Recovering the Fields of Point-Like Scatterers in the Presence of a Penetrable Sphere

In this work, the scattering problem pertaining to the excitation of a penetrable sphere surrounded by a cluster of point-like scatterers, by a point-generated primary field is considered. By means of the Foldy-Lax approximation the problem is reduced to a scattering problem of excitation of a penetrable sphere by an arbitrary point-source distribution, enabling the recovery of the fields of the point-like scatterers by an inverse scheme that utilizes far-field measurements. Furthermore, a dense cluster approximation of the scattering cross section attributed to the cluster’s scatterers is obtained when certain conditions are met and explicit numerical results that demonstrate the accuracy and highlight aspects of the method’s stability, are presented.