利用TE入射波重建掩埋完全導體之影像

本論文之目的在於研究利用遺傳演算法對完全導體的影像重建問題。針對不同平面波入射的情況，就完全導體的逆散射問題進行探討。首先探討完全導體掩埋在半空間介質中的逆散射，將一個未知形狀、未知材質的二維完全導體掩埋在半空間介質中，吾人在第一層以TE極化電磁波照射掩埋於第二層的物體，並於第一層量得其散射場。吾人將利用接收到的散射場及適當的邊界條件，導出一組非線性積分方程式，再利用動差法將此積分方程式化為矩陣形式，把成像問題化成一個求最佳化問題。再引用遺傳演算法將逆散射問題轉成求解最佳化的問題。遺傳演算法是一種模擬自然界生物進化的搜尋法則，利用簡單的位元複製、交配及突變，可完成搜尋的程序。不論初始的猜測值為何，遺傳演算法總會收斂到整體的極值(global extreme)，而非只收斂於局部極值，藉此可重建物體的形狀函數及導電率。所以在數值模擬中，即使初始的猜測值與實際值相去甚遠，我們仍可求得精準的數值解，成功的重建出物體形狀函數與導電率。而以微分為基礎求取極值的方法(calculus-based method)，常會陷入區域極值(local extreme)的陷阱裡。最後將電磁成像的結果與原先假設者做比較，藉以驗證並改進電磁成像理論。

關鍵字

完全導體；遺傳演算法；半空間； TE極化電磁波

並列摘要

The paper presents a computational approach to the image reconstruction of a perfectly conductor cylinder illuminated by transverse electric (TE) waves. A perfectly conducting cylinder of unknown shape buried in one half-space and scatters the incident wave from another half-space where the scattered field is recorded. 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. The steady state genetic algorithm is then employed to find out the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, good reconstruction can be obtained. In such a case, the gradient-based methods often get trapped in a local extreme. In addition, the effect of different noise on the reconstruction is investigated.

並列關鍵字

Electromagnetic imaging ； Transverse electric (TE) ； Half-space structure ； Perfect Conductor ； Steady-state genetic algorithm

參考文獻

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國際替代計量

利用TE入射波重建掩埋完全導體之影像

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