Connection of scattering principles: a visual and mathematical tour

Inverse scattering, Green’s function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these scattering principles have a similar functional form. We first lead the reader through a visual explanation of the relationship between these principles and then present the mathematics that illustrates the link between the governing equations of these principles. Throughout this work, we describe the importance of the interaction between the causal and anti-causal Green’s functions.