粗糙面散射及其与目标复合散射快速方法研究
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摘要
电磁波散射对无损探测、通讯、雷达导航、隐身技术、地震勘探和遥感等有重要意义。而粗糙面的电磁散射研究更是在国防军事领域和民用技术领域都具有显著的学术价值和广泛的应用前景。周期起伏表面作为一种基本粗糙面,在频率扫描反射器、耦合器、极化器以及带通滤波器等方面得到了广泛的应用。而目标探测时,有必要以随机粗糙面模拟复杂的地表,进行目标与粗糙面的复合散射研究,以恰当考虑各种地形或海面背景的杂波。本文主要研究了粗糙面电磁散射相关的两类散射问题的快速计算方法：周期表面的散射和目标与随机粗糙面的复合散射。对于第一类问题,提出了变换方法(Transform method)来计算中、轻度起伏时的介质周期表面的散射；之后又提出用复镜像法来加速周期格林函数,以解决矩量法求解周期表面散射时存在的周期格林函数收敛慢的问题。对于第二类问题,提出了KA (Kirchhoff approximation)+MoM (method of moment)的混合方法,它综合了KA算法的高效和MoM算法的广泛适用性的优势。本文的主要工作如下：
1、将变换方法进行扩展以计算介质周期表面的电磁散射。它是一种用平面场展开槽内场的方法,能高效简便地计算槽内的场点,解决了以往方法或不能计算槽内的场或能计算但较费时的问题,但该方法不能计算深的光栅。
2、针对矩量法计算周期表面的电磁散射问题时,其积分核周期格林函数收敛慢的问题,提出用复镜像法来加速。再针对高频时一级复镜像法存在的问题,提出了二级复镜像法。当入射频率较高时,复镜像法比Kummer-Poisson方法的计算效率更高,而且当频率越高时,复镜像法的优势将更明显。
3、将基于表面电流的KA+MoM混合方法推广到介质目标位于理想导体/介质粗糙面上方的情况。混合算法将目标用MoM建模,粗糙面用KA建模,最后可以直接在目标上得到一组目标感应电流和磁流的积分方程,其运算时间和对计算机内存的需求主要取决于目标的网格划分情况。在计算粗糙面对目标的散射场时,根据粗糙面的局部反射特性,可以对粗糙面进行截取以进一步减少计算量。
4、将KA+MoM混合方法推广到多理想导体目标位于理想导体粗糙面上方的情况。以两个圆柱目标位于高斯粗糙面上方为例,数值分析了相距不同水平距离时两个目标之间的耦合作用。
Many fields in modern science and technology cannot get away from the scattering of electromagnetic waves, such as non-destructive detection, communication, radar navigation, stealth technology, seismic exploration and remote sensing. Research on rough surface electromagnetic scattering has significant academic value and broad application prospects in the national defense and military fields and civilian technology. Periodic surface as a very important optical reflection rough surface, it has been widely used in the frequency scanning reflector, coupler, polarizer and band-pass filter, etc. When detecting target in a complex background, it is necessary to simulate the complex background as random rough surface and carry out the research on the composite scattering from the target above the rough surface, to properly consider the terrain or sea clutter. This paper studies fast method of two type of scattering problems related to the rough surface scattering:periodic surface scattering and the composite scattering of target above rough surface. For the first type problem, we propose a transform method to calculate the scattering from dielectric periodic surface whose surface corrugation is not deep. Then the complex image method is proposed to accelerate the calculation of periodic Green's function, which is kernel of integral equation used in method of moment (MoM). For the second type problem, we propose the hybrid method which combines the analytic Kirchhoff approximation (KA) and numerical MoM. This method is of high efficiency, and as its less limitations, it has more general applicability. The main works are as follows:
1. The extended transform method is developed for calculating the2-D scattering problem from dielectric periodic interfaces. The method transforms the problem into scattering from two imaginary planes, one of which cuts across the maximum points and another across the minimum points of the periodic interface. Compared with other methods, this method is a high efficient and simple method to solve the scattering field in the trough region of the corrugation, but it can not get accurate result with periodic surface whose surface corrugation is deep.
2. One-level complex image method to derive closed form periodic Green's function for problem of scattering from perfectly conducting periodic surfaces, is considered. Then the integral equation with the complex images periodic Green's function in the kernel is solved by the method of moments. However as the frequency increases, this one-level complex image method has difficult to find an adequate approximation parameter. So the two-level complex image method is derived to provide compensation for the contribution neglected in the previous one-level approach.
3. The current based hybrid method combining analytic KA and numerical MoM is developed to solve the two-dimensional (2D) scattering problem of a dielectric target with arbitrary cross section above a conducting/dieletric rough surface under TE-polarize and TM-polarized tapered incident. The KA is used for the calculation of the Gaussian rough surface and MoM for the target, and the integral equations of the induced electric and magnetic currents on the target only can be derived, so the problem depends mainly on the number of unknown of the target. Based on the local specular reflection of the rough surface, the rough surface can be truncated to speed up computation of the scattering contribution from the rough surface to the target.
4. The current based hybrid method is generalized for multiple targets above a conducting rough surface under TE-polarized tapered incident. Taking two cylindrical targets above a PEC rough surface as an example, the coupling effect between two targets with different horizontal distance is analized.
1、将变换方法进行扩展以计算介质周期表面的电磁散射。它是一种用平面场展开槽内场的方法,能高效简便地计算槽内的场点,解决了以往方法或不能计算槽内的场或能计算但较费时的问题,但该方法不能计算深的光栅。
2、针对矩量法计算周期表面的电磁散射问题时,其积分核周期格林函数收敛慢的问题,提出用复镜像法来加速。再针对高频时一级复镜像法存在的问题,提出了二级复镜像法。当入射频率较高时,复镜像法比Kummer-Poisson方法的计算效率更高,而且当频率越高时,复镜像法的优势将更明显。
3、将基于表面电流的KA+MoM混合方法推广到介质目标位于理想导体/介质粗糙面上方的情况。混合算法将目标用MoM建模,粗糙面用KA建模,最后可以直接在目标上得到一组目标感应电流和磁流的积分方程,其运算时间和对计算机内存的需求主要取决于目标的网格划分情况。在计算粗糙面对目标的散射场时,根据粗糙面的局部反射特性,可以对粗糙面进行截取以进一步减少计算量。
4、将KA+MoM混合方法推广到多理想导体目标位于理想导体粗糙面上方的情况。以两个圆柱目标位于高斯粗糙面上方为例,数值分析了相距不同水平距离时两个目标之间的耦合作用。
Many fields in modern science and technology cannot get away from the scattering of electromagnetic waves, such as non-destructive detection, communication, radar navigation, stealth technology, seismic exploration and remote sensing. Research on rough surface electromagnetic scattering has significant academic value and broad application prospects in the national defense and military fields and civilian technology. Periodic surface as a very important optical reflection rough surface, it has been widely used in the frequency scanning reflector, coupler, polarizer and band-pass filter, etc. When detecting target in a complex background, it is necessary to simulate the complex background as random rough surface and carry out the research on the composite scattering from the target above the rough surface, to properly consider the terrain or sea clutter. This paper studies fast method of two type of scattering problems related to the rough surface scattering:periodic surface scattering and the composite scattering of target above rough surface. For the first type problem, we propose a transform method to calculate the scattering from dielectric periodic surface whose surface corrugation is not deep. Then the complex image method is proposed to accelerate the calculation of periodic Green's function, which is kernel of integral equation used in method of moment (MoM). For the second type problem, we propose the hybrid method which combines the analytic Kirchhoff approximation (KA) and numerical MoM. This method is of high efficiency, and as its less limitations, it has more general applicability. The main works are as follows:
1. The extended transform method is developed for calculating the2-D scattering problem from dielectric periodic interfaces. The method transforms the problem into scattering from two imaginary planes, one of which cuts across the maximum points and another across the minimum points of the periodic interface. Compared with other methods, this method is a high efficient and simple method to solve the scattering field in the trough region of the corrugation, but it can not get accurate result with periodic surface whose surface corrugation is deep.
2. One-level complex image method to derive closed form periodic Green's function for problem of scattering from perfectly conducting periodic surfaces, is considered. Then the integral equation with the complex images periodic Green's function in the kernel is solved by the method of moments. However as the frequency increases, this one-level complex image method has difficult to find an adequate approximation parameter. So the two-level complex image method is derived to provide compensation for the contribution neglected in the previous one-level approach.
3. The current based hybrid method combining analytic KA and numerical MoM is developed to solve the two-dimensional (2D) scattering problem of a dielectric target with arbitrary cross section above a conducting/dieletric rough surface under TE-polarize and TM-polarized tapered incident. The KA is used for the calculation of the Gaussian rough surface and MoM for the target, and the integral equations of the induced electric and magnetic currents on the target only can be derived, so the problem depends mainly on the number of unknown of the target. Based on the local specular reflection of the rough surface, the rough surface can be truncated to speed up computation of the scattering contribution from the rough surface to the target.
4. The current based hybrid method is generalized for multiple targets above a conducting rough surface under TE-polarized tapered incident. Taking two cylindrical targets above a PEC rough surface as an example, the coupling effect between two targets with different horizontal distance is analized.
引文
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