Inversion of two-dimensional Fresnel experimental dataset using orthogonality sampling method with single and multiple sources: the case of transverse magnetic polarized waves

This paper considers the application of the orthogonality sampling method (OSM) with single and multiple sources for a fast identification of small objects in the limited-aperture inverse scattering problem. First, we apply the OSM with a single source and demonstrate that the indicator function of the OSM with a single source can be expressed by the Bessel function of order zero of the first kind, an infinite series of Bessel functions of nonzero integer order of the first kind, the range of the signal receiver, and the emitter location. We then explain that the objects can be identified using the OSM with a single source; however, the identification is strongly influenced by the location of the source and the applied frequency. To realize effective improvement, we consider the OSM with multiple sources. Based on the identified structure of the OSM with a single source, we propose an indicator function for the OSM with multiple sources and demonstrate that it can be expressed by the square of the Bessel function of order zero of the first kind and an infinite series of the square of the Bessel function of nonzero integer order of the first kind. This result shows that the locations of objects can be uniquely identified using the designed OSM. Simulation results with experimental data provided by the Institute Fresnel demonstrate the advantages and disadvantages of the OSM with a single source and how the proposed OSM with multiple sources behaves.