論文名稱：二維週期性物體之影像重建 頁數：74
校系(所)組別： 淡江大學 電機工程學系 通訊系統組
畢業時間及提要別：八十九學年度第 二 學期 碩士 學位論文提要
研究生： 何政勳 指導教授：丘建青 博士
論文提要內容：
本論文的目的在研究二維週期性完全導體與不完全導體之電磁成像問題。
我們針對平面波入射的情況下，分別就週期性完全導體及不完全導體的逆散射進行探討。
首先探討週期性完全導體在自由空間的逆散射，文中對凹形物體的重建做深入的探討，另外也分析近場量測與遠場量測對影像重建的影響。接著配合表面阻抗的概念將逆散射法則推廣到非完全導體的情形。然後引入基因法則將逆散射問題轉化為求解最佳化的問題。藉以重建物體的週期大小、形狀函數與導電率。
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)，因此在數值模擬顯示中，即使最初的猜測值遠大於實際值，我們仍可求得準確的數值解，成功的重建出物體的週期大小、形狀函數與導電率。而且在數值模擬顯示中，量測的散射場即使加入均勻分佈的雜訊存在，依然可以得到良好的重建結果，研究證實其有良好的抗雜訊能力。而以微分為基礎求取極值的方法(calculus-based method)，卻常常會陷入區域極值(local extreme)的陷阱裡。
我們也發現，無論在完全導體以及非完全導體中，週期大小的收斂速度總是優於形狀函數。且在非完全導體中，另可發現形狀函數的收斂速度總是優於導電率，因此可知週期大小對散射場之貢獻最大，形狀函數對散射場的貢獻次之，導電率對散射場的貢獻最小。

The paper presents a computational approach to the imaging of a two-dimensional periodic perfectly and imperfectly conducting cylinder. The image reconstruction of a two-dimensional periodic perfectly and imperfectly conductor by the genetic algorithm is investigated. A periodic perfectly and imperfectly conducting cylinder of unknown periodic length, shape and conductivity scatters the incident wave in free space and the scattered field is recorded outside. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is then employed to find out the global extreme solution of the cost function. As a result, the periodic length, the shape and the conductivity of the conductor can be obtained. Numerical results are given to demonstrate that even in the presence of noise, good reconstruction has been obtained.

第一章簡介 ………………………………………………………… 1
1-1節研究動機與相關文獻 ……………………………… 1
1-2節本研究之貢獻…………………………………………… 6
1-3節各章內容簡述…………………………………………… 7
第二章週期性完全導體在自由空間之逆散射 ………………… 8
2-1節 理論推導………………………………………………… 8
2-2節 數值方法……………………………………………… 10
2-2-1 動差法求正散射公式……………………………… 11
2-2-2 基因演算法則……………………………………… 12
2-2-3 基因法則在逆散射的應用………………………… 21
2-3節 模擬結果………………………………………………… 22
2-4節 結論……………………………………………………… 25
第三章週期性不完全導體在自由空間之逆散射………………… 40
3-1節 理論推導 ……………………………………………… 40
3-2節 數值方法 ……………………………………………… 43
3-2-1 動差法求正散射公式……………………………… 43
3-2-2 基因法則在逆散射的應用………………………… 44
3-3節 模擬結果 ………………………………………………45
3-4節 結論 ……………………………………………………50
第四章結論與展望 ……………………………………………… 63
附錄一 加快週期性格林函數收斂的方法 ………………………… 66
附錄二 當 時改進週期性格林函數收斂的方法………… 68
參考文獻……………………………………………………………… 69

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