Inverse problem of near-field scattering in multilayer media

Abstract

The inverse problem of scattering is solved for 3D inhomogeneities of the complex permittivity in multilayer media. The proposed solution involves an analysis of the 2D lateral distributions of the scattered field with the imposed condition of the probing field invariability relative to the receiver. A generalization of the solution beyond the Born approximation is given. Necessary k-space representations of Green functions for a multilayer medium with an arbitrary located source are obtained analytically in closed forms. Based on this solution, methods of multifrequency and multilevel subwavelength tomography are developed; their feasibility is shown for multifrequency tomography in a three-layered absorbing medium and for multilevel tomography with a perfect lens that can enhance the sounding depth. The developed approach is valid not only in electromagnetic theory, but also in similar problems of quantum mechanics and acoustics.

The method of multifrequency near-field acoustical tomography of bulk inhomogeneities of the sea bottom

“…Such an approach makes it possible to obtain explicit expressions for Green's functions [19] depending on transverse wavenumbers, which are used in the analysis below. A similar representation of the Green's functions is also obtained for an arbitrary multi-layer medium [20,21].…”

“…(1) assuming 100 elements for each coordinate, one would need 10 12 memory units. To overcome this difficulty, here we use an approach based on the reduction of the equation for the scattered field to convolution over transverse coordinates [16,20,21] and apply it to the discussed acoustical tomography problem as suggested in [17,22]. If such a problem formulation is possible, this allows one to reduce the three-dimensional problem to solving an onedimensional integral equation with respect to the depth profile of the spectrum of the inhomogeneities over the transverse wavenumbers.…”

“…The third approach proposed for solving similar problems in electrodynamics [20,21] uses the fact that the sounding field keeps its structure with respect to the receiver during the scanning, which is achieved by performing scanning by rigidly connected "source-receiver" system. In this case, the distribution of the sounding field in Eq.…”

“…From the practical viewpoint this scheme has a great advantage that all variations of the signal are determined only by the presence of the sub-bottom inhomogeneity. As is shown in [20,21], even certain correction of the solution beyond the limits of the Born approximation is possible within the framework of such an approach, although the rigorous reduction to an one-dimensional equation becomes impossible. We already mentioned that the data of two-dimensional scanning over the inhomogeneity region with respect to the transverse coordinates (x, y) are not sufficient to restore the sought three-dimensional function.…”

Numerical Modeling and Experimental Investigation of the Breadboard Model of a Near-Field Interference Microscope

“…Recently more and more researchers direct their attention to investigation of possibilities of near-field microwave diagnostics [1][2][3][4][5][6][7]. Such diagnostics involves medical (detection of human tumor formations) and industrial applications (flaw detection and hygroscopy), but in both cases restriction is imposed on the depth of field penetration into the examined medium or object.…”