On the surface field integral equations

Surface field integral equations are the basic tools for electromagnetic waves scattering calculations. They are of particular importance for the evaluation of the ocean or soil surface contributions to backscattering and emissivity in remote sensing applications based on the use of radars or microwave radiometers. The proofs of these fundamental integral equations are disseminated in the scientific literature, and the original references are old. This paper proposes a comprehensive derivation of these relationships for both perfectly conducting and dielectric bodies, starting from Maxwell equations, through Kottler's formulas. Several basic properties for discontinuities in vector surface integrals are required, and the derivations are included. Some original proofs are also provided.