Development of `Optimal polarimetric contrast enhancement coefficients: OPCEC´ for the analysis or depolarization due to rain, ice and surface scatter utilizing POL-RAD and POL-SAR measurements

In order to fully analyze depolarization effects of various kinds of surface and volumetric scatterer ensembles both the coherency and the stochasticity of the scatter returns need to be optimized. This is achieved, first by solving the eigenvalue and optimization problems for the scattering matrices [S(AB)],[G(AB)], [C(AB)], [M] and [K] from which the optimal (characteristic) polarization states are derived; second, by optimizing the stochasticity expressions (degree of coherency and polarization) and by equally or more importantly devicing the exact and correct expressions for the enhancement of the ´optimal contrast´ between two (or more) classes of scatterer ensembles. In general, two distinct classes of scatterers may be defined as T´ and ´C´, where T defines the desirable (useful) scatterer, the target: T, and ´G´ the undesirable scatter ensemble, the clutter ´G´, against which T is to be discriminated or to be optimally contrasted. The formal development of the related ´OPCEC´ expressions associated with a specific matrix description in terms of either [S], [G], [Σ], [K] and/or any combination of such is addressed in this presentation. The formal solutions of various ´OPCEC´ expressions for [S], [G], [4, [M] and [K] are presented and the obtained canonical results are compared