We present a fully coherent, analytic model of the backscattering intensity in all H H,H V,V H, and V V channels, for the volume scattering of radiation from a layer of finite thickness, such as a vegetation layer over bare soil. We aim for a simple, not numerically intensive, model that could be used either as a forward model in a Bayesian estimation scheme, or else as a preliminary means to identify key features of a concrete problem, for its further analysis by more sophisticated theoretical and numerical approaches.