On the optimum polarizations of incoherently reflected waves

In radar imaging, the scattered waves are usually partially polarized. Accordingly, the concept of optimum polarization must be extended to the case of incoherent scattering where the scattered waves are partially polarized. Here, it will be shown that the Stokes scattering operator is the most suitable characterization of incoherent scattering. The problem of finding the polarization that would yield an optimum amount of power received from the scatterer is solved by assuming a knowledge of the Stokes scattering operator instead of the
2 \times 2
scattering matrix with complex elements. The advantage of this method is that it may be used to find the optimum polarizations for the case wherein the scatterers can only be fully characterized by their Stokes scattering operator (incoherent scattering) and the case wherein the scatterer can be fully characterized by the complex
2 \times 2
scattering matrix (coherent scattering). In this report, it will he shown that the optimum polarizations reported thus far in the literature, i.e., when the problem is solved by using a knowledge of the
2 \times 2
scattering matrix, form the solutions for a subset of a more general class of problems. When the solution of the problem is based on a knowledge of the Stokes scattering operator, it is found that for incoherent scattering six optimum polarizations can exist, whereas when the solution is based on the
2 \times 2
scattering matrix, the number of optimum polarizations is necessarily limited to four.