The Linear Sampling Method as a Tool for “Blind” Field Intensity Shaping

Arbitrary shaping the field intensity is a challenging problem relevant in many applications. To date, procedures addressing such a challenging problem have been developed assuming a full knowledge of both the scenario and the target within embedded. However, this is not the case in many applications where the investigated scenario is only approximately known and/or modeled on the basis of some auxiliary imaging methods. In this article, we propose a novel adaptive procedure able to shape the field intensity in an unknown (or partially unknown) scenario without the need of a quantitative scenario retrieval. The approach takes advantage from the linear sampling method, which belongs to the class of qualitative imaging methods, in order to focus the field intensity with respect to different control points belonging to the target. Then, the desired spatial field intensity shaping is obtained by recombining the results from such single-focusing problems and by exploiting an additional degree of freedom, which is represented by phase shifts of the field in the considered control points. A preliminary numerical validation and assessment are given for in-homogeneous and lossy unknown 2-D scenarios.