Well posed inversion mechanisms

This paper is a study of topological direct and inverse scattering. We discuss an exact and compact inversion method. The aim is to image the bodies with one to one correspondence. For this purpose we study the surface waves travelling on 3D curved surfaces with several singularities and extend some of the topological approaches. We construct the rules of topological diffraction. Those rules construct the law of topological diffraction (LTD). Multiple diffractions and near field calculations are taken into consideration. Approaches based on surface theory give the extraction of the physical mechanisms. Those extractions are used to obtain the field distribution. Following this the law of topological inversion (LTI) is obtained and constructed. With those rules we construct a well-posed inversion method, that is, the physical and surface theory of inverse scattering (PASTIS).