Circular polarization of scattered solar radiation is essentially zero for almost all aerosol and cloud cases. Required conditions for non-zero circular polarization include multiple-scattering and large scatterer size relative to wavelength. The single-scattering of incident solar radiation can produce linearly polarized light but not circularly polarized light. A second scattering event can transform some of the linearly polarized light into circularly polarized light. Additional scattering events can both create and destroy circular polarization via the transformation process with linear polarization. The peak in circular polarization ratio magnitude occurs at the optical depth for which the multiplescattering processes have maximized its creation-to-destruction rate. Provided multiple-scattering has occurred, circular polarization can only exist for scatterers of large size relative to the wavelength. For aerosols, this implies desert dust or oceanic aerosols and short wavelength observations (i.e., less than 0.5μm). All cloud particles are considered large as they are roughly an order of magnitude larger than aerosols.
This paper presents a conceptual approach toward the remote sensing of cirrus cloud particle size and optical depth using the degree of polarization and polarized reflectance associated with the first three Stokes parameters I, Q, and U for the 0.865 and 2.25 μm wavelengths. A vector line-by-line equivalent radiative transfer program including the full Stokes parameters based on the adding method was developed. The retrieval algorithm employs the steepest descent method in the form of a series of numerical iteration procedures to search for the simulated polarization parameters that best match the measured polarization parameters. Sensitivity studies were performed to investigate the behavior of phase matrix elements as functions of scattering angles for three ice crystal size-shape combinations. Overall, each phase matrix element shows some sensitivity toward ice crystal shape, size, and suface roughness due to the various optical effects. Synthetic retrievals reveal that the retrieval algorithm itself is highly accurate, while polarimetric and radiometric error sources cause very small retrieval errors. Finally, an illustrative example of applying the retrieval algorithm to airborne POLDER data during EUCREX is presented.