本論文模擬研究介質掩埋物體的電磁成像重建。設有一空間分成兩個半空間，ㄧ未知的不均勻介質物體掩埋在其中一半空間，吾人可以在另一半空間中安排入射波，其入射波採用多方向連續照射之方式，以收集較完整之材質特性資訊。於理論推導方面，本研究考慮完整之非線性公式，以提高解之精確度。
    數值方法之執行過程，即使介電物體具有較複雜之材質特性分佈(不平滑)，或者介電體材質特性分佈與環境之材質特性具有較高之對比度，此數值方法亦能適用。
    就大部分較簡單之例子而言，遺傳演算法即可得到相當良好之解。然而，對於較複雜之例子，即考驗著遺傳演算法之強健性。本論文以演傳演算法所得之解，當作牛頓法之初始猜測值。藉由遺傳演算法之全域搜尋特性，以求得可接受之解，期望此解對於區域性搜尋之牛頓法而言，可能為適當之初始猜測值。串疊之方法比較單一遺傳演算法，或者單一牛頓迭代法，其解之精確度勢必較高。本研究模擬之數值結果顯示，此串疊之數值方法運用於重建非均勻介電物體之材質特性分佈，得到良好之重建結果。

In this paper, a cascaded method is employed to determine the permittivity distribution of a dielectric cylinders buried in a half-space. Assume that dielectric cylinders of unknown permittivity distribution is buried in one half-space and scatters the field incident from another half-space where the scattered filed is measured. 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. A cascaded method which composed a genetic algorithm (GA) and a Newton iteration is used to maximize the objective function. First, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a steady-state genetic algorithm (SSGA). Then, the solution obtained by the SSGA is taken as an initial guess for the Newton-type iteration method. Numerical results show that the performance of this combination method is better than the individual SSGA and the individual Newton-type iteration method. Satisfactory reconstruction has been obtained by using this cascaded method.

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.............................................................................7
1.3 各章內容簡述.............................................................................8
第二章	非均勻介電物體之電磁成像......................................................9
    2.1 理論推導.....................................................................................9
    2.2 數值方法.....................................................................................12
       2.2.1 差動法於積分方程式之應用............................................12
       2.2.2 散射場之計算與.... .............................................. ............14
       2.2.3 遺傳演算法........................................................... ............14
       2.2.4 遺傳演算法於逆散射之應用............................................24
       2.2.5 牛頓迭代法於逆散射之應用............................................25
       2.2.6 串疊方法於逆散射之應用................................................27
第三章	數值模擬結果..............................................................................31
第四章	結論..............................................................................................41
參考文獻....................................................................................................46


圖目錄
圖2.1在半空間中，非均勻介質物體在X,Y平面上的示意圖............29
圖2.2 遺傳演算法之流程圖...................................................................30
圖3.1 模擬之環境結構圖.......................................................................35
圖3.2 第一個例子之介電係數分佈圖 (a) (b) (c)..................................36
圖3.3 第二個例子之介電係數分佈圖 (a) (b) (c)..................................37
圖3.4 第三個例子之介電係數分佈圖 (a) (b) (c)..................................38
圖3.5 第四個例子之介電係數分佈圖 (a) (b) (c)..................................39
圖3.5 第四個例子之介電係數分佈圖 (d) (e)........................................40




表目錄
表2.1 遺傳演算法相關之名詞解釋與中英對照表................................23

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