Imaging of Dielectric Objects Buried under an Arbitrary Rough Surface

Abstract

A method for the reconstruction of cylindrical bodies buried in a half-space having a locally rough interface is addressed. Through the Green's function of the two-half spaces medium with rough interface the problem is reduced to the solution of a Fredholm integral equation of the first kind involving the object function related to the unknown bodies. The integral equation is solved via an application of MoM by the use of Tikhonov regularization. The method yields quite satisfactory results in the case of multi-incidence and for the objects having relatively small sizes. I. INTRODUCTION Imaging of objects buried in a layered medium constitutes an important class of problems in electromagnetic theory due to the fact that the results of such investigations have various applications in practice in the areas of detection and location of dielectric mines, non-destructive testing, determination of underground tunnels and pipelines etc. Although during the last two decades several techniques have been developed, most of them are deals with the layered backgrounds with planar boundaries (1,2). Whereas in most of the real applications the bodies are buried in layered media having rough interfaces and the roughness has a strong effect on the scattering phenomena as well as inversion algorithms. For instance, in the case of bodies buried underground the roughness of the earth surface can potentially modify object scattering returns from those with a flat interface. For that reason the problem has to be considered in its actual conditions. The main objective of this paper is to give a method to solve the inverse scattering problem related to the inhomogeneous cylindrical bodies buried in a half-space with rough interface in the case of plane wave illumination. The scattered field measurements are assumed to be performed at the far field region in the half-space not containing the bodies. For the sake of simplicity only the surfaces having one-dimensional profiles are considered. The material of the bodies are assumed to be inhomogeneous, i.e: their dielectric permittivities and con- ductivities are functions of the location. Through the Green's function of the back-ground medium with rough interface the problem is first reduced to the solution of a Fredholm integral equation of the first kind for an unknown function which is multiple of the object function and the total field. On the other hand the determination of the Green's function constitutes a separate and difficult problem. In the open literature not much work has been done in that direction except (3), which is valid only for the slightly rough surfaces. Here we give a new and general method which is based on buried object approach (BOA) given in (4), where the perturbations of the rough surface from the flat one are assumed to be buried objects in a two-part space with planar interface. The inverse scattering problem is then solved by an application of MoM to the resulting Fredholm integral equation for the object function. Since the integral equation has a continuous kernel, it is severely ill-posed and a regularization in the sense of Tikhonov is applied. The reconstructions obtained for a number of illuminations show that the method yields quite satisfactory results for the objects having relatively small sizes.