Estimating Polarization Purity With Noise

We formulate a problem of estimating and monitoring mismatch (unwanted departure from orthogonality) of two ostensibly orthogonal polarization channels in a fully polarimetric general device such as a polarimetric weather radar. A statistical approach is proposed by using thermal noise or, more generally, a 'polarimetric noise' class of sources. The suitable noise class of distributions is shown to be rooted in the complex multivariate Gaussian probability density function (pdf), the latter possessing a uniform pdf on the Poincare sphere (PS), with a probability measure given by a fractional surface area. To that end, we develop a parameter to estimate polarization purity. By relating an inner (dot) product of noisy electric fields to their cross-correlation coefficient, we arrive at a simple relation between the ellipticity delta -{epsilon } and tilt delta -{tau } mismatches and the measured complex voltage cross-correlation coefficient rho : rho approx mp cos (2epsilon)delta -{tau } pm idelta -{epsilon }. Our results are confirmed by Monte Carlo simulations. Thermal noise microwave data collected by the S-band radar of the National Center for Atmospheric Research (NCAR) during solar calibration scans is used to set bounds on delta -{epsilon } and delta -{tau } , thereby characterizing polarization purity.