The time-dependent Mueller matrix solution of vector radiative transfer for stratified random media of nonspherical scatterers is presented. Copolarized and cross-polarized bistatic scattering for a polarized pulse incidence are numerically simulated. Numerical results well demonstrate volumetric and surface scattering mechanism and depict the fraction distribution of random scatterers of stratified random media. The peak tails in polarized echoes due to wave reflections from the underlying surface can be identified. Its copolarized peaks in the specular direction are employed for simultaneous retrievals of the underlying surface roughness and moisture with the presence of stratified vegetation canopy.

Polarimetric scattering from inhomogeneous random media of non-spherical scatterers under a pulse incidence is studied. The time-dependent Muller matrix solution of vector radiative transfer for layering random media is derived. Co-polarized and cross-polarized bistatic and backscattering are numerically calculated. The shape and intensity of polarized echoes well depict the inhomogeneous fraction profile of random scatterers. Its functional dependence upon the fraction profile, layering thickness, and other parameters are discussed. This technique is applicable to the reconstruction of inhomogeneous fraction profile and inversion of the media thickness.

To measure fully polarimetric scattering from random chiral small spheroids, the 2 × 2 dimensional (2 × 2-D) complex scattering amplitude matrix of randomly oriented, chiral small spheroid is derived. Polarimetric scattering from a bounded layer of non-uniformly oriented, chirally-active small spheroids in the Mueller matrix solution is obtained. Co-polarized and cross-polarized backscattering and polarization degree for any polarized incidence (χ, ψ) are numerically calculated. Transmitting of coherent Stokes parameters through the layer are also discussed. Either non-uniform orientation or chirality can yield non-diagonal extinction matrix {ie130-1} and full eigenmatrix Ē due to the fact of forward depolarized-scattering functions 〈f 〉, 〈f 〉 ≠ 0. Comparisons of fully polarimetric scattering from the chiral and achiral particulate media demonstrate the chirality effect on wave scattering and transmitting.