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## Investigation of the scattering characteristics from discrete random scatterers based on recursive aggregate T-matrix algorithm

Cui Shuai, Zhang Xiao-Juan, Fang Guang-You
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• #### 摘要

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式，并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型. 通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应，结果表明：矢量递归T矩阵算法具有很高的计算精度，算法中包含多散射体间的高阶散射效应，因此能够精确计算多散射体总的散射效应. 本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.

#### Abstract

In this paper, we derive in vector form the recursive aggregate T-matrix algorithm based on the principles of electromagnetic wave multipole expansion of vector spherical wave functions and the vector addition theorem. After that we establish a three-dimensional electromagnetic scattering model for multiple spherical scatterers by simulating the scattering of subsurface discrete random scatterers using the derived algorithm. Calculating the scattering from different sizes, randomly distributed spherical scatteres and analyzing the high-order scattering effects, we can conclude that the vector recursive aggregate T-matrix algorithm has a high computation accuracy, and contains the interaction effects among multiple scatterers, therefore we can calculate the total scattering effects accurately from multiple scatterers. The established model can be served as a powerful tool in applications for retrieving the impact caused by the scattering of subsurface discrete random scatterers in soil moisture from radar measurements.

#### 作者及机构信息

###### 1. 中国科学院电磁辐射与探测技术重点实验室, 北京 100190; 2. 中国科学院大学, 北京 100190
• 基金项目: 国家自然科学基金（批准号：61172017）资助的课题.

#### Authors and contacts

###### 1. Key Laboratory of Electromagnetic Radiation and Sensing Technology, Chinese Academy of Sciences, Beijing 100190, China; 2. University of Chinese Academy of Sciences, Beijing 100190, China
• Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61172017).

#### 参考文献

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#### 施引文献

•  [1] Duan X Y, Moghaddam M 2011 Geoscience and Remote Sensing Symposium (IGARSS), 2011 IEEE International Vancouver, July 24, 2011, p1227 [2] [3] Zhang Y, Zhang X J, Fang G Y 2012 Acta Phys. Sin. 61 184203 (in Chinese) [张宇, 张晓娟, 方广有 2012 物理学报 61 184203] [4] [5] [6] Zhang Y, Zhang X J, Fang G Y 2013 Acta Phys. Sin. 62 044204 (in Chinese) [张宇, 张晓娟, 方广有 2013 物理学报 62 044204] [7] [8] Qi Y Z, Huang L, Zhang J G, Fang G Y 2013 Acta Phys. Sin. 62 234201 (in Chinese) [齐有政, 黄玲, 张建国, 方广有 2013 物理学报 62 234201] [9] [10] Lin Z W, Xu X, Zhang X J, Fang G Y 2011 Chin. Phys. Lett. 28 014101 [11] Lin Z W, Xu X, Zhang X J, Fang G Y 2011 Chin. Phys. Lett. 28 014102 [12] [13] [14] Foldy L L 1945 Phys. Rev. 67 107 [15] Lax M 1952 Phys. Rev. 85 261 [16] [17] Peterson B, Strom S 1974 J. Acoust. Soc. Am. 56 771 [18] [19] [20] Waterman P C 1956 Proc. IEEE 53 805 [21] Waterman P C 1961 J. Math. Phys. 2 700 [22] [23] [24] Twersky V 1967 J. Math. Phys. 8 589 [25] [26] Liang C, Lo Y T 1967 Radio Sci. 2 1481 [27] [28] Bruning J H, Lo Y T 1971 IEEE Trans. Antennas Propagat. AP-19 378 [29] Peterson B, Strom S 1973 Phys. Rev. D 8 3667 [30] [31] Han G X, Han Y P 2010 Acta Phys. Sin. 59 2434 (in Chinese) [韩国霞, 韩一平 2010 物理学报 59 2434] [32] [33] Cui S, Zhang X J, Fang G Y 2013 Chin. Phys. Lett. 30 034101 [34] [35] Cui S, Zhang Y, Zhang P, Zhang X J, Fang G Y 2011 Geoscience and Remote Sensing Symposium (IGARSS), 2011 IEEE International Vancouver, July 24, 2011, p289 [36] [37] [38] Wang H H, Sun X M 2012 Chin. Phys. B 21 054204 [39] Ulaby T F, Moore K R, Fung K A 1981 Microwave Remote Sensing: Active and Passive (Vol. 3) (Addison: Wesley Publishing Company) p1085 [40] [41] Chew W C 1989 Micro Opt. Tech. Lett. 2 380 [42] [43] Wang Y M, Chew W C 1990 Micro Opt. Tech. Lett. 3 102 [44] [45] [46] Chew W C, Wang Y M 1990 Micro Opt. Tech. Lett. 3 164 [47] Chew W C, Gurel L, Wang Y M, Otto G, Wagner R 1992 IEEE Trans Microwave Theory Tech. 40 716 [48] [49] [50] Chew W C, Friedrich A J, Geiger R 1990 IEEE Trans Geosci Remote 28 207 [51] [52] Chew W C, Wang Y M, Gurel L 1992 J. Electromag Waves Appl. 6 1537 [53] Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particles (New York: A Wiley-Interscience Publication) p57 [54] [55] Tsang L, Kong J A, Ding K H 2000 Scattering of Electromagnetic Waves-Theories and Applications (New York: A Wiley-Interscience Publication) p2 [56] [57] Stein S 1961 Quarterly Journal Appl. Math. 19 15 [58] [59] Cruzan O R 1962 Quarterly Journal Appl. Math. 20 33 [60] [61] Wittmann R C 1988 IEEE Trans Antennas Propagat 36 1078 [62] [63] Tsang L, Kong J A, Ding K H 2001 Scattering of Electromagnetic Waves-Numerical Simulations (New York: A Wiley-Interscience Publication) p533 [64] [65] Chew W C 1995 Waves and Fields in Inhomogeneous Media (New York: IEEE Press) p430 [66] [67] Wang Y H, Zhang Y M, Guo L X 2011 Acta Phys. Sin. 60 021102 (in Chinese) [王运华, 张彦敏, 郭立新 2011 物理学报 60 021102] [68] [69] Xu C W, Feng Z, Liu L N, Niu D P 2012 Microwave and Millimeter Wave Circuits and System Technology (MMWCST), 2012 International Workshop on, Chengdu, April 19-20, 2012, p1 [70] [71] [72] Khajeahsani M S, Mohajeri F, Abiri H 2011 IEEE Trans Antennas Propagat 59 3819 [73] Yan W Z, Du Y, Wu H 2008 PIER 85 39 [74] [75] Wang A Q, Guo L X, Chai C 2011 Chin. Phys. B 20 050202
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##### 出版历程
• 收稿日期:  2014-01-27
• 修回日期:  2014-03-25
• 刊出日期:  2014-08-05

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