The Role of Point Sources and Their Power Fluxes in the Linear Sampling Method

In this paper we investigate the linear sampling method by focusing on energy conservation inside a lossless background, in the case of a three-dimensional, impenetrable and acoustic scattering set-up. We analyze, from both a numerical and a theoretical viewpoint, how average power fluxes are carried throughout the host medium by the flow tubes of radiating fields. As a result, the far-field equation, which is the core of the linear sampling method, can be regarded as a physical constraint linking the power flux of the scattered wave with that of the field radiated by a point source. Then, we show that this constraint, together with appropriate assumptions on the flow tubes of the scattered field, gives rise to a physical framework whereby some theoretical flaws of the linear sampling method can be overcome.