随机粗糙表面电磁散射解析方法的研究
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摘要
随机粗糙表面电磁散射理论的研究,因为它在军事和海洋等诸多领域的重要应用,成为专家学者们关注的热点。本文针对粗糙面电磁散射的相关解析理论进行了较深入的研究工作。
本文首先介绍了粗糙面电磁散射的基本理论,讨论了包括微扰法和基尔霍夫近似方法(KA)在内的经典的解析计算方法。传统的驻留相位KA算法在粗糙面上点的斜率计算中,采用的是在稳相点展开的零阶近似,忽略了表面上点的随机特性;并且在计算散射强度时,是将粗糙面上任意一对邻近点的高度和斜率被看成是相互独立的,即不相关的。事实上,只要粗糙面上任一对邻近点之间的水平距离不大于相关长度(但仍大于入射波长),它们的高度和对方的斜率就是相关的。并且这种高度与斜率的相关性对散射强度的贡献是明显的,应当计入散射强度的计算中去。
本文就以上问题,针对二维高斯粗糙面提出了新的KA改进算法——COR-KA算法。与传统的KA算法相比,该算法的改进之处在于:(1)在粗糙面任意一点上的斜率表达采用的是稳相点展开的一阶近似,进而能用统计的方法处理随机表面上任一点的局部坐标、斜率和菲涅尔反射系数(传统KA算法采用的是稳相点展开的零阶近似,忽略了粗糙面上点的随机特性);(2)引入了二维粗糙表面两点间高度及法向量的联合概率分布函数(六维)来表征高度和斜率的随机分布规律,完整地考虑了粗糙面两点间高度和高度、高度和斜率、斜率和斜率的相关性。
文中详细给出了COR-KA算法计算二维粗糙面散射特性的推导过程,得到了散射系数的解析表达式,建立了一种更准确的二维粗糙面散射理论模型。最后将COR-KA算法的仿真结果与矩量法(MOM)及传统的KA算法等其它相关算法的仿真结果进行对比,验证了COR-KA算法的有效性。
The electromagnetic scattering from randomly rough surfaces has been attracting wide interest of researchers, thanks to their significant application in the spheres of military, oceanography and so on. This dissertation makes intensive research on electromagnetic(EM) scattering from randomly rough surfaces from analytical theory.
In this paper, the fundamental theory of electromagnetic scattering from the rough surfaces is introduced; different methods of electromagnetic scattering from the rough surfaces including the small perturbation method and the Kirchhoff approximation are discussed. When using the conventional Kirchhoff approximation to calculate the slope of rough surface, people used to use zero-order approximation of the steady point, and neglect the random characteristics of surface. The height and slope of two neighboring points on rough surfaces are seen as independent, while calculating the scattering coefficient by using the conventional Kirchhoff approximation model. In fact, their height and the opponent’s slope could be related, if the level distance between any two neighboring points on rough surfaces is no more than the correlation length of rough surfaces (however, is more than the incident wave length). In addition, it is obvious that the contribution of the correlation of height and slope to scattering intensity, and it should be considered while calculating the scattering intensity.
On the above issues, a new KA algorithm is proposed for two-dimensional Gaussian rough surface, which is called COR-KA algorithm. Comparing the COR-KA algorithm with the conventional KA algorithm, there are two improvements between them. First, the slope at any point on the rough surface is presented by the first-order approximation of a steady point in COR-KA algorithm. And then statistical method can be adopted to process the local coordinates, the slope and the Fresnel’s reflection coefficient on the random surface(the conventional KA algorithm uses the zero-order approximation of a steady point, which overlooks the feature of the points on the randomly rough surfaces). Second, this algorithm introduces the heights and vector’s joint probability distribution function (6-dimensional) of two points to represent random distribution of height and slope, which fully describes the relevance of height and height, height and slope, slope and slope of the points on the two-dimensional rough surface.
In this paper, the derivation process of two-dimensional rough surface scattering of the COR-KA algorithms are detailed, and the analytical expressions of the scattering coefficient are acquired. And more accurately gains two-dimensional scattering model of rough surface. Finally, the paper makes a simulation of the COR-KA algorithms, and conventional KA, and compares and contrasts the results with MOM’s results. It shows that the effectiveness of the COR-KA algorithm.
本文首先介绍了粗糙面电磁散射的基本理论,讨论了包括微扰法和基尔霍夫近似方法(KA)在内的经典的解析计算方法。传统的驻留相位KA算法在粗糙面上点的斜率计算中,采用的是在稳相点展开的零阶近似,忽略了表面上点的随机特性;并且在计算散射强度时,是将粗糙面上任意一对邻近点的高度和斜率被看成是相互独立的,即不相关的。事实上,只要粗糙面上任一对邻近点之间的水平距离不大于相关长度(但仍大于入射波长),它们的高度和对方的斜率就是相关的。并且这种高度与斜率的相关性对散射强度的贡献是明显的,应当计入散射强度的计算中去。
本文就以上问题,针对二维高斯粗糙面提出了新的KA改进算法——COR-KA算法。与传统的KA算法相比,该算法的改进之处在于:(1)在粗糙面任意一点上的斜率表达采用的是稳相点展开的一阶近似,进而能用统计的方法处理随机表面上任一点的局部坐标、斜率和菲涅尔反射系数(传统KA算法采用的是稳相点展开的零阶近似,忽略了粗糙面上点的随机特性);(2)引入了二维粗糙表面两点间高度及法向量的联合概率分布函数(六维)来表征高度和斜率的随机分布规律,完整地考虑了粗糙面两点间高度和高度、高度和斜率、斜率和斜率的相关性。
文中详细给出了COR-KA算法计算二维粗糙面散射特性的推导过程,得到了散射系数的解析表达式,建立了一种更准确的二维粗糙面散射理论模型。最后将COR-KA算法的仿真结果与矩量法(MOM)及传统的KA算法等其它相关算法的仿真结果进行对比,验证了COR-KA算法的有效性。
The electromagnetic scattering from randomly rough surfaces has been attracting wide interest of researchers, thanks to their significant application in the spheres of military, oceanography and so on. This dissertation makes intensive research on electromagnetic(EM) scattering from randomly rough surfaces from analytical theory.
In this paper, the fundamental theory of electromagnetic scattering from the rough surfaces is introduced; different methods of electromagnetic scattering from the rough surfaces including the small perturbation method and the Kirchhoff approximation are discussed. When using the conventional Kirchhoff approximation to calculate the slope of rough surface, people used to use zero-order approximation of the steady point, and neglect the random characteristics of surface. The height and slope of two neighboring points on rough surfaces are seen as independent, while calculating the scattering coefficient by using the conventional Kirchhoff approximation model. In fact, their height and the opponent’s slope could be related, if the level distance between any two neighboring points on rough surfaces is no more than the correlation length of rough surfaces (however, is more than the incident wave length). In addition, it is obvious that the contribution of the correlation of height and slope to scattering intensity, and it should be considered while calculating the scattering intensity.
On the above issues, a new KA algorithm is proposed for two-dimensional Gaussian rough surface, which is called COR-KA algorithm. Comparing the COR-KA algorithm with the conventional KA algorithm, there are two improvements between them. First, the slope at any point on the rough surface is presented by the first-order approximation of a steady point in COR-KA algorithm. And then statistical method can be adopted to process the local coordinates, the slope and the Fresnel’s reflection coefficient on the random surface(the conventional KA algorithm uses the zero-order approximation of a steady point, which overlooks the feature of the points on the randomly rough surfaces). Second, this algorithm introduces the heights and vector’s joint probability distribution function (6-dimensional) of two points to represent random distribution of height and slope, which fully describes the relevance of height and height, height and slope, slope and slope of the points on the two-dimensional rough surface.
In this paper, the derivation process of two-dimensional rough surface scattering of the COR-KA algorithms are detailed, and the analytical expressions of the scattering coefficient are acquired. And more accurately gains two-dimensional scattering model of rough surface. Finally, the paper makes a simulation of the COR-KA algorithms, and conventional KA, and compares and contrasts the results with MOM’s results. It shows that the effectiveness of the COR-KA algorithm.
引文
[1] Maradudin A. Multiple-scattering phenomena in the scattering of light from randomly rough surfaces[J]. Physical Stat Sol, 1999, 175: 241-252.
[2]叶震,王元利.粗糙表面电磁散射的解析近似法研究[J].战术导弹技术, 2006(4): 24- 27
[3]罗英靓.粗糙面和植被电磁散射解析及数值方法研究[D].浙江:浙江大学, 2007.
[4]胡来平,刘占军.电磁学计算方法的比较[J].现代电子技术, 2003, 10(10): 75-78.
[5] Sancer M I. Shadow-corrected electromagnetic scattering from a randomly rough surface[J]. IEEE Transaction on Antennas and Propagation, 1969, 17(5): 577-585.
[6] G Soriano and M Saillard. A two-scale model for the scattering[J]. Proceeding of IGARSS 2003.
[7] Joel T Johnson and Zhang Min. Theoretical study of the small slope approximation for ocean polarimetric thermal emission[J]. IEEE transactions on geoscience and remote sensing, 1999, 37(5): 2305-2316.
[8] Fung A K and S Tjuatja. Backscattering and emission signatures of randomly rough surfaces based on IEM[J]. IEEE transactions on geoscience and remote sensing, 1993, 3: 1006-1008.
[9]杜晓光.粗糙面电磁散射及其应用[D].西安:西安电子科技大学, 2006.
[10]张延冬.海面电磁与光散射特性研究[D].西安:西安电子科技大学, 2004.
[11] J A Ogilvy. Theory of wave scattering from random rough surfaces[M]. Adam Hilger, 1991.
[12] A G Voronorvich. Wave scattering from rough surfaces[M]. Springier-Verlag, 1994.
[13] J T Johnson. Fourth- and higher-order small-perturbation solution for scattering[J]. J. Opt. Soc. Am, 2003, 20(12): 412-415.
[14] Huang X Z and Jin Y Q. Scattering and emission from two-scale randomly rough sea surface with foam scatters[J]. IEE Proc.- Microw. Antennas Propagat, 1995, 142(2): 109-114.
[15]姚纪欢.粗糙海面的电磁散射研究[D].西安:西安电子科技大学.
[16]王家礼,朱满座.电磁场与电磁波[M].西安:西安电子科技大学出版社, 2003.
[17]孔金瓯.电磁波理论[M].北京:电子工业出版社, 2003.
[18]符果行.电磁场中的格林函数法[M].高等教育出版社, 1993.
[19]戴振铎.电磁理论中的并矢格林函数[M].武汉大学出版社, 1995.
[20]赵家升.电磁场与电磁波(第三版)[M].高等教育出版社, 2004.
[21] Adrian K Fung. Backscattering from a randomly rough dielectric surface[J]. IEEE Transactions on geoscience and remote sensing, 1992, 30(2): 356-369.
[22]乌拉比,穆尔,冯健超.微波遥感(第二卷)雷达遥感和面目标的散射、辐射、理论[M].科学出版社, 1987.
[23]黄泽贵,童创明,王积勤.高阶基尔霍夫法求解理想导体粗糙面的电磁散射特性[J].电波科学学报, 2006, 21(2)
[24] G Franceschetti, M Migliaccio and D Riccio. Strategies to apply the Kirchhoff approximation in electromagnetic scattering from Gaussian surfaces: a comparison[J]. IEEE AP-S, 1999: 514-517.
[25] C Bourlier, G Berginc, and J Saillard, The Kirchhoff analysis from one- and two-dimensional random surface with the statistical shadowing function[J]. 2001: 2427-2429
[26]郭立新,王运华,吴振森.修正双尺度模型在非高斯海面散射中的应用[J].电波科学学报, 22(2).
[27] Warner R J. Shadowing of randomly rough surfaces[J]. J. Acoust. Soc. Am, 1967.
[28]张延冬,吴振森.二维粗糙海面的光散射及其红外成像[J].光学学报, 2002, 22(9).
[29]金亚秋.随机粗糙表面上相关点的散射[J].光学学报, 1989, 9(5): 434-440.
[30]逯贵祯,王宝发.高斯随机粗糙表面电磁散射研究[J] .电子学报, 2002, 30(6): 907-909
[31] Yang Du, J A Kong. A statistical Integral Equation Model for shadow-corrected EM scattering from a Gaussian rough surface[J]. IEEE Transactions on antennas And Propagation, 2007, 55(6): 1843-1855.
[32]林元烈,梁宗霞.随机数学引论[M].北京:清华大学出版社, 2003.
[33] Yaqiu Jin. Multiple scattering from a randomly rough surface[J]. J. Appl. Phys, 1988, 63(5): 1286-1292.
[34]陆光华.随机信号处理[M].西安:西安电子科技大学出版社, 2002.
[35] Fung A K. Microwave scattering and emission models and their applications[M]. Norwood, MA: Artech House, 1994.
[36]金亚秋.随机粗糙面上后向散射的增强[J].物理学报, 1989, 38(10): 1612-1621.
[37] F T Ulaby, R K Moore and A K Fung. Microwave remote sensing: Volume II: Radar remote sensing and surface scattering and emission theory[M]. New York: Addison-Wesley Publication Company, 1982.
[38] Yang Du, J A Kong and Y L Luo. Electromagnetic scattering from a Gaussian rough surface based on slope statistics and covariance matrix decomposition[J]. Radio Sci.,in revision.
[39] Yang Du, Yingliang Luo. Bistatic scattering from rough surfaces based on joint slope statistics and covariance matrix decomposition[J]. 2006: 2930-2933.
[40]金亚秋.电磁散射和热辐射的遥感理论出版社[M].北京:科学出版社, 1993.
[41]新谷隆一,范爱英,康昌鹤.偏振光[M].北京:原子能出版社, 1994.
[42]韦国晖.高斯和非高斯粗糙面电磁散射的小斜率近似方法研究[D].西安:西安电子科技大学, 2006.
[43] Torrungrueng D and Johnson J T. Numercial studies of back—scattering enhancement of electromagnetic waves from two-dimensional random rough surfaces with the forward backward novel spectral acceleration method[J]. J Opt Socam, 2001, 18(10): 2518-2516.
[44] Chen R M and West J C. Analysis of scattering from rough surfaces at large incidence angles using a periodic-surface moment method[J]. IEEE Trans Geosci Remote Sensing, 1995, 33(5): 1206-1213.
[45] Ye H X and Jin Y Q. Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface[J]. IEEE Trans Anten Propagation, 2005, 53(3): 1234-1237.
[46] Bourlier C. Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: Application to the backscattering coefficient for a perfectly-conducting surface[J]. Waves in Random Media, 2001, 11: 91-118.
[47] Tsang L and Chan C H. Monte Carlo simulations of a two-dimensional random rough surface using the sparse-matrix flat-surface iterative approach[J]. Electronic Letters, 1993, 29(13): 1153-1154.
[48] Johnson J T. Third order small perturbation method for scattering from dielectric rough surfaces[J]. J. Opt. Soc. Amen, 1999, 16: 2720-2726.
[49] D E Hasselmann. Directional wave spectra observed during JONSWAP[J]. J Phys Oceanogr, 1980, 10(7): 1264-1280.
[50] E Jakeman. Scattering by a corrugated random surface with fractal slope[J]. J Phys Math Gen, 1982, 15(2): 55-59.
[2]叶震,王元利.粗糙表面电磁散射的解析近似法研究[J].战术导弹技术, 2006(4): 24- 27
[3]罗英靓.粗糙面和植被电磁散射解析及数值方法研究[D].浙江:浙江大学, 2007.
[4]胡来平,刘占军.电磁学计算方法的比较[J].现代电子技术, 2003, 10(10): 75-78.
[5] Sancer M I. Shadow-corrected electromagnetic scattering from a randomly rough surface[J]. IEEE Transaction on Antennas and Propagation, 1969, 17(5): 577-585.
[6] G Soriano and M Saillard. A two-scale model for the scattering[J]. Proceeding of IGARSS 2003.
[7] Joel T Johnson and Zhang Min. Theoretical study of the small slope approximation for ocean polarimetric thermal emission[J]. IEEE transactions on geoscience and remote sensing, 1999, 37(5): 2305-2316.
[8] Fung A K and S Tjuatja. Backscattering and emission signatures of randomly rough surfaces based on IEM[J]. IEEE transactions on geoscience and remote sensing, 1993, 3: 1006-1008.
[9]杜晓光.粗糙面电磁散射及其应用[D].西安:西安电子科技大学, 2006.
[10]张延冬.海面电磁与光散射特性研究[D].西安:西安电子科技大学, 2004.
[11] J A Ogilvy. Theory of wave scattering from random rough surfaces[M]. Adam Hilger, 1991.
[12] A G Voronorvich. Wave scattering from rough surfaces[M]. Springier-Verlag, 1994.
[13] J T Johnson. Fourth- and higher-order small-perturbation solution for scattering[J]. J. Opt. Soc. Am, 2003, 20(12): 412-415.
[14] Huang X Z and Jin Y Q. Scattering and emission from two-scale randomly rough sea surface with foam scatters[J]. IEE Proc.- Microw. Antennas Propagat, 1995, 142(2): 109-114.
[15]姚纪欢.粗糙海面的电磁散射研究[D].西安:西安电子科技大学.
[16]王家礼,朱满座.电磁场与电磁波[M].西安:西安电子科技大学出版社, 2003.
[17]孔金瓯.电磁波理论[M].北京:电子工业出版社, 2003.
[18]符果行.电磁场中的格林函数法[M].高等教育出版社, 1993.
[19]戴振铎.电磁理论中的并矢格林函数[M].武汉大学出版社, 1995.
[20]赵家升.电磁场与电磁波(第三版)[M].高等教育出版社, 2004.
[21] Adrian K Fung. Backscattering from a randomly rough dielectric surface[J]. IEEE Transactions on geoscience and remote sensing, 1992, 30(2): 356-369.
[22]乌拉比,穆尔,冯健超.微波遥感(第二卷)雷达遥感和面目标的散射、辐射、理论[M].科学出版社, 1987.
[23]黄泽贵,童创明,王积勤.高阶基尔霍夫法求解理想导体粗糙面的电磁散射特性[J].电波科学学报, 2006, 21(2)
[24] G Franceschetti, M Migliaccio and D Riccio. Strategies to apply the Kirchhoff approximation in electromagnetic scattering from Gaussian surfaces: a comparison[J]. IEEE AP-S, 1999: 514-517.
[25] C Bourlier, G Berginc, and J Saillard, The Kirchhoff analysis from one- and two-dimensional random surface with the statistical shadowing function[J]. 2001: 2427-2429
[26]郭立新,王运华,吴振森.修正双尺度模型在非高斯海面散射中的应用[J].电波科学学报, 22(2).
[27] Warner R J. Shadowing of randomly rough surfaces[J]. J. Acoust. Soc. Am, 1967.
[28]张延冬,吴振森.二维粗糙海面的光散射及其红外成像[J].光学学报, 2002, 22(9).
[29]金亚秋.随机粗糙表面上相关点的散射[J].光学学报, 1989, 9(5): 434-440.
[30]逯贵祯,王宝发.高斯随机粗糙表面电磁散射研究[J] .电子学报, 2002, 30(6): 907-909
[31] Yang Du, J A Kong. A statistical Integral Equation Model for shadow-corrected EM scattering from a Gaussian rough surface[J]. IEEE Transactions on antennas And Propagation, 2007, 55(6): 1843-1855.
[32]林元烈,梁宗霞.随机数学引论[M].北京:清华大学出版社, 2003.
[33] Yaqiu Jin. Multiple scattering from a randomly rough surface[J]. J. Appl. Phys, 1988, 63(5): 1286-1292.
[34]陆光华.随机信号处理[M].西安:西安电子科技大学出版社, 2002.
[35] Fung A K. Microwave scattering and emission models and their applications[M]. Norwood, MA: Artech House, 1994.
[36]金亚秋.随机粗糙面上后向散射的增强[J].物理学报, 1989, 38(10): 1612-1621.
[37] F T Ulaby, R K Moore and A K Fung. Microwave remote sensing: Volume II: Radar remote sensing and surface scattering and emission theory[M]. New York: Addison-Wesley Publication Company, 1982.
[38] Yang Du, J A Kong and Y L Luo. Electromagnetic scattering from a Gaussian rough surface based on slope statistics and covariance matrix decomposition[J]. Radio Sci.,in revision.
[39] Yang Du, Yingliang Luo. Bistatic scattering from rough surfaces based on joint slope statistics and covariance matrix decomposition[J]. 2006: 2930-2933.
[40]金亚秋.电磁散射和热辐射的遥感理论出版社[M].北京:科学出版社, 1993.
[41]新谷隆一,范爱英,康昌鹤.偏振光[M].北京:原子能出版社, 1994.
[42]韦国晖.高斯和非高斯粗糙面电磁散射的小斜率近似方法研究[D].西安:西安电子科技大学, 2006.
[43] Torrungrueng D and Johnson J T. Numercial studies of back—scattering enhancement of electromagnetic waves from two-dimensional random rough surfaces with the forward backward novel spectral acceleration method[J]. J Opt Socam, 2001, 18(10): 2518-2516.
[44] Chen R M and West J C. Analysis of scattering from rough surfaces at large incidence angles using a periodic-surface moment method[J]. IEEE Trans Geosci Remote Sensing, 1995, 33(5): 1206-1213.
[45] Ye H X and Jin Y Q. Parameterization of the tapered incident wave for numerical simulation of electromagnetic scattering from rough surface[J]. IEEE Trans Anten Propagation, 2005, 53(3): 1234-1237.
[46] Bourlier C. Theoretical study of the Kirchhoff integral from a two-dimensional randomly rough surface with shadowing effect: Application to the backscattering coefficient for a perfectly-conducting surface[J]. Waves in Random Media, 2001, 11: 91-118.
[47] Tsang L and Chan C H. Monte Carlo simulations of a two-dimensional random rough surface using the sparse-matrix flat-surface iterative approach[J]. Electronic Letters, 1993, 29(13): 1153-1154.
[48] Johnson J T. Third order small perturbation method for scattering from dielectric rough surfaces[J]. J. Opt. Soc. Amen, 1999, 16: 2720-2726.
[49] D E Hasselmann. Directional wave spectra observed during JONSWAP[J]. J Phys Oceanogr, 1980, 10(7): 1264-1280.
[50] E Jakeman. Scattering by a corrugated random surface with fractal slope[J]. J Phys Math Gen, 1982, 15(2): 55-59.