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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.