本論文是研究一個未知形狀及表面可變導電率的不完全導體之電磁成像，利用TM極化波照射於物體上，然後測量物體外的散射場，經由數學計算來重建具有角形的物體形狀及其內部特性。對於非完全導體之邊界條件，可藉由表面阻抗的概念配合導體表面感應電流，可導出非線性積分方程式，然後使用動差法求得正散射公式。換句話說，電磁成像是透過求解散射電場的非線性積分方程來獲得目標之形狀函數，吾人假設目標的形狀函數為二維空間並以極座標型式表示，形狀函數可以簡單地以少數項次的傅立葉級數來表示，然而當目標物為非平滑形狀或甚至包含角形，此時傅立葉級數則無法有效地表達出目標物輪廓，而且描述複雜形狀往往造成無法得到最佳收斂解。三次樣條插值的描述方式則可在較少的變數個數，獲得良好的形狀描述結果，故本研究利用極座標型式的三次樣條插值來建構具有角形之非平滑目標物的輪廓。在本研究中假設環境為自由空間且所有的散射電場都是藉由動差法來做數值計算而得，以不同方向入射的平面波照射目標物，對於每個入射方向，以等角、等距的位置來搜集散射電場，這些位置真正的散射電場可以通過實際測量或理論計算而來。初始猜測三次樣條插值的座標點來產生各線段多項式係數值，接著藉由互相吸引行為的螢火蟲演算法、鄰近吸引的螢火蟲演算法與螺旋氣泡網捕獵策略的鯨魚演算法來更新座標點，透過疊代來逼近目標物之形狀函數，且在相同的量測位置計算散射電場，並將計算出的散射電場與真正的散射電場進行比較，直到散射電場的相對誤差低於預設值，從而目標物的形狀可以被成功地重建出來。最後數值模擬結果顯示，本論文題出的電磁成像方法可以成功地重建具角形之非平滑目標物體，如正方形、三角形、梯形、星形、楓葉形的輪廓。吾人使用螢火蟲演算法、變形螢火蟲演算法與鯨魚演算法來比較電磁成像，鯨魚演算法可以減少計算正散射的疊代次數，重建實際物體的效能遠優於螢火蟲演算法與變形螢火蟲演算法，主要是鯨魚演算法有隨機搜索捕食的機制使其收斂時不會陷入區域最佳解，而且收斂時間也相當穩定，實驗結果顯示，利用鯨魚演算法求解可獲得大幅改善。

This thesis is to study the electromagnetic imaging of an imperfect conductor with unknown shape and surface variable conductivity. The goal is to reconstruct the shape of a conducting target with corners by collecting scattered electric fields. The electromagnetic imaging is to obtain the target’s shape function by solving a nonlinear integral equation of scattered electric fields. For convenience, the target’s shape function is assumed to be two dimensional and is expressed as polar coordinates. According to scattering theories, the integrand within the integral of scattered electric fields contains the target’s shape function and its derivative with respect to angle in polar coordinates. For a target with smooth contours, the shape function can be easily expressed as a Fourier series with only a small number of terms. However, as the target is non-smooth or even contains corners, it becomes inefficient to express the target’s contour as a Fourier series. Alternatively, this study utilizes the cubic spline interpolation in polar coordinates to model the contour of a non-smooth target with corners. With the use of cubic spline interpolation, the contour of a non-smooth target with corners can be efficiently modeled and such a model of the target’s shape can be easily treated in implementing integrals of scattered electric fields. The goal becomes to obtain the polynomial coefficients of cubic spline interpolation. In this study, the environment is assumed to be free space and all scattered electric fields are numerically calculated by the Moment Method. The target is illuminated by plane waves from different incident directions. For each incident direction, the scattered electric fields are collected in several equiangular and equidistant locations. The true scattered electric fields at these locations can be obtained by practical measurement or theoretical calculation. Values for polynomial coefficients of cubic spline interpolation are initially guessed, and are then updated by the Firefly algorithm, Firefly algorithm with neighborhood attraction and Whale algorithm. For each temporarily guessed shape of the target, scatted electric fields at the same measurement locations are calculated. These calculated electric fields of scattering are then compared with the true scattered electric fields. Update of guessed shape will continue until the relative error of scattered electric fields is below a threshold. Thus the target’s shape can be successfully reconstructed and the electromagnetic imaging is achieved. Numerical simulation results show that the proposed electromagnetic imaging algorithm can successfully reconstruct a non-smooth target with corners such as rectangular, triangular, trapezoid, star, maple leaf contours.

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