Electromagnetic Inverse Profiling: Theory and Numerical Implementation
This monograph is concerned with the direct-scattering of electromagnetic waves by one- and two-dimensional objects, and the use of this technique in one-dimensional inverse profiling. It discusses results of research into the method of this technique and its application to specific problems. Several techniques are presented for solving transient electromagnetic direct-scattering problems. These problems are solved indirectly, via a Fourier or Laplace transformation to the real- or complex-frequency domain, as well as directly in the time domain. For the one-dimensional case it is described how the special features of the respective techniques are also exploited to tackle the inverse problem of determining obstacle properties from the scattered field excited by a known incident field. The problems of both identification and of inverse profiling are addressed. For a range of specific problems representative numerical results are presented and discussed. Particular attention is devoted to the numerical implementation and to the physical interpretation of the theoretical numerical results obtained. With respect to inverse-scattering the emphasis is on the band-limiting effects that may arise due to approximation errors in the various inversion schemes employed.
Table of Contents
Introduction General introduction DIRECT SCATTERING FREQUENCY-DOMAIN TECHNIQUES Introduction Scattering by a homogeneous, lossy dielectric slab: singularity expansion method Appendix: Influence of the conductivity on the location of the poles Scattering by an inhomogeneous, lossy dielectric slab: singularity expansion method Appendix: The natural modes of a symmetric Epstein layer Scattering by an inhomogeneous, lossy dielectric slab in between two homogeneous, lossless half-spaces: Fourier inversion Scattering by a lossy, radially inhomogeneous dielectric circular cylinder: singularity expansion method and Fourier inversion Appendix: Mean-square convergence of the angular Fourier series as a function of and t Scattering by a lossy, radially inhomogeneous dielectric circular cylinder: complementary interpretation of singularity expansion method Appendix: The residue of at a pole Conclusions References TIME-DOMAIN TECHNIQUES Introduction General aspects of the marching-on-in-time method Appendix: A relaxation method for the solution of an ill-conditioned system of linear equations Scattering by an inhomogeneous, lossy dielectric slab Scattering by a perfectly conducting cylinder Appendix: Source representation for two-dimensional electromagnetic-field quantities Appendix: Determination of and its space derivatives Scattering by an inhomogeneous, lossy dielectric cylinder Conclusions References IDENTIFICATION A PRONY-TYPE METHOD Introduction Prony's algorithm Application to a slab signal Conclusions References INVERSE-PROFILING FREQUENCY-DOMAIN TECHNIQUES Introduction General aspects of the one-dimensional inverse-scattering problem The one-dimensional inverse-scattering problem for low contrast and oblique incidence The one-dimensional inverse-scattering problem for a lossless dielectric slab Conclusions References TIME-DOMAIN TECHNIQUES Introduction Born-type iterative procedure with a vacuum as the background medium Appendix: Smoothing procedure Optimization approach Born-type iteractive procedure with the reference medium as the background medium Conclusions References Subject index