本論文將對週期性非平坦表面進行研究，首先運用馬克斯威爾方程式、週期性格林函數和邊界條件推導出正散射理論之積分方程式，再配合動差法將其轉為矩陣，計算散射場，並進行數值模擬。吾人運用所得到的積分方程式及量測到的散射場，將逆散射問題轉化成最佳化問題，搭配自我適應之動態差異型演化法來處理電磁成像的大量未知數。對於不同的週期長度、介電常數和表面形狀參數，使用自我適應之動態差異型演化法(SADDE)重建，測試其對週期性非平坦表面的重建結果和抗雜訊能力。
利用自我適應之動態差異性演化法重建出週期性非平坦表面，不論初始的猜測值如何，自我適應之動態差異性演化法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，成功的重建出表面形狀函數、週期長度和相對介電常數，模擬結果顯示在雜訊低於1%的情況下，吾人都可得到良好的實驗結果。

This thesis presents the reconstruction of the periodic rough surface.By self-adaptive dynamic differential evolution(SADDE) using the Maxwell equations, the periodic Green functions and the boundary conditions, we can get the integral equations,then convert them into matrix form by the method of moment(MoM). We can reconstruct the shape of periodic rough surface through the application of the integral equations and the measured scattered field. The inverse scattering problem is transformed into an optimization problem and solved by self-adaptive dynamic differential evolution(SADDE) which can process a lot of unknowns for the electromagnetic imaging problems. The thesis tests the search ability and the resistance to noise for SADDE by different initial guesses for the periodic rough surface. 
By using the SADDE to reconstruct the periodic rough surface, numerical results show that the SADDE converges to the overall extreme value (global extreme) regardless of the initial guess. Even if the initial guess is far away from the actual value, SADDE can get the correct shape,the periodic length and the relative permittivity of the periodic rough surfaces. Simulation results also show that when the noise in less than 1%, we can also reconstruct the good result.

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 週期性非平坦表面之逆散射理論	9
2.1 正散射的理論公式推導	9
2.2 動差法求正散射公式	13
2.3 正散射的理論數值驗證	16
第三章  自我適應之動態差異型演化法(Self-Adaptive Dynamic
Differential Evolution)	18
第四章  數值分析及模擬結果	26
4.1 模擬環境介紹	26
4.2 模擬結果	29
第五章 結論	48
參考文獻	50
附錄一 加快週期性格林函數收斂的方法	56
附錄二 當y≈y'時改進週期性格林函數收斂的方法	58

圖目錄
圖2.1 週期性非平坦表面示意圖	10
圖2.2 驗證正散射模擬示意圖	17
圖3.1 自我適應之動態差異型演化法流程圖	20
圖3.2 自我適應之動態差異型進化法中突變方法一的示意圖	22
圖3.3 自我適應之動態差異型進化法中突變方法二的示意圖	23
圖4.1 模擬環境示意圖	27
圖4.2  DF、DP之趨勢圖(a)d=0.04m (b)d=0.05m	30
圖4.2  DF、DP之趨勢圖(c)d=0.06m (d)d=0.07m	31
圖4.2  DF、DP之趨勢圖(e)d=0.083m	32
圖4.3 DF、DEPS之趨勢圖(a)d=0.04m (b)d=0.05m	33
圖4.3 DF、DEPS之趨勢圖(c)d=0.06m (d)d=0.07m	34
圖4.3 DF、DEPS之趨勢圖(e)d=0.083m	35
圖4.4 表面之重建結果(a)d=0.04m (b)d=0.05m	36
圖4.4 表面之重建結果(c)d=0.06m (d)d=0.07m	37
圖4.4 表面之重建結果(e)d=0.083m	38
圖4.5 不同週期長度之重建錯誤率趨勢圖	39
圖4.6 d=0.06m加入不同雜訊比之DF、DP和DEPS趨勢圖	41
圖4.7 例子二之DF、DP趨勢圖	43
圖4.8 例子二之DF、DEPS趨勢圖	43
圖4.9 例子二之表面重建結果	44
圖4.10 例子二加入不同雜訊比之DF、DP和DEPS趨勢圖	44
圖4.11 例子三之DF、DP趨勢圖	46
圖4.12 例子三之DF、DEPS趨勢圖	46
圖4.13 例子三之表面重建結果	47
圖4.14 例子三加入不同雜訊比之DF、DP和DEPS趨勢圖	47

表目錄
表2.1 切不同段數之三個測量點的散射場值	16
表4.1 不同週期長度之重建錯誤率	39

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