Airlight-imposed errors for space-object polarimetric observations from the ground

We discuss and characterize how polarimetric sensing is contaminated by various "airlight" phenomena, as well as unpolarized light from the target, when space objects are observed with a ground-based telescope. Estimates of the polarization state are limited by unpolarized target light regardless of sensor technology or estimator algorithm, and increased target brightness actually degrades estimation of the S₁, S₂, and S₃ Stokes parameters if the added light is unpolarized. Unpolarized airlight in the field of view has an identical degrading effect. Atmospheric scattering can significantly polarize airlight, so airlight polarization must be calibrated and subtracted from the estimated target polarization. We derive an expression for the mean-square Stokes estimation error when noisy, biased estimates for the airlight polarization state are subtracted from noisy, biased estimates of the target polarization state; this expression shows that target and airlight Stokes estimation noise and bias generally sum in the ms estimation error for airlight-calibrated target Stokes. While SNR for the estimate of a given Stokes parameter increases with the magnitude of that parameter, estimation bias also appears to be correlated with magnitude. We note that when the linear Stokes reference is not arbitrary, requiring a rotational transformation of the estimated Stokes vector, the SNRs of the S₁ and S₂ estimates vary with the rotation angle. Finally, we show that measured data can be used in numerical calculations described here to approximate the errors associated with Stokes estimation, with or without airlight calibration.