Polarization measurements have become nearly indispensible in lidar cloud and aerosol studies. Despite polarization’s widespread use in lidar, its theoretical description has been widely varying in accuracy and completeness. Incomplete polarization lidar descriptions invariably result in poor accountability for scatterer properties and instrument effects, reducing data accuracy and disallowing the intercomparison of polarization lidar data between different systems. We introduce here the Stokes vector lidar equation, which is a full description of polarization in lidar from laser output to detector. We then interpret this theoretical description in the context of forward polar decomposition of Mueller matrices where distinct polarization attributes of diattenuation, retardance, and depolarization are elucidated. This decomposition can be applied to scattering matrices, where volumes consisting of randomly oriented particles are strictly depolarizing, while oriented ice crystals can be diattenuating, retarding, and depolarizing. For instrument effects we provide a description of how different polarization attributes will impact lidar measurements. This includes coupling effects due to retarding and depolarization attributes of the receiver, which have no description in scalar representations of polarization lidar. We also describe how the effects of polarizance in the receiver can result in nonorthogonal polarization detection channels. This violates one of the most common assumptions in polarization lidar operation.
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