Inverse scattering for an impedance cylinder buried in a dielectric cylinder
Inverse scattering for an impedance cylinder buried in a dielectric cylinder
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DOI：
10.1080/17415970802131760
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发表时间：
2009-01
影响因子：
1.3
通讯作者：
R. Kress;F. Yaman;A. Yapar;I. Akduman
中科院分区：
文献类型：
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作者：
R. Kress;F. Yaman;A. Yapar;I. Akduman
研究了埋在任意形状圆柱形介质中的具有非均匀阻抗边界的任意形状圆柱形物体的逆散射问题。给定阻抗物体和介质的形状，反问题包括从入射时谐平面波的测量远场图重建非均匀边界阻抗。扩展了Akduman和Kress[任意形状的非均匀阻抗圆柱的正逆散射问题]提出的方法。对于均匀背景介质中的阻抗圆柱，用边界积分方程求解了正散射和逆散射问题。无线电科学38 (2003),pp. 1055-1064。对于反问题，将散射场表示为势会导致密度的第一类严重不适定的线性积分方程。对于它们的稳定数值解，采用了Tikhonov正则化。在已知散射场的情况下，边界阻抗函数可以由边界条件直接求得，也可以用最小二乘法求得。给出了逆方法的数学基础，并通过数值算例说明了逆方法的可行性。
An inverse scattering problem is considered for arbitrarily shaped cylindrical objects that have inhomogeneous impedance boundaries and are buried in arbitrarily shaped cylindrical dielectrics. Given the shapes of the impedance object and the dielectric, the inverse problem consists of reconstructing the inhomogeneous boundary impedance from a measured far field pattern for an incident time-harmonic plane wave. Extending the approach suggested by Akduman and Kress [Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape. Radio Sci. 38 (2003), pp. 1055–1064] for an impedance cylinder in an homogeneous background medium, both the direct and the inverse scattering problem are solved via boundary integral equations. For the inverse problem, representing the scattered field as a potential leads to severely ill-posed linear integral equations of the first kind for the densities. For their stable numerical solution Tikhonov regularization is employed. Knowing the scattered field, the boundary impedance function can be obtained from the boundary condition either by direct evaluation or by a least squares approach. We provide a mathematical foundation of the inverse method and illustrate its feasibility by numerical examples.