Bifocusing-Based Imaging of Small Penetrable Dielectric Objects From Fresnel Dataset

The bifocusing method (BFM) is one of the most effective non-iterative techniques for recognizing the existence and outline shape of a set of objects. In most previous studies, the BFM was designed under the assumption that complete elements of the multi-static response (MSR) matrix are collectable. Unfortunately, in the setup in some laboratory-controlled experiments, it is impossible to collect complete elements of the MSR matrix. In other words, the applicability and effectiveness of the BFM are still heuristic. In this paper, we consider the application of the BFM for identifying small circular objects from the 2D Fresnel dataset. To show its applicability and unique determination of objects when complete elements of the MSR matrix are not available, an analytical expression of the BFM imaging function in terms of the infinite series of Bessel function is derived. To demonstrate the theoretical result, the results of numerical simulations with experimental data are presented.