Theoretical Identification of Coupling Effect and Performance Analysis of Single-Source Direct Sampling Method

Abstract

Although the direct sampling method (DSM) has demonstrated its feasibility in identifying small anomalies from measured scattering parameter data in microwave imaging, inaccurate imaging results that cannot be explained by conventional research approaches have often emerged. It has been heuristically identified that the reason for this phenomenon is due to the coupling effect between the antenna and dipole antennas, but related mathematical theory has not been investigated satisfactorily yet. The main purpose of this contribution is to explain the theoretical elucidation of such a phenomenon and to design an improved DSM for successful application to microwave imaging. For this, we first survey traditional DSM and design an improved DSM, which is based on the fact that the measured scattering parameter is influenced by both the anomaly and the antennas. We then establish a new mathematical theory of both the traditional and the designed indicator functions of DSM by constructing a relationship between the antenna arrangement and an infinite series of Bessel functions of integer order of the first kind. On the basis of the theoretical results, we discover various factors that influence the imaging performance of traditional DSM and explain why the designed indicator function successfully improves the traditional one. Several numerical experiments with synthetic data support the established theoretical results and illustrate the pros and cons of traditional and designed DSMs.

Localization of Small Objectives from Scattering Parameter via Bistatic Measurement Configuration

“…Recently, as an alternative, various imaging techniques in the monostatic measurement configuration have been investigated; refer to [27][28][29]. However, in some problems, it is difficult to measure the scattering parameter data when the transmitter and receiver are in the same position and to discern the weak scattered signal from the relatively high antenna reflection (see [30,31] for instance). Thus, it is natural to consider the development of an imaging technique in which the positions of the transmitter and receiver are different.…”

Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem

“…An extension to the real-world problem can be found in [29][30][31] for subspace migration, refs. [32][33][34][35] for the direct sampling method, and [36][37][38][39][40] for the orthogonality sampling method.…”