电磁场的面散射与体散射理论的研究

摘要

电磁场的面散射与体散射理论的研究，作为电磁面散射和体散射的典型代表，因其在气象、海洋、环境、军事等诸多领域的重要应用，成为专家学者们关注的热点。本文主要针对粗糙面及体电磁散射的相关解析理论进行了较深入的研究工作，并对涉及了以上两种散射理论的植被散射问题给出了新的思路。

粗糙面散射的研究方面，本文就前人解析模型中对粗糙面斜率的随机分布特性只做了简单近似这一问题，针对高斯介质粗糙面提出了统计积分方程模型，完整地考虑了粗糙面高度和斜率两组随机特性，建立了较为准确的散射理论模型。该模型引入了表面法向量的联合概率分布函数来表征法向量之间的联合分布规律；为计算散射幅度统计平均中涉及的多重概率积分，模型引入了具有较明确物理意义的协方差矩阵分解机制，并对该分解机制进行了较为完整的理论推导，得到散射功率的分解机制，从而对散射系数表达式中的六重变量积分进行了简化，最终得到散射系数的简单解析表达式。另一方面，针对常规双尺度模型的缺陷，从该统计模型和小斜率近似方法出发，提出了一个改进的双尺度模型来有效地对复合型粗糙面进行建模。改进模型将小斜率近似方法所具有的双尺度特性与统计积分方程模型的特点结合在一起，不但可以根据表面参数自适应地调节，使得模型可以覆盖更广的粗糙度区域，同时也避免了常规的双尺度模型在尺度划分上的不确定性，从而可以更好的应用在诸如海面等复合型粗糙面电磁散射问题。

体散射的研究方面，针对常规扩展边界条件方法在计算较大长径比的散射体时会存在着收敛性的问题，本文提出的迭代方法通过使用若干虚拟面来对一个较长的圆柱体进行等体分割，并建立线性方程组的过程中严格满足分割面上的边界条件，可以适用于任意长径比的有限长介质圆柱体散射问题；同时将该方法也被应用于多个有限长圆柱体的电磁散射问题中，并给出了相应的计算方法。由于方法中所应用到的分割技术，可以大大的减小了圆柱体的外包络球，从而对于圆柱体的间距可以有更宽松的要求；同时，对于高阶近场效应不可忽视的情况，本方法在考虑相干散射时不仅仅包括二阶效应而是同时包括了所有阶效应，因而更加精确。

植被电磁散射的方面，本文对作为典型矮植被的大豆的后向散射场的进行了研究，所采用的方法吸取了分支模型和相位幅度修正模型的长处。在建立植株间分布模型时，考虑到大豆植株在栽种时所具有的准周期性的特点，引入了天线阵的方法来描述植株间的分布情况。再次，对于粗糙表面的散射贡献，不同于通常采用的经典基尔霍夫近似模型或小扰动模型，本文采用了的本文提出的统计斜率

基尔霍夫模型。而在考虑散射体－地面双径散射机制时，对于涉及粗糙面的反射部分，本文采用了修正的费涅尔反射系数，相比传统的反射系数，能够更好地考虑土壤表面粗糙度的影响。通过仿真结果和实验结果的比较，验证了本文提出模型的正确性。

关键词粗糙面散射；统计特性；体散射；扩展边界条件；植被散射；分支模型

Abstract

The electromagnetic scattering from randomly rough surfaces and volume scatterers have been an active research topic of in many areas, such as meteorology, oceanography, environment, military and so on. This dissertation made intensive research on random rough surface and volume electromagnetic wave scattering from analytical theory. Based on these two aspects of researches, we also paid attention to the problem on EM wave scattering from vegetation canopy on the rough surface.

In terms of scattering from randomly rough surfaces, this dissertation carefully treated statistical distribution of slope or normal vector of surface, which were oversimplified by former analytical models, and proposed a statistical model in conjunction with the integral equation formalism for electromagnetic scattering from Gaussian rough surfaces with small to moderate heights and Gaussian power spectra where the statistical features of the surface slopes and the effect of shadowing were included. The proposed model introduced joint probability density function of surface normals to characterize their random distribution; furthermore, to simplify multiple fold integral involved in calculating ensemble averaging of scattering amplitudes, a decomposition scheme of slope covariance matrix was presented, which contained explicit physical meaning relating to correlation of slopes, and made possible the entire theory deduction and final simple analytical formulae for scattering coefficient computation. Then based on this proposed statistical method and the small slope approach, we also proposed a new two-scale model for wave scattering from a composite surface. For such model, it may capture the actual scattering mechanisms and lead to more accurate predictions, also may have promising applications for electromagnetic scattering from the ocean surface, whose entire roughness spectrum can be usually discomposed into small- and large-scale components.

For volume scattering, the conventional T-matrix approach based on extended boundary condition method is reported to suffer from convergence problems for particles with extreme geometries represented by very large aspect ratios. This dissertation proposed a new iterative technique based on the T-matrix approach for the electromagnetic scattering by dielectric cylinders with arbitrary length. In this method, hypothetic surfaces were used to divide a cylinder into a cluster of N identical sub-cylinder, for each the T matrix can be directly calculated. Since any two neighboring subcylinder are touching via the division interface, the conventional

multiscatterer equation method is not directly applicable. The coupling among sub-cylinder and boundary conditions at the interfaces were taken care of in our approach. Additionally, we extended this method to the problem of electromagnetic scattering from a cluster of parallel dielectric circular cylinders. Due to the division of the elongated cylinders, the intersection volume of the circumscribing spheres is strongly reduced. Therefore, the proposed method can be applied to the cases of when any pair of cylinders is close to each other. It should be noted that since no approximation is introduced in the procedure, this approach is thus more rigorous.

In the field of electromagnetic scattering from vegetation, this dissertation made research on backscattering from the soybean, a typical species of short vegetation, and presented a model incorporating the benefits of branch model and phase and amplitude correction theory. In modeling inter-plant structure, the model introduced an antenna theory to take into consideration the quasi-periodic characteristics common in agricultural planting practice. Moreover, the proposed statistical integral equation model was adopted for direct scattering contribution of only randomly rough surfaces instead of traditional Kirchhoff approximation or small perturbation method; and in terms of the ground-scatter bounce scattering, conventionally used Fresnel reflection coefficient was modified to make full consideration of the impact of roughness of underlying surfaces. Finally, comparisons of model predictions with measuremental results validated this proposed model.

Keywords surface scattering; statistical characteristics; volume scattering; extended boundary condition; vegetation; branch model