利用基因法則及TE極化波照射重建二維非完全導體之研究

Electromagnetic Transverse Electric Wave Inverse Scattering of a Two-dimensional Imperfectly Conducting Cylinder by Genetic Algorithm

蔡明峯(Ming-Feng Tasi)

指導教授 ： 丘建青

淡江大學/工學院/電機工程學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00140

摘要

本論文針對TE極化波入射的情況下,對於非完全導體的電磁成像問題進行探討。
對於非完全導體而言，我們利用非完全導體表面阻抗的觀念再加上表面電流的觀念，在物體的邊界上，可導出非線性積分方程式，繼而利用動差法求得正散射公式。經由推導出的正散射公式，我們可以得到散射場的相關資料。在於逆散射部分，我們使用了基因法則(Genetic Algorithm)，經由適當地選取參數，同時結合所推導的散射公式，我們可以由觀測點所測得的散射場值，經由基因法則的運算，來反求得物體的形狀函數。
就整體而言不論初始的猜測值如何，基因法則總會收歛到整體的極值(global extreme)，因此，在數值模擬中，即使最初的猜測值與實際值相距甚遠，我們仍可求得準確的數值解，成功的重建出物體形狀函數與導電率。而且量測的散射場即使加入高斯分佈的雜訊存在，依然可以得到良好的重建結果。此外我們也對於形狀函數跟導電率的雜訊容忍量予以比較。

關鍵字

基因法則 ； 逆散射 ； 非完全導體

並列摘要

This paper presents a computational approach to the transverse electric (TE) wave imaging of an imperfectly conducting cylinder. An imperfectly conducting cylinder of unknown shape and conductivity scatters the incident wave in the free space, and the scattered field is recorded outside the object. Based on the boundary condition and measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization one that solved by Genetic Algorithm. Numerical results demonstrated that, the even when the initial guess is far away from the exact one, good reconstruction for shape and conductivity of the object can be obtained and the object’s conductivity also can be reconstruction excellent, In addition, the effect of noise is also be investigated.

並列關鍵字

Genetic algorithm ； imperfectly conducting cylinder ； Transverse Electric-Wave

參考文獻

[1] A. G. Ramm, “Uniqueness result for inverse problem of geophysics: I,” Inverse Problems, vol. 6, pp. 635-641, Aug. 1990

[3] V. A. Morozonv, Methods for Solving Incorrectly Posed Problems. New York: Spring-Verlag, 1984

[6] N. N. Bojarski, “A survey of the physical optics inverse scattering identity,” IEEE Trans. Antennas Propagat., vol. 30, pp.980-989, Sept.1982.

[7] R. M. Lewis, “Physical optics inverse diffraction,” IEEE Trans. Antennas Propagat., vol. 17, pp. 308-314, May 1969

[8] T. H. Chu and N. H. Farhat, “Polarization effects in microwave diversity imaging of perfectly conducting cylinders,” IEEE Trans. Antennas Propagar., vol.37, pp. 235-244, Feb. 1989.