Forward and inverse scattering problems in the time domain
Moghaddam, Mahta
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Permalink
https://hdl.handle.net/2142/23644
Description
Title
Forward and inverse scattering problems in the time domain
Author(s)
Moghaddam, Mahta
Issue Date
1991
Doctoral Committee Chair(s)
Chew, Weng Cho
Department of Study
Engineering, Electronics and Electrical
Discipline
Engineering, Electronics and Electrical
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
An efficient method of solving the 2${1\over 2}$-dimensional electromagnetic forward scattering problem in the time domain is developed, which circumvents the use of three-dimensional arrays to solve the vector wave problem. The method is based on calculating the three-dimensional fields as a summation of Fourier-transformed two-dimensional fields. Each 2D problem is solved via the finite-difference time-domain algorithm. The solution is used to develop a realistic model of the subsurface interface radar.
The nonlinear two-dimensional electromagnetic inverse scattering problem is solved using spatially-sparse transient data with TM incidence. The method uses Born-type iterations on a volume integral equation for the scattered field. We call this the Born iterative method. Both the full-angle and the limited-angle inverse problems are solved. In each case, resconstructions are obtained when the linear Born approximation is severely violated. It is shown that the permittivity and conductivity profiles can be reconstructed simultaneously. The effect of noise is considered, and it is shown that the algorithm has a robust noise performance. The high-resolution capability of the algorithm is demonstrated and discussed.
The nonlinear two-dimensional electromagnetic TE inverse problem is formulated and solved using the Born iterative method. Although a very important problem, the TE inverse problem has rarely been considered before, due to the more complex form of the wave equation: The unknown is acted upon by a derivative operator, rendering the solution prone to numerical error. Here, several profiles are successfully inverted, but it is shown that the resolution limit is degraded by a factor of two compared to the TM inverse problem. This is attributed to the high level of noise arising from numerical differentiations.
The two-unknown linear acoustic inverse problem is solved using a diffraction tomography-type method. Having established the limits of applicability of the linear solution, the nonlinear problem is formulated and solved via the Born iterative algorithm using a double-criterion optimization. The acoustic problem also involves the differentiation of one of the unknown profiles and the field inside the scatterer. Therefore, while the algorithm is able to invert smooth profiles, the resolution in this case is also deteriorated compared to the TM case because of numerical noise.
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