Real-time inversion of two-dimensional Fresnel experimental database using orthogonality sampling method with single and multiple sources: the case of transverse electric polarized waves

This paper concerns an application of the orthogonality sampling method (OSM) for a real-time identification of small objects from two-dimensional Fresnel experimental dataset in transverse electric polarization. First, we apply the OSM with a single source by designing an indicator function based on the asymptotic expansion formula for the scattered field in the presence of small objects. We demonstrate that the indicator function can be expressed by an infinite series of Bessel functions of integer order of the first kind, the range of the signal receiver, and the location of the emitter. Based on this, we then investigate the applicability and limitations of the designed OSM. Specifically, we find that the imaging performance is strongly dependent on the source and the applied frequency. We then apply the OSM with multiple sources to improve imaging performance. Based on the identified structure of the OSM with a single source, we design an indicator function with multiple sources and demonstrate that it can be expressed by an infinite series of the Bessel function of integer order of the first kind, and we explain that objects can be identified uniquely using the designed OSM. Numerical simulation results obtained with the Fresnel experimental dataset demonstrate the advantages and disadvantages of the OSM with a single source and confirm that the designed OSM with multiple sources improves imaging performance.