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.
