一些反散射問題重構方法的介紹

Survey on reconstruction methods in the inverse scattering problem

林彥亨(Yem-Heng Lin)

指導教授 ： 王振南

國立臺灣大學/理學院/數學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.10311

摘要

反散射問題一個主要的目的是如何利用散射場（波）的數據來得到未知物體的形狀。
這篇論文主要是介紹一些在三維空間中，如果利用平面波當成入射場（波）相對於未知物體所得到的散射場（波）跟其遠場（far field）的數據資料來重構出這個未知物體的外部形狀或整體形態。

關鍵字

反散射 ； 入射場 ； 散射場 ； 遠場 ； 平面波

並列摘要

Inverse scattering problems are concerned with the determining the shape of unknow obstacle from the information of scattered waves.
The goal of this work is to introduce some methods of reconstructive the shape of a three-dimensional obstacle from the knowledge of the far field pattern of the scattered wave whose incident field is time-harmonic plane wave.

並列關鍵字

inverse scattering ； scattered wave ； far field ； plane wave ； reconstructive

參考文獻

F. Cakoni,D. Colton ,Adrian (2006) - Qualitative Methods in Inverse scattering Theory - An Introduction (Springer-Verlag,Berlin Heidelberg)

D. Colton ,R. Kress, (1998) - Inverse Acoustic and Electromagnetic Scattering Theory.2nd (Applied Mathematical Science,93. Springer-Verlag,Berlin)

M. Ikehata, (1999) - Reconstruction of obstacle from boundary measurements (Wave motion 30 (1999) 205-223)

A. Kirsch ,(1998) - Characterization of the shape of the scattering obstacle using the spectral data of the far field operator (Inverse Problem 14(6), 1489-1512 (1998))

G. Nakamura ,R. Potthast ,(2005) The no-response approach and its relation to non-iterative methods for the inverse scattering (Annali di Mathematica (2008) 187:7-37. Springer-Verlag 2006)