時域中重建二維非均勻介質柱體之研究

Time Domain Inverse Scattering of 2-D Inhomogeneous Dielectric Cylinders

陳紹仁(Shoa-Jen Chen)

指導教授 ： 丘建青

淡江大學/工學院/電機工程學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00161

摘要

本論文研究埋藏於半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半空間中二維非均勻介質柱體之特性參數。
為了探究埋藏於半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，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動態差異形演化法（DDE）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介電參數。
本論文探討以動態差異演化法對於半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。動態差異型演化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。

關鍵字

有限時域差分法 ； 時域逆散射 ； 動態差異演化法

並列摘要

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 half-space media. For the forward scattering the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering Dynamic Differential Evolution (DDE) is utilized to determine the permittivity of the cylindrical scatterer with arbitrary cross section.
In order to explore the unknown dielectric cylinder in half-space , 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 Dynamic Differential Evolution to minimize the discrepancy between the measured and calculated scattered field data. Dynamic Differential Evolution is tested and employed to search the parameter space to determine the permittivity of the dielectric cylinder.
The suitability and efficiency of applying DDE 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 Dynamic Differential Evolution. However, the DDE can reduce the convergent speed in terms of the number of the objective function calls.

並列關鍵字

Time Domain Inverse scattering ； Finite Difference Time Domain ； Dynamic Differential Evolution

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