Cubic-spline expansion for a two-dimensional periodic conductor in free space

Article type: Research Article

Authors: Chien, Wei^a | Huang, Chung-Hsin^a | Chiu, Chien-Ching^a

Affiliations: [a] Electrical Engineering Department, Tamkang University, Tamsui, Taiwan. E-mail: chiu@ee.tku.edu.tw

Abstract: This paper presents a computational approach to the imaging of a two-dimensional periodic conductor. Both cubic-spline method and trigonometric series for shape description are used and compared. A periodic conducting cylinder with unknown shape in free space and the scattered field is recorded outside. Based on the boundary condition and the recorded scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. The genetic algorithm is employed to find out the global extreme solution of the object function. It is found that the shape described by cubic-spline can be reconstructed. In such a case, Fourier series expansion will fail. Even when the initial guess is far away from the exact one, the cubic-spline expansion and genetic algorithm can avoid the local extreme and converge to a global extreme solution. Numerical results are given to show that the shape description by using cubic-spline method is much better than that by the Fourier series. In addition, the effect of Gaussian noise on the reconstruction is investigated.

DOI: 10.3233/JAE-2006-780

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 24, no. 1-2, pp. 105-114, 2006