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Statistics of the Stokes Parameters for the Signal Scattered by Layered Structures With an Arbitrary Number of Slightly Rough Interfaces

Horizontally stratified structures are commonly used to represent naturally occurring structures, such as soils. The electromagnetic signature of such a medium illuminated by radar and the polarization state of the scattered wave are fully determined by the knowledge of the four Stokes parameters. In this article, we determine the statistics of the four Stokes parameters for the signal scattered by layered structures with an arbitrary number of slightly rough interfaces. The rough interfaces are realizations of second-order stationary centered Gaussian stochastic processes and the layered structure is illuminated by an elliptically polarized monochromatic wave. The zenithal and azimuthal components of the far scattered electric field are derived from the first-order small perturbation method. The derivation leads to a multivariate Gaussian model for the underlying complex scattered amplitudes, and we establish the closed-form expressions of the probability density function, the cumulative density function, and the first- and second-order moments for the four Stokes parameters. For an observation direction outside the incidence plane, we establish the condition on the incidence wave parameters for which the zenithal and azimuthal components are uncorrelated. For an air/snow cover/frozen soil/unfrozen soil structure, we analyze the marginal probabilities and validate the theory by comparison with Monte Carlo simulations. More generally, when the two complex components of the field scattered by the illuminated zone are Gaussian random variables, these statistics offer possibilities for in-depth investigating the polarization of scattering processes from random media.