Reconstruction Of Permittivity Profile Research Articles

Reconstruction of Permittivity Profiles Through a Transformation of the Differential Equation for the Reflection Coefficient

In this paper a one-dimensional inverse scattering problem is considered. An approximate inversion formula in a closed-form is derived. Using this formula, an approximate permittivity profile is generated from the partial knowledge of the frequency domain reflection coefficient. This formula is deduced through the application of a linear transformation to a nonlinear differential equation for the frequency domain reflection coefficient. Examples are given to demonstrate the accuracy of this approximate inversion formula.

Reconstruction of the permittivity profile using a nonlinear guided wave technique

A new method is developed to reconstruct the permittivity profile of a dielectric slab in a guided wave formulation. The propagation constants of the slab eigenmodes are used as input data for inversion of the boundary-value problem for the nonlinear differential equation representing the condition of existence of the modes. The permittivity profile is expanded into a set of special functions so that the propagation constant of a particular mode depends mainly on only one term of the set. This ensures fast convergence of an iterative procedure to find the coefficients of expansion. The method is shown to be valid for the discontinuous profiles of high contrast as well as for both symmetrical and asymmetrical profiles provided that in the last case additional measurements of the slab placed on a metal plate are performed. Several simulated and experimental examples are presented.

Angular spectral inversion for reconstruction of complex permittivity profiles

AbstractFormulation in cylindrical coordinates for the reconstruction of the permittivity profiles using the moment method is presented. Angular spectral domain reconstruction is shown to be less sensitive to the ill‐posedness due to the noise in the scattered field than the configuration‐domain reconstruction. © 1992 John Wiley & Sons, Inc.

Reconstruction of permittivity and conductivity profiles of a dielectric slab in the time domain by descent methods

An optimisation approach is presented for the problem of reconstructing the permittivity and conductivity profiles of a dielectric slab from the reflected and transmitted field data. The problem is treated as an optimal control problem where the norm of the difference of measured and calculated boundary data is minimised subject to the state equation governing the system. The original constrained optimisation problem is reduced to the evaluation of stationary points of an augmented functional which is obtained by the method of Lagrange multipliers. To find the necessary conditions for optimality, a variational approach is used which leads to a coupled system of four equations. The first two of these are differential equations named as state and costate equations, and the remaining two expressions are obtained by equating the gradients of the augmented functional, with respect to the permittivity and conductivity, to zero. Profile reconstruction is carried out by descent methods. At every iteration the state and costate equations are solved by the time domain finite element method. New estimates for the permittivity and conductivity profiles are obtained by a one dimensional search in a suitable descent direction.

Filtering effects on permittivity profiles reconstructed by a spectral inverse scattering technique

A further study is made of the reconstruction of permittivity profile by using the spectral inverse scattering scheme with the moment-method procedures. Based on earlier works, the reconstructed profiles have been affected by large errors even with a negligible random noise of the measured field. One of the intuitive approaches to reduce these errors has been implemented successfully by employing a polynomial basis function to the induced field on each enlarged cell in conjunction with a suitable weighting function. Another method is presented which adopts a low-pass filter to the spatial- Fourier transform of the equivalent source distribution induced in a dielectric object. The accuracy and validity of the spectral filtering are assured by a number of numerical simulations for a simple test geometry.

Spectral inverse technique for reconstruction of complex permittivity profiles

The inverse technique, which was exploited for the reconstruction of complex permittivity profiles by the moment method, is modified to be applicable in the spectral domain. Compared with previous schemes, this is conceptually simple and provides a proper way to regularise the difficulty inherent in inverse scattering problems.

On Some Inverse Methods in Electromagnetics

The purpose of this paper is to review some of the inverse methods in electromagnetics for the reconstruction of one-dimensional permittivity and conductivity profiles using transient or spectral data. Two different categories of inversion schemes, viz., the differential-inverse and integral-inverse algorithms, are discussed, and their relationships to other approaches developed in the fields of quantum mechanics and geophysics are pointed out.

Simultaneous reconstruction of permittivity and conductivity profiles in a radially inhomogeneous slab

This paper considers the simultaneous reconstruction of permittivity and conductivity profiles in a cylindrically stratified geometry. It is assumed that both the permittivity and conductivity may only vary in the radial direction, and that the unknown region, to be probed, is an annulus of known thickness. An iterative method for the simultaneous inversion of the radial permittivity and conductivity profiles inside this annulus is presented. This method employs a distorted‐Born approximation at each iteration step. The inherent nonuniqueness of the problem is circumvented by imposing additional constraints that limit the set of feasible solutions. Numerical simulations show that good results can be obtained for smoothly varying profiles even when a limited number of measurements at a single frequency are used.

Spectral and time domain approaches to some inverse scattering problems

Four methods of electromagnetic probing of an inhomogeneous plane stratified medium are presented. They differ by the nature of the incident wave used in the diagnostic. In the first method, the medium is considered as a structure propagating guided modes, and permittivity profiles are determined from the knowledge of one of the guided modes. In the next three, the medium is considered as a scatterer illuminated by a plane wave. Two of them are devoted to reconstruction of conductivity or permittivity profiles from time domain analysis of the reflected field. The last one allows one to obtain permittivity profiles from spectral domain analysis of the reflection coefficient. In spite of their apparent diversity, all these methods are issued from integral representations of the electromagnetic fields. These representations provides the simulated experimental data for the inverse problems. The behavior of these processes has been examined when parameters of practical interest are varied.

Reconstruction of permittivity profiles from a spectral analysis of the reflection coefficient

A spectral-domain approach to the inverse problem is considered. The permittivity profile of an inhomogeneous lossless dielectric slab is reconstructed from multifrequency measurements of the reflection coefficient. Simple and easy to use analytical relations are obtained. A simple experimental setup has been used, and the results obtained are in good agreement with those predicted by the theory.