General description of polarization in lidar using Stokes vectors and polar decomposition of Mueller matrices

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.