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Time series of thermal emissions from water vapor and air molecules at ≈2.8 GHz, collected by the National Center for Atmospheric Research’s (NCAR) S-band polarimetric radar S-Pol are examined for polarization probability distributions. A nearly uniform distribution of states on the Poincaré sphere surface is found. This uniformity is consistent with the four-dimensional circular Gaussian distribution of electric fields (pairs of in-phase and quadrature components for two orthogonal directions) for unpolarized radiation. Analysis of experimental data and the derived sampling distribution of the degree of polarization of the finite time series both yield a mean of about 0.02, within bounds of sampling variability of unpolarized Gaussian-distributed radiation. Weak inhomogeneity of polarization states on the Poincaré sphere detected in the experimental data is within the error bounds of the radar receiver. 

We consider the question of monitoring polarization purity, that is, measuring deviations from orthogonalityδ_τandδ_ϵof an ostensibly orthogonal polarization basis with a reference channel of ellipticityϵand tiltτ. A simple result was recently derived for a phase-sensitive receiver observing unpolarized radiation [IEEE Trans. Geosci. Remote Sens.62,2003610(2024)10.1109/TGRS.2024.3380531]: withρ⁽¹⁾denoting the Pearson complex correlation coefficient between channelcomplex fields, it states that ∓cos⁡(2ϵ)δ_τ±iδ_ϵ≈ρ⁽¹⁾whenδ_τ,ϵ≪1. However, phase-sensitive (in-phase and quadrature) data are seldom available at optical frequencies. To that end, here we generalize the result by deriving a new equation for the polarization “alignment” error:cos²(2ϵ)δ_τ²+δ_ϵ²≈ρ⁽²⁾, whereρ⁽²⁾is the intensity cross-correlation coefficient. Only the measurement of the(real) intensitycross-correlation coefficient is needed when observing unpolarized light. For the special case of a linearly polarized basis, the tilt error is simplyδ_τ≈ρ⁽²⁾, and for the circular basis case, with ellipticity deviationδ_ϵfrom circular helicityπ/4 (the reference channel of opposite helicity),δ_ϵ≈ρ⁽²⁾. These results provide simple means to gauge the quality of polarimeters and depolarizers.