When a penetrable target is located in a lossy half space of ground, one may excite the incident field and measure the scattered fields above the lossy half space by, for example, the ground penetration radar and verify the existence and the location of the target. It is shown here that the reconstruction of a large ($2.0λ_b$ by $1.5 λ_b$) and high contrast ($ε_r=25,ε_b=10,σ_b=0.01[s/m]$) two-dimensional object is possible from the two-dimensional formulation, where $λ_b$ is the half space wavelength,$ε_r$,$ε_b$ and $σ_b$ are respectively the relative permittivity of the buried target, the relative permittivity of the background medium, and the conductivity of the background medium.
The measured fields which is excited by a line source may be represented by the integral of plane wave spectrum consisting of terms corresponding to the direct coupling, reflected from the interface of the half space, and scattered by the target, where the two-dimensional half space Green's function is used.
One may assume that the strong direct-coupled and the interface-reflected fields may be subtracted from the measured fields. It is shown then that the target reconstruction becomes possible by using the iterative inversion method with the optimization algorithm combining the Lenvenberg-Marquardt algorithm and the simulated annealing algorithm. It is known that the reconstruction becomes unstable if the scattered fields are contaminated by the noise or the measurement error, which is defined as the illposedness. It is shown here that the resolution of half a wavelength may be obtained for a deep target by taking only the propagating modes of the scattered field, while the higher resolution may be obtained for a shallow target by taking the propagting modes and the evanescent modes of comparatively large amplitudes in the presence of noise in the scattered fields.
Excitation and measurement unit of fixed transmitting and receiving antenna may be constructed and moved along (and above) the interface to excite and measure the scattered fields. With this configuration, it is shown here that the depth, the width, and the height of the target may be estimated from the measurement fields and that the direct coupling and the interface reflection may be subtracted by filtering out the zero spatial frequency component from the Fourier transform of the measured total fields along the interface. From the measured fields, one may reconstruct the dielectric profile of the target.
