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.

In this study, we consider a topological derivative-based imaging technique for the fast identification of short, linear perfectly conducting cracks completely embedded in a two-dimensional homogeneous domain with smooth boundary. Unlike conventional approaches, we assume that the background permittivity and permeability are unknown due to their dependence on frequency and temperature, and we propose a normalized imaging function to localize cracks. Despite inaccuracies in background parameters, application of the proposed imaging function enables recognition of the existence of cracks, but it is still impossible to identify accurate crack locations. Furthermore, the shift in crack localization of imaging results is significantly influenced by the applied background parameters. In order to theoretically explain this phenomenon, we show that the imaging function can be expressed in terms of the zero-order Bessel function of the first kind, the crack lengths, and the applied inaccurate background wavenumber corresponding to the applied inaccurate background permittivity and permeability. Various numerical simulation results with synthetic data polluted by random noise validate the theoretical results.

In this paper, we consider the application of the bifocusing method (BFM) for a fast identification of two-dimensional circle-like small inhomogeneities from measured scattered field data. Based on the asymptotic expansion formula for the scattered field in the presence of small inhomogeneities, we introduce the imaging functions of the BFM for both dielectric permittivity and magnetic permeability contrast cases. To examine the applicability and the various properties of the BFM, we show that the imaging functions can be expressed by the Bessel function of orders zero and one, as well as the characteristics (size, permittivity, and permeability) of the inhomogeneities. To support the theoretical results, various numerical results with synthetic and experimental data are presented.

For a successful application of subspace migration algorithm to retrieve the exact location and shape of small anomaly in microwave imaging, one must begin the reconstruction process under the assumption that complete information about the homogeneous background medium, such as background permittivity and conductivity, is available. In many studies, the statistical value of the background medium was adopted, raising the possibility of an incorrect value being applied. Thus, simulation results have been examined in order to identify cases in which an inaccurate location and shape of anomaly were retrieved. However, the theory explaining this phenomenon has not been investigated. In this paper, we apply an alternative wavenumber instead of the true one and identify the mathematical structure of the subspace migration imaging function for retrieving two-dimensional small anomaly by establishing a relationship with an infinite series of Bessel functions of the first kind. The revealed structure explains the reason behind the retrieval of an inaccurate location and shape of anomaly. The simulation results with synthetic data are presented to support the theoretical result.

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix without diagonal elements, whose elements are measured scattering parameters, is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies some of its properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted.