随机粗糙表面电磁散射与逆散射中的若干问题研究
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摘要
随机粗糙表面的电磁波散射研究在微波遥感、雷达成像、海洋工程、无线通信、表面光学和半导体物理等领域均具有重要实际应用。本论文就随机粗糙表面的电磁散射与逆散射的若干问题开展了系统的理论研究工作。论文首先研究了一维随机粗糙表面的时谐波、超宽带脉冲波的电磁散射。然后将一维粗糙表面模型推广到二维粗糙表面模型,研究二维随机粗糙表面的时谐波、超宽带脉冲波的电磁散射。在前几章的基础上又开展了非高斯分布的粗糙表面的电磁散射研究。最后研究了粗糙表面的逆散射相关问题,对粗糙表面轮廓进行了重构和统计参数反演。主要工作和成果如下:
1.对一维粗糙表面的基尔霍夫单次散射模型进行了推广,建立了基尔霍夫二次散射模型。从理论分析和数值计算两方面分析了后向散射增强效应主要是由于多次散射引起的。
2.针对传统的稀疏矩阵规范网格方法的不足,提出了契比雪夫规范网格方法,用契比雪夫多项式级数来一致逼近二维空间的格林函数,并且借助于快速傅立叶变换进行快速计算。通过与矩量法的计算结果比较,验证了契比雪夫规范网格方法具有比较高的计算精度。
3.提出了一种求解一维粗糙表面的超宽带脉冲准波束的电磁散射的解析计算方法。结合基尔霍夫散射理论、波束分解与合成理论和近轴远区近似,求解了脉冲电磁波的时域散射电场的解析表达式。采用四阶瑞利脉冲电磁波作为入射波,计算了干沙表面模型的时域散射电场,并检验了这种解析方法的计算精度。
4.提出了一种适合求解均方根斜率较大的二维粗糙表面多次散射的解析计算方法,讨论了双站散射系数随方位角以及后向散射系数随均方根斜率的变化规律。将理论模型应用于计算镍涂层表面的毫米波散射问题,将理论计算结果与华盛顿大学的测量数据进行比较,检验了理论模型的正确性。
5.将第三章的一维粗糙表面的超宽带脉冲准波束的电磁散射的解析方法推广到了二维粗糙表面模型。给出了二维粗糙表面的超宽带脉冲准波束的时域散射电场的解析表达式,分析了地面背景下二阶瑞利脉冲电磁波的传播与衰减特性。
6.推广了高斯分布的粗糙表面模型,建立了Alpha-stable非高斯分布的粗糙表面模型。基于磁场积分方程研究Alpha-stable非高斯分布的金属材料表面的时谐波、超宽带脉冲波的电磁散射特性。研究结果表明金属材料表面的概率密度分布对电磁散射特性具有重要的影响。
7.提出了基于空间场重构理论的时谐电磁波逆散射算法和超宽带脉冲电磁波的逆散射算法。分别针对周期粗糙表面、非周期粗糙表面、高斯相关的随机粗糙表面和Alpha-stable非高斯分布的粗糙表面进行了轮廓重构。重构结果充分说明该逆散射算法具有比较高的重构精度。
8.建立了分数布朗运动粗糙表面的高斯波束电磁散射模型,应用最小二乘法建立了一种多频率反演粗糙表面分维数的逆散射算法。除此之外,还提出了高斯相关的随机粗糙表面的统计参数的理论反演方法,即分别根据镜向的相干散射强度和非相干散射强度反演高度起伏均方根和相关长度。
The study of electromagnetic wave scattering from random rough surfaces has been the subject of intensive investigation for its application in a number of important research areas, such as the remote sensing, radar imaging, ocean engineering, wireless communications, surface optics, as well as the semiconductor physics. This dissertation presents theoretical studies of electromagnetic scattering and inverse scattering from random rough surfaces. The first topic in this dissertation mainly focuses on the scattering of time harmonic wave and ultra-wide-band (UWB) pulse wave by one-dimensional (1-D) random rough surfaces. The 1-D model is then extended to the two-dimensional (2-D) model. Moreover, the characteristics of scattering by non-Gaussian distributed rough surfaces are examined. Finally, emphasis is also put on studying the inverse scattering from random rough surfaces, including the reconstruction of surface profile and the retrieval of statistical parameters. The main works and results are as follows:
1. The Kirchhoff single-scattering model for 1-D rough surfaces is extended to the Kirchhoff double-scattering model. Numerical simulations and theoretical analysis lead to the conclusion that the backscattering enhancement is caused by multiple scattering paths.
2. A Chebyshev canonical-grid (CCG) method is proposed by expanding the Green's function in the series of Chebyshev polynomials, and it is proved to be more convenient than the conventional Sparse-Matrix canonical-grid (SMCG) method. The multiplication in the CCG method can be readily calculated by the FFT. The numerical results are compared with those obtained by the moment method, and it demonstrates that the CCG method has high efficiency in numerical simulations.
3. An analytic method is constructed for the scattering problem of 1-D rough surfaces, which are illuminated by a UWB pulse quasi-beam. The analytic expression of the electromagnetic scattered field in the time domain is derived combining with the Kirchhoff scattering theory, the decomposition and synthesis of the incident quasi-beam, as well as the paraxial far zone approximation. The scattered electric field from the surface of dry sand is calculated with the fourth-order Rayleigh pulse illuminating. The precision of analytic method is also examined by comparing with the results obtained by time domain moment method.
4. A new method is proposed to calculate the multiple scattering from 2-D rough surfaces with large surface root-mean-square (RMS) slope. The dependency of bistatic scattering coefficients on azimuth angles and the backscattering coefficients on RMS slope is discussed. The theoretical model is applied to the calculation of the millimeter wave scattering from nickel coated surfaces, the numerical results are also compared with the experimental data from University of Washington, and the validity of the model is tested.
5. The analytic method of the UWB pulse quasi-beam constructed for the scattering problem of 1-D rough surfaces (Chap. 3 in this dissertation) is then extended to the 2-D rough surface model. The analytic expression for the scattered electric filed of the UWB pulse quasi-beam in the time domain by 2-D rough surfaces is presented. The characteristics of propagation and attenuation of the second-order Rayleigh pulse scattered by 2-D bare soil surfaces are analyzed.
6. As an extension of Gaussian distributed surface model, the electromagnetic scattering model on Alpha-stable non-Gaussian distributed surfaces is developed. The magnetic field integral equation (MFIE) is formulated to study the electromagnetic scattering from Alpha-stable non-Gaussian metallic material surface with a time harmonic wave and a UWB pulse wave incidence. Numerical simulations show that the scattered field from metallic material surfaces is affected significantly by the probability distribution of the surfaces.
7. Based on the spatial reconstruction of total field, the algorithm is proposed to solve the inverse scattering of a time harmonic wave and a UWB pulse wave from rough surfaces, respectively. Reconstructions of sinusoidal surfaces, non-sinusoidal surfaces, Gaussian correlated random rough surfaces and Alpha-stable non-Gaussian distributed surfaces are performed using this technique. Good agreements of these results demonstrate that the inverse scattering method is reliable.
8. The Gaussian beam scattering model is developed to analyze the scattering from Fractional Brownian Motion (FBM) rough surfaces. A multi-frequency inverse algorithm is set up to estimate the fractal dimension of the FBM surfaces with the least-square method. In addition, a new fully theoretical framework for the retrieval of the statistical parameters of Gaussian correlated rough surfaces is proposed, and the suggested scheme is to retrieve the RMS height and the correlation length with the use of the specular coherent scattering intensity and incoherent scattering intensity, respectively.
1.对一维粗糙表面的基尔霍夫单次散射模型进行了推广,建立了基尔霍夫二次散射模型。从理论分析和数值计算两方面分析了后向散射增强效应主要是由于多次散射引起的。
2.针对传统的稀疏矩阵规范网格方法的不足,提出了契比雪夫规范网格方法,用契比雪夫多项式级数来一致逼近二维空间的格林函数,并且借助于快速傅立叶变换进行快速计算。通过与矩量法的计算结果比较,验证了契比雪夫规范网格方法具有比较高的计算精度。
3.提出了一种求解一维粗糙表面的超宽带脉冲准波束的电磁散射的解析计算方法。结合基尔霍夫散射理论、波束分解与合成理论和近轴远区近似,求解了脉冲电磁波的时域散射电场的解析表达式。采用四阶瑞利脉冲电磁波作为入射波,计算了干沙表面模型的时域散射电场,并检验了这种解析方法的计算精度。
4.提出了一种适合求解均方根斜率较大的二维粗糙表面多次散射的解析计算方法,讨论了双站散射系数随方位角以及后向散射系数随均方根斜率的变化规律。将理论模型应用于计算镍涂层表面的毫米波散射问题,将理论计算结果与华盛顿大学的测量数据进行比较,检验了理论模型的正确性。
5.将第三章的一维粗糙表面的超宽带脉冲准波束的电磁散射的解析方法推广到了二维粗糙表面模型。给出了二维粗糙表面的超宽带脉冲准波束的时域散射电场的解析表达式,分析了地面背景下二阶瑞利脉冲电磁波的传播与衰减特性。
6.推广了高斯分布的粗糙表面模型,建立了Alpha-stable非高斯分布的粗糙表面模型。基于磁场积分方程研究Alpha-stable非高斯分布的金属材料表面的时谐波、超宽带脉冲波的电磁散射特性。研究结果表明金属材料表面的概率密度分布对电磁散射特性具有重要的影响。
7.提出了基于空间场重构理论的时谐电磁波逆散射算法和超宽带脉冲电磁波的逆散射算法。分别针对周期粗糙表面、非周期粗糙表面、高斯相关的随机粗糙表面和Alpha-stable非高斯分布的粗糙表面进行了轮廓重构。重构结果充分说明该逆散射算法具有比较高的重构精度。
8.建立了分数布朗运动粗糙表面的高斯波束电磁散射模型,应用最小二乘法建立了一种多频率反演粗糙表面分维数的逆散射算法。除此之外,还提出了高斯相关的随机粗糙表面的统计参数的理论反演方法,即分别根据镜向的相干散射强度和非相干散射强度反演高度起伏均方根和相关长度。
The study of electromagnetic wave scattering from random rough surfaces has been the subject of intensive investigation for its application in a number of important research areas, such as the remote sensing, radar imaging, ocean engineering, wireless communications, surface optics, as well as the semiconductor physics. This dissertation presents theoretical studies of electromagnetic scattering and inverse scattering from random rough surfaces. The first topic in this dissertation mainly focuses on the scattering of time harmonic wave and ultra-wide-band (UWB) pulse wave by one-dimensional (1-D) random rough surfaces. The 1-D model is then extended to the two-dimensional (2-D) model. Moreover, the characteristics of scattering by non-Gaussian distributed rough surfaces are examined. Finally, emphasis is also put on studying the inverse scattering from random rough surfaces, including the reconstruction of surface profile and the retrieval of statistical parameters. The main works and results are as follows:
1. The Kirchhoff single-scattering model for 1-D rough surfaces is extended to the Kirchhoff double-scattering model. Numerical simulations and theoretical analysis lead to the conclusion that the backscattering enhancement is caused by multiple scattering paths.
2. A Chebyshev canonical-grid (CCG) method is proposed by expanding the Green's function in the series of Chebyshev polynomials, and it is proved to be more convenient than the conventional Sparse-Matrix canonical-grid (SMCG) method. The multiplication in the CCG method can be readily calculated by the FFT. The numerical results are compared with those obtained by the moment method, and it demonstrates that the CCG method has high efficiency in numerical simulations.
3. An analytic method is constructed for the scattering problem of 1-D rough surfaces, which are illuminated by a UWB pulse quasi-beam. The analytic expression of the electromagnetic scattered field in the time domain is derived combining with the Kirchhoff scattering theory, the decomposition and synthesis of the incident quasi-beam, as well as the paraxial far zone approximation. The scattered electric field from the surface of dry sand is calculated with the fourth-order Rayleigh pulse illuminating. The precision of analytic method is also examined by comparing with the results obtained by time domain moment method.
4. A new method is proposed to calculate the multiple scattering from 2-D rough surfaces with large surface root-mean-square (RMS) slope. The dependency of bistatic scattering coefficients on azimuth angles and the backscattering coefficients on RMS slope is discussed. The theoretical model is applied to the calculation of the millimeter wave scattering from nickel coated surfaces, the numerical results are also compared with the experimental data from University of Washington, and the validity of the model is tested.
5. The analytic method of the UWB pulse quasi-beam constructed for the scattering problem of 1-D rough surfaces (Chap. 3 in this dissertation) is then extended to the 2-D rough surface model. The analytic expression for the scattered electric filed of the UWB pulse quasi-beam in the time domain by 2-D rough surfaces is presented. The characteristics of propagation and attenuation of the second-order Rayleigh pulse scattered by 2-D bare soil surfaces are analyzed.
6. As an extension of Gaussian distributed surface model, the electromagnetic scattering model on Alpha-stable non-Gaussian distributed surfaces is developed. The magnetic field integral equation (MFIE) is formulated to study the electromagnetic scattering from Alpha-stable non-Gaussian metallic material surface with a time harmonic wave and a UWB pulse wave incidence. Numerical simulations show that the scattered field from metallic material surfaces is affected significantly by the probability distribution of the surfaces.
7. Based on the spatial reconstruction of total field, the algorithm is proposed to solve the inverse scattering of a time harmonic wave and a UWB pulse wave from rough surfaces, respectively. Reconstructions of sinusoidal surfaces, non-sinusoidal surfaces, Gaussian correlated random rough surfaces and Alpha-stable non-Gaussian distributed surfaces are performed using this technique. Good agreements of these results demonstrate that the inverse scattering method is reliable.
8. The Gaussian beam scattering model is developed to analyze the scattering from Fractional Brownian Motion (FBM) rough surfaces. A multi-frequency inverse algorithm is set up to estimate the fractal dimension of the FBM surfaces with the least-square method. In addition, a new fully theoretical framework for the retrieval of the statistical parameters of Gaussian correlated rough surfaces is proposed, and the suggested scheme is to retrieve the RMS height and the correlation length with the use of the specular coherent scattering intensity and incoherent scattering intensity, respectively.
引文
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