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Inverse Scattering Problem (inverse + scattering_problem)
Selected AbstractsImage reconstruction for a partially immersed imperfectly conducting cylinder by genetic algorithmINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2009Wei Chien Abstract This article presents a computational approach to the imaging of a partially immersed imperfectly conducting cylinder. An imperfectly conducting cylinder of unknown shape and conductivity scatters the incident transverse magnetic (TM) wave in free space while the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations, and the inverse scattering problem are reformulated into an optimization problem. We use genetic algorithm (GA) to reconstruct the shape and the conductivity of a partially immersed imperfectly conducting cylinder. The genetic algorithm is then used to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient-based methods often get trapped in a local extreme. In addition, the effect of random noise on the reconstruction is investigated. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 299,305, 2009 [source] Structure Determination in Colloidal Crystal Photonic Bandgap StructuresJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 6 2002John Ballato Structure/optical property relationships in photonic bandgap structures are evaluated by a novel combination of sample sectioning, microscopy, and image analysis. Disordered colloidal crystals of solution-derived, monosized SiO2 particles were sectioned by focused ion beam (FIB) milling and then imaged using field emission scanning electron microscopy (FE-SEM). Pair correlation and radial distribution functions of the particulate arrangement were generated directly from a binary color scale rendering of the FE-SEM images, therein defining the level of order or disorder in the structure. These experimentally obtained spatial correlation functions were used to compute the scattering spectral properties in an analogous, although inverse (i.e., solving the inverse scattering problem), method to that used in X-ray diffraction for structure determination. Using a first-order approximation to the scattering from a disordered structure, the bandwidth and midgap values for the colloidal crystal photonic bandgap materials were within 15% of those measured. This new methodology promises to provide a simple and direct approach for quantifying the structure/optical property relationships in ordered and disordered photonic crystals directly from standard microstructural imaging techniques. [source] Reconstruction of cracks of different types from far-field measurementsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2010Jijun Liu Abstract In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far-field map. The scattering problem models the diffraction of waves by thin two-sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far-field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd. [source] Combined far-ield operators in electromagnetic inverse scattering theoryMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2003Fioralba Cakoni Abstract We consider the inverse scattering problem of determining the shape of a perfect conductor D from a knowledge of the scattered electromagnetic wave generated by a time-harmonic plane wave incident upon D. By using polarization effects we establish the validity of the linear sampling method for solving this problem that is valid for all positive values of the wave number. We also show that it suffices to consider incident directions and observation angles that are restricted to a limited aperture. Copyright © 2003 John Wiley & Sons, Ltd. [source] The Schrödinger equation and a multidimensional inverse scattering transformMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002Swanhild Bernstein Abstract The Schrödinger equation is one of the most important equations in mathematics, physics and also engineering. We outline some connections between transformations of non-linear equations, the Schrödinger equation and the inverse scattering transform. After some remarks on generalizations into higher dimensions we present a multidimensional ,¯ method based on Clifford analysis. To explain the method we consider the formal solution of the inverse scattering problem for the n -dimensional time-dependent Schrödinger equations given by A.I. Nachman and M.J. Ablowitz. Copyright © 2002 John Wiley & Sons, Ltd. [source] Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearityMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2001Ricardo Weder In this paper we consider the inverse scattering problem for the non-linear Schrödinger equation on the line \def\dr{{\rm d}}$$i{\partial\over\partial t}u(t,x)=-{\dr^2\over\dr x^2}u(t,x)+V_0(x)u(t,x)+\sum_{j=1}^{\infty}V_j(x)|u|^{2(j_0+j)}u(t,x)$$\nopagenumbers\end We prove, under appropriate conditions, that the small-amplitude limit of the scattering operator determines uniquely Vj, j=0,1,, . Our proof gives also a method for the reconstruction of the Vj, j=0,1,, . Copyright © 2001 John Wiley & Sons, Ltd. [source] On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equationCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2004Alexander Tovbis We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t , 0. We utilize the Riemann-Hilbert problem formulation of the inverse scattering problem to obtain the leading-order term of the solution. Error estimates are provided. © 2004 Wiley Periodicals, Inc. [source] | ||||||||||