本論文研究埋藏於自由空間、半空間與三層空間中二維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不同空間中二維均勻介質柱體之特性參數。其中，對於描述形狀的方法，於正散射我們使用傅立葉函數展開(Fourier series expansion) ，並於逆散射中使用三次仿樣函數展開（cubic spline），另外，為了使柱體的形狀更為圓滑我們使用了次網格技術。 為了探究埋藏於不同空間中未知形狀的均勻介質柱體，概念上吾人可向散射體發射電磁脈波，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改良式粒子群聚法（PSO）、動態差異形演化法（DDE）與改良式基因法則（NU-SSGA）將逆散射問題轉化為求解最佳化問題。藉由量測而得的散射場以及計算而得的散射場數值互相比較，進而重建介電散射體的形狀函數、位置與介電參數。 本論文探討上述三種最佳化方法對於不同環境下的二維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，此三種最佳化方法皆可以成功地重建出柱體的位置、形狀與介電參數。在此三種最佳化方法收斂速度部份，動態差異型演化法與粒子群聚法可以大幅減少計算正散射次數，獲取優於基因法則效能並且減少逆散射問題收斂時間。 This dissertation presents the studies of microwave image reconstructions that are approached based on the time-domain technique (finite difference time domain, FDTD) and several optimization methods for a 2-D homogeneous dielectric cylinder. The dielectric cylinder is located in free space, or buried in half-space media, or embedded in a three-layered material medium, respectively. For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering several optimization methods are utilized to determine the shape, location and the permittivity of the cylindrical scatterer with arbitrary cross section. The subgirdding technique is implemented for the FDTD code in order to model the shape of the cylinder more smoothly. In order to describe an unknown cylinder with arbitrary cross section more effectively during the course of searching, the closed cubic-spline expansion is adopted to represent the scatterer contour instead of the frequently used trigonometric series. The former is still used in the forward scattering part. In order to explore the unknown dielectric cylinder in different environments, 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 some optimization scheme to minimize the discrepancy between the measured and calculated scattered field data. Three optimization schemes are tested and employed to search the parameter space to determine the shape, location and permittivity of the dielectric cylinder. They are the modified particle swarm optimization (MPSO), the dynamic differential evolution (DDE) and the non-uniform steady state genetic algorithm (NU-SSGA).
The suitability and efficiency of applying the above methods for microwave imaging of a 2D dielectric cylinder 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 all these optimization methods. However, the DDE and MPSO outperform the NU-SSGA regarding the reconstruction accuracy and the convergent speed in terms of the number of the objective function calls.
