Reciprocity, coupling and scattering: A new look at SPM for rough surface

In this paper, following an intrinsically-reciprocal approach we demonstrate how to straightforwardly derive the classical SPM scattering solution for a rough surface in a surprisingly simple way. The proposed new mathematical formulation for the relevant scattering problem then results, with respect to the classical one, neater, more concise, clearer, and as such offers a more direct comprehension in a methodological perspective. The mathematical structure presented not only represents a conceptually clean formulation for the classical SPM, but itself provides a new way of thinking about the perturbation theory applied to the scattering problem, especially in view of future developments.