Including Arbitrary Antenna Patterns in Microwave Imaging of Buried Objects

A linear inversion scheme for microwave imaging of buried objects is presented in which arbitrary antennas are accounted for through their plane-wave transmitting and receiving spectra. INTRODUCTION Ground penetrating radar (GPR) is an efficient tool for microwave imaging of buried objects. Within the concept of diffraction tomography, as proposed by Devaney [1], several linear inversion schemes (LIS’s) have been developed for GPR [2][5]. Since the GPR antennas are located close to the air-soil interface it is, as illustrated by Hansen et al. [3], important to take into account the presence of this interface. In the LIS by Hansen et al. [3] the GPR antennas are modeled as ideal (Hertzian) dipoles close to a planar interface. Since the radiation patterns of many practical GPR antennas differ from that of an ideal dipole, inaccuracies in the image occur. A formal theory for including models of arbitrary antennas in the LIS of [3] was suggested by Meincke [4] by expressing the transmitting antenna in terms of a current density and the receiving antenna in terms of its plane-wave receiving spectrum. However, no methods for obtaining the current density and the receiving spectrum were presented. This problem was overcome for linear wire antennas by Meincke et al. [5] by using the plane-wave scattering matrix formulation of Meincke et al. [6]. In this paper we extend the formulation by Meincke et al. [5] to hold for arbitrary antennas. For simplicity the 2.5-D case is considered, that is, it is assumed that the scattering object in the soil is invariant in one direction, which for instance is the case for a pipe. We show through a numerical example the performance of the LIS developed here for a configuration in which the antennas are planar equiangular spiral antennas. THE 2.5-D FORWARD MODEL The GPR configuration involving the planar air-soil interBuried object Air Soil Transmitter Receiver , , Figure 1: The fixed-offset GPR configuration involving arbitrary antennas and a buried -invariant object. face is shown in Figure 1. A Cartesian coordinate system is introduced such that the plane coincides with the interface and such that is air. An object, which is assumed infinitely long in the direction, is buried in the soil. The propagation constant of air is and that of soil is , assuming for simplicity that the soil is lossless. The position of the receiving antenna is described by & ( & ( & and that of the transmitting antenna is . ( . ( . & 3 5 ( & 3 5 ( & with the offset 5