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( varepsilon;) and tilt delta(tau) mismatches and the measured complex voltage cross-correlation coefficient rho : rho approximate to -/+ cos(2 varepsilon;)delta(tau)+/- i delta( varepsilon;) . 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( varepsilon;) and delta(tau) , thereby characterizing polarization purity.