本論文研究埋藏於三層空間中二維非均勻介質柱體的電磁影像重建。此研究以有限時域差分法 (FDTD) 為基礎，利用最佳化方法於時域中重建埋藏於三層空間中二維非均勻介質柱體之特性參數。為了探究埋藏於三層空間中未知的非均勻介質柱體，概念上吾人可向散射體發射電磁脈波/平面波，並量測其周圍的散射電磁波，再針對此量測散射電磁波分別以非同步粒子群聚法法（APSO）將逆散射問題轉化為求解最佳化問題。然而分別以族群大小為未知數(49)的3倍、5倍、以及10倍來模擬比較，本論文探討以非同步粒子群聚法法對於三層空間下的二維非均勻介質柱體逆散射問題的適用性。模擬結果顯示，即使最初的猜測值與實際散射體位置相距甚遠，此最佳化方法皆可以成功地重建出柱體的介電參數。使用非同步粒子群聚法法可以大幅減少計算正散射次數，並且減少逆散射問題收斂時間。

This paper presents the studies of microwave image reconstructions that are approached based on the time-domain technique (finite difference time domain, FDTD) and optimization method for 2-D inhomogeneous dielectric cylinders. The dielectric cylinder is buried in a slab media. For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering asynchronous particle swarm optimization (APSO) is utilized to determine the permittivity of the cylindrical scatterer with arbitrary cross section.  
In order to explore the unknown dielectric cylinder in a three-layered slab medium, an electromagnetic pulse can be conducted to illuminate the cylinder, for which the scattered E fields can then be measured. The inverse problem is then resolved by an optimization approach. The idea is to perform the image reconstruction by utilization of Asynchronous Particle Swarm Optimization to minimize the discrepancy between the measured and calculated scattered field data. Three times,five times and ten times of the unknows population size are also investigated. 
The suitability and efficiency of applying APSO for microwave imaging of 2D dielectric cylinders are examined in this dissertation. Numerical results show that even when the initial guesses are far away from the exact one, good reconstruction can be obtained by Asynchronous Particle Swarm Optimization. However, the APSO can reduce the convergent speed in terms of the number of the objective function calls.

目錄 
第一章 
簡介………………………………………………………………...1 
1.1 研究動機與相關文獻………………………………………………1 1.2 本研究之貢獻………………………………………………………6 1.3 各章內容簡述………………………………………………………6 第二章 
時域有限差分法…………………………………………………...7 
2.1 馬克斯威爾方程式………………………………………………....7 
2.2 馬克斯威爾方程式於FDTD方法中差分離散現………………....10 
2.2.1 Yee單胞(Yee cell)的空間解析方法與蛙跳式(leap-frog)時間步進計算方法………………………………………………………….10 2.2.2 FDTD更新方程式……………………………………………….12 2.3 數值色散現象與Courant穩定準則………………………………13 2.4 吸收邊界條件(Absorbing Boundary Conditions)………………...15 2.5 非同步粒子群聚最佳化法(Asynchronous Particle Swarm Optimization)…………………….…………………………….....17 
第三章 
埋藏於三層空間中二維均勻介質柱體影像建………………….26 
3.1 模擬環境與相關參數設定………………………………………..26 
3.2 目標函數與最佳化方法搜尋參數………………………………..27 
3.3 數值模擬結果………………………..………………………28 
第四章 
結論………………………………………………………………...43 
參考文獻....................................................44 
圖目錄 
圖2.1 FDTD中二維Yee單胞於TMz模態(左)與TEz模態(右)表示圖.11 圖2.2 FDTD中電磁場計算時序圖............................11 圖2.3 粒子群聚法流程圖..................................18 圖2.4 粒子群聚法中於二維目標函數等位線圖.................20 圖2.5 二維問題中，三種不同邊界條件示意圖。 與 表示更新後的粒子位置與速度.............................................22 圖2.6改良式粒子群聚法流程圖.............................25 圖3.1埋藏於三層空間中任意形狀非均勻介質柱體模擬環境示意圖27 圖3.2重建例子一之原始結構示意圖………………………………..30 圖3.3族群大小3倍重建例子一示意圖…………………….……..…31 圖3.4族群大小5倍重建例子一示意圖……………………………...31 圖3.5族群大小10倍重建例子一示意.........................32 圖3.6加入高斯雜訊後重建例子一示意圖………………………...33 圖3.7重建例子二之原始…………………………………….… ….35 圖3.8族群大小3倍重建例子二示意圖……………….…………….35 圖3.9族群大小5倍重建例子二示意圖…………… ……………….36 圖3.10族群大小10倍重建例子二示意圖…………………………..36 圖3.11加入高斯雜訊後重建例子二示意圖…………………………37 圖3.12重建例子三之原始……………………………………………39 圖3.13族群大小3倍重建例子三示意圖……………………………40 
圖3.14族群大小5倍重建例子三示意圖……………………………40 
圖3.15族群大小10倍重建例子三示意圖………………………..41 
圖3.16加入高斯雜訊後重建例子三示意圖…………………....42 
表目錄
表3.1三種倍數於例子一之相對誤差率統計數據分析……32 
表3.2三種倍數於例子一之相對誤差率統計數據分析…………...37 表3.3三種倍數於例子三之相對誤差率統計數據分析………….…41

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