Factorization Methods for Photonics and Rough Surfaces 1st Edition by Armin Lechleiter ISBN 3866442564 978-3866442566 by Armin Lechleiter 9783866442566, 3866442564 instant download after payment.

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ISBN 10: 3866442564 

ISBN 13: 978-3866442566

Author: Armin Lechleiter 

This book investigates non-destructive testing problems for rough and periodic surfaces, where the task is to determine such structures from scattered waves. Such problems are non-linear and ill-posed. We are interested in the analysis of the Factorization method applied to this class of inverse scattering problems. This method does not attempt to solve a non-linear operator equation for the unknown object but computes a binary criterion characterizing points inside and outside the structure.

Table of contents:

I. The Factorization Method and its Regularization
I-1. Introduction
I-2. Scattering by an Inhomogeneous Medium
I-3. The Inverse Medium Problem
I-4. Range Identity for Factorizations
I-5. Regularization of the Factorization Method
I-6. A Perturbation Lemma for the Factorization Method

II. The Factorization Method for Photonic Crystals
II-1. Introduction
II-2. The Direct Transmission Problem
II-3. Quasiperiodic Potentials
II-4. Auxiliary Scattering Problems
II-5. The Near Field Operator and its Factorization
II-6. Properties of the Factorization
II-7. A Factorization Method
II-8. Remarks on the Dirichlet Scattering Problem

III. Detecting Contamination on a Rough Surface
III-1. Introduction
III-2. The Unperturbed Surface Scattering Problem
III-3. Local Contamination and Boundary Integral Operators
III-4. The Inverse Contamination Problem
III-5. Approximation of the Sources

IV. The Factorization Method for Rough Surfaces
IV-1. Introduction
IV-2. Mapping Properties of the Single Layer Potential
IV-3. Variational Formulations for Rough Surface Scattering
IV-4. Factorization of the Near Field Operator
IV-5. Why Weighted Spaces Do Not Help

List of Symbols
Index
Bibliography

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Tags: Armin Lechleiter, Factorization Methods, Photonics, Rough Surfaces