Virtually all the detailed numerical calculations of low grazing angle EM scattering described in this book, and the published literature, represent the sea surface as a corrugated structure. As we discussed in Chapter 3, in this special case the solution of the vector Maxwell's equations reduces to that of an appropriate scalar Helmholtz equation. In this appendix we will discuss this simpler problem in some detail. Using this formalism we are able to demonstrate theoretical techniques used in the solution of scattering problems and derive the equations implemented in the Forward/Back computational method with relatively little effort. By exploiting reciprocity and a simple Fourier representation of the Helmholtz equation Green's function we can derive several practically important results more concisely and clearly than is done in the literature. This development of perturbation and other approximate theories also presents their results in a form that makes direct comparison with the numerical results quite straight forward.

This appendix will be long and perhaps overburdened with technical detail. Possibly as a result of this, it should provide a reasonably thorough introduction to the theory of electro magnetic scattering in the lowgrazing an gleregime that is particularly pertinent to the discussion of sea clutter. The reader who wishes to carry out controlled calculations of this kind and to interpret their output sensibly, has no alternative but to study their theoretical background in some depth. Much of the relevant material is spread throughout the physics and engineering literature and is expressed in a variety of...