电子学报 ›› 2016, Vol. 44 ›› Issue (2): 385-391.DOI: 10.3969/j.issn.0372-2112.2016.02.020

• 学术论文 • 上一篇    下一篇

时域反演德鲁色散媒质的电磁逆散射技术

刘广东1, 葛新同2   

  1. 1. 阜阳师范学院物理与电子工程学院, 安徽阜阳 236037;
    2. 阜阳师范学院数学与统计学院, 安徽阜阳 236037
  • 收稿日期:2015-05-22 修回日期:2015-08-11 出版日期:2016-02-25 发布日期:2016-02-25
  • 作者简介:刘广东 男,1972年生于江苏灌云.现为阜阳师范学院物电学院副教授、工学博士.研究方向为微波医学成像.E-mail:liu_guang_dong@126.com;葛新同 男,1966年生于安徽蒙城.现为阜阳师范学院数学与统计学院讲师、工学博士.研究方向为不确定最优控制及金融数学.E-mail:gxtong01234@163.com
  • 基金资助:

    国家自然科学基金(No.51271059);安徽高校省级自然科学研究重点项目(No.KJ2014A193);安徽省科技计划项目(No.1501031114);阜阳师范学院自然科学研究项目(No.2014FSKJ14)

An Electromagnetic Inverse Scattering Technique in Time Domain for Drude Dispersive Media

LIU Guang-dong1, GE Xin-tong2   

  1. 1. School of Physics and Electronic Engineering, Fuyang Normal College, Fuyang, Anhui 236037, China;
    2. School of Mathematics and Statistics, Fuyang Normal College, Fuyang, Anhui 236037, China
  • Received:2015-05-22 Revised:2015-08-11 Online:2016-02-25 Published:2016-02-25

摘要:

德鲁(Drude)经验模型常用于描述等离子体、金属等媒质的电色散特性.利用宽带的时域测量数据直接反演电参数,相比单频(频域)技术而言,具有信息量大、成像分辨率高的优势.时域直接反演色散媒质电参数的主要困难在于它们是频率相关的.为了克服该困难,本文提出了一种时域电磁(EM)逆散射新技术:转而同时反演德鲁模型的4类频率无关的模型参数.该技术的主要环节为:(1)描述为含正则化项的约束最小化问题;(2)转化为无约束最小化问题;(3)解析导出梯度;(4)分别利用时域有限差分(FDTD)法、共轭梯度(CG)法迭代求解正演、反演子问题.在一维(1-D)、二维(2-D)两个数值算例中,所需的测量数据也由FDTD仿真值代替,并加入了加性高斯白噪声(AWGN).反演结果初步证实了该技术的性能.

关键词: 电磁逆散射, 德鲁色散媒质, 正则化, 时域有限差分法, 共轭梯度法

Abstract:

Drude empirical models are frequently used for description of dispersion characteristics of many media, such as plasmas, and metals.Reconstructed electrical properties by directly using wide-band measured data in time domain, are better than those by application of any single-frequency technique, in amount of information, and resolution of generated images.One of difficulties in time-domain reconstruction of dispersive characteristics is their frequency correlation.In order to overcome this difficulty, an electromagnetic (EM) inverse scattering technique in time domain is proposed, in which four kinds of frequency-independence parameters from a Drude model are estimated simultaneously.Main segments for the technology are:(1) formulating the inverse scattering problem as a constrained minimization problem with a term of regularization;(2) transforming resulting problem into an unconstrained minimization one;(3) deriving a set of closed gradients of its cost functional;(4) solving iteratively resulting forward and backward sub-problems by a finite-difference time-domain (FDTD) method and any conjugate gradient (CG) algorithm, respectively.In one-dimensional (1-D) and two-dimensional (2-D) numerical examples, necessary measurements are replaced by simulated fields based on the FDTD method, and it is assumed that they are corrupted by an additive white Gaussian noise (AWGN).Numerical results preliminarily confirm performance of the inversion methodology.

Key words: electromagnetic (EM) inverse scattering, Drude dispersive media, regularization, finite-difference time-domain (FDTD) method, conjugate gradient (CG) algorithm

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