The full wave approach to problems of scattering by rough surfaces has been applied to the problem of depolarization of the scattered radiation fields by objects of finite conductivity and irregular shape. In the analysis, complete expansions are employed, exact boundary conditions are imposed, and a variable coordinate system that conforms with the local features of the irregular surface is used. The full wave solutions are expressed in forms that can be readily compared with earlier solutions, and they can be used to reconcile the differences and bridge the wide gap between these solutions. Thus the full wave solutions for the backscatter cross section are shown to reduce to the physical optics solutions when the high-frequency, stationary phase approximations are used. Similarly, for slightly rough surfaces the full wave expressions reduce to the perturbational solutions for the backscatter cross section. The full wave solutions are shown to be consistent with the duality reciprocity and realizability relationships in electromagnetic theory. These solutions are invariant to coordinate transformations. Since upward and downward scattering are considered in the analysis, multiple scattering and shadowing effects are taken into account in a self-consistent manner. Thus the total scattered field varies continuously as the observer moves across a shadow boundary, and there is no need to introduce transition terms derived from other theories. The full wave approach can be applied to deterministic, periodic, and random rough surfaces. It can also be used to determine the scattering by finite scatterers in the presence of rough land or sea.