Reconstruction of the dyadic dielectric constant profile of anisotropic inhomogeneous media

Abstract

The dyadic dielectric constant profile in a general inhomogeneous and anisotropic object can be uniquely reconstructed by a series of near field measurements of the scattered field resulting from illuminating the object by electromagnetic waves with properly chosen properties. This can be made either in the time domain, if the object is illuminated by short pulses, or in the frequency domain, if the frequency of a monochromatic illumination is swept. The lateral variation of the dielectric constant tensor can be obtained in terms of the measured reflected field at a number of points in the vicinity of the object. How near the measurements should be conducted depends on the resolution with which the lateral variation of the dielectric constant is to be reconstructed. This is mainly due to the fact that waves with high lateral resolution decay rapidly against the distance from the object. The normal (depth-dependent) variation of the dielectric constant, on the other hand, can be reconstructed in terms of the frequency dependence of the measured scattered field via an inverse Fourier transform or equivalently in terms of the time dependent reflection coefficient, if a short duration pulse is used for illumination. This procedure is usually used to reconstruct the dielectric constant profile for planar stratified media. A new method for reconstructing the three-dimensional permittivity profile of an inhomogeneous dielectric object located within a cavity resonator is presented. It utilizes the measured frequency response of the scattering parameters associated with connecting the resonator to properly chosen coupling ports. The cavity resonator is necessary to avoid dealing with continuous spectra related to open structures. This doesn't however restrict the validity of the method as the resonator can be arbitrarily chosen. The resolution of the method is arbitrarily controllable via the choice of the number and location of the coupling ports on the one hand and the frequency range over which the scattering parameters are measured on the other hand. Application to a simple one dimensional case shows excellent agreement between originally assumed and reconstructed dielectric profiles. The presented method represents new basis for a wide class of inverse problems, e.g., filter design, microwave imaging and remote sensing.