本論文是研究具有角形之金屬目標導體的電磁成像，目的是藉由測量到的散射場來重建具有角形之目標導體形狀。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。方便起見，假設目標的形狀函數為二維空間並以極座標型式表示，根據散射理論，散射電場積分內的被積分式(函數)包含了以極座標表示之目標形狀函數及其對角度之微分。對於平滑輪廓之目標物來說，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。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。在三次樣條插值的使用中，角形之非平滑目標物可以被有效地建模且此目標物形狀模型可以便利地應用於散射電場積分中，所以此時目的將變為取得三次樣條插值之每條線段的多項式係數來重建出目標物之形狀。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，接著藉由使用差分進化策略的魚群演算法來更新座標點，對於每次猜測目標物的形狀 ( 即三次樣條插值之座標點產生各線段多項式組合成之形狀 )，在相同測量位置進行散射電場的計算，然後比較計算的散射電場與實際的散射電場並持續地更新猜測形狀直到散射電場的相對誤差小於預設門檻，從而目標物的形狀可以被成功地重建出來即達到電磁成像。數值模擬結果顯示，本論文題出的電磁成像算法可以成功地重建角形之非平滑目標物，如正方形、三角形、梯形輪廓。魚群演算法結合差分進化本質上是一種進化的優化演算法，它不需要任何梯度運算，使得它可以實現複雜的優化系統甚至是黑盒子系統。該研究可應用於複雜目標的雷達探測，如船舶。

In this thesis, the electromagnetic imaging of a conducting target with corners is given. 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 (i.e., function for integration) 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 Fish Swarm algorithm together with differential evolution. For each temporarily guessed shape (i.e., cubic spline interpolation) 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 and trapezoid contours. The Fish Swarm algorithm together with differential evolution is inherently an evolutionary optimization algorithm. It does not require any gradient operation so that it can achieve global optimization of complicated or even black-box systems. This study can be applied to radar detection of complicated targets such as ships.

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