical exam- ples of these parameters applied to the Parkes radio telescope, the Westerbork synthesis radio telescope, and the Effelsbergtelescope. Index Terms—Instrumentation, polarime