Localization of Small Anomalies via the Orthogonality Sampling Method from Scattering Parameters

We investigate the application of the orthogonality sampling method (OSM) in microwave imaging for a fast localization of small anomalies from measured scattering parameters. For this purpose, we design an indicator function of OSM defined on a Lebesgue space to test the orthogonality relation between the Hankel function and the scattering parameters. This is based on an application of the Born approximation and the integral equation formula for scattering parameters in the presence of a small anomaly. We then prove that the indicator function consists of a combination of an infinite series of Bessel functions of integer order, an antenna configuration, and material properties. Simulation results with synthetic data are presented to show the feasibility and limitations of designed OSM.