斜程湍流大气中激光波束传输及目标回波特性
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摘要
湍流大气中激光波束传输特性作为近代大气光学及其工程应用领域相当活跃的研究内容之一,对地-空路径的激光通信、成像、目标特征的提取与定标、遥感及激光制导和激光武器系统的开发和应用具有重要的指导作用和现实意义。
本文围绕斜程湍流大气中激光波束传输与目标回波特性开展研究,主要成果如下:
第一、讨论了斜程路径高斯波束的对数振幅方差随无量纲参量–发射和接收参数的变化关系,分析了高斯波束的光学湍流效应,当大气结构常数为定值时可以退化到水平传输情形的结果。数值计算了不同类型入射波的对数振幅方差随不同接收机高度、Fresnel比及接收机参数的变化关系。
第二、通过在完全饱和情况高斯解的基础上添加非高斯修正项的方法推导了波在湍流大气中传输时强起伏情况场的(m + m)阶对称矩的解析解。其中高斯项部分可以由二阶矩的乘积和求得;非高斯修正项部分通过求其Rytov近似解得出。利用上述理论框架和解析求解方法导出了波在湍流介质中传播的四阶矩和八阶矩的解析解。高阶对称矩求解过程没有对湍流强度和入射波源作任何限定,所以所得解析解具有通用性。最后给出了平面波入射时的闪烁指数随湍流强度、天顶角以及传输距离的变化关系。
第三、讨论了从弱到强大气湍流中光波传播闪烁和修正Rytov理论,给出了考虑湍流内、外尺度效应时斜路径高斯波束从弱起伏到强起伏区的闪烁指数统一理论模型。根据ITU-R大气结构常数C n2模型,分析了光波的斜径闪烁指数随Rytov方差的变化关系,其结果和实验的结果相符。该模型可退化到斜路径平面波和球面波的闪烁指数模型,也能在C n2为定值的条件下,简化到均匀湍流的水平传输波束闪烁模型。基于广义Huygens-Fresnel原理,利用Mellin变换技术,推导了激光波束的扩展半径和考虑外尺度效应时的漂移方差,并利用ITU-R湍流大气结构常数模型数值分析了不同接收机高度波束的扩展半径和漂移方差随传输距离的变化关系。
第四、利用Huygens-Fresnel原理,考虑大气湍流对激光束从发射机到目标和从目标到接收机双程路径的影响,研究了斜程湍流大气中漫射目标和目标上含一个或多个镜反射点(该镜反射点半径远小于束宽)的散射统计特性。导出了考虑对数振幅和相位起伏影响,激光波束在湍流大气中斜程传输时其散射场的互相关函数、强度协方差和强度方差的计算公式,讨论了不同湍流强度、波长、目标高度和传播距离对它们的影响,以及镜反射点的半径和离轴远近对归一化强度方差的影响。
第五、根据Rytov近似和ABCD传输矩阵表示法,应用Kolmogorov功率谱推导了双程斜路径湍流大气中平面镜和后向反射器回波的互相关函数、平均强度以及闪烁指数。当大气结构常数为一定值时均可以退化到水平传输情况,与以前文献中的结果一致。给出了高斯波束、球面波,平面波入射到平面镜和后向反射器上,反射波的数值计算结果。
Laser propagation in the turbulent atmosphere is one of important research topics of latter-day optics and its engineering application, and is significant for laser satellite-Earth communication, target characteristic extracting and calibrating, laser tracking, controlling and guiding.
The topic of laser beam propagation on the slant path through the atmospheric turbulence and the characteristics of returned waves by targets have great value.The main topics and results are as follows:
First, the transmitter and receiver parameters become apparent in the derived analytical expressions for the log-amplitude variance of the Gaussian beam propagation on the slant path. The expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam wave analysis and can be reduced to a Gaussian beam wave model on horizontal sight paths of invariable C_n~2. The numerical results of different form beam log-amplitude variance with the height of receiver, Fresnel zone size and receiver parameters are given.
Second, by adding a non-Gaussian correction to the Gaussian solution to the m + mth order moment equation under complete saturation case, an analytical solution is deriveded for general strong scattering regime. The Gaussian term is the sum of the product of the second order moment, while the equation for the non-Gaussian part can be treated by Rytov approximate method. Based on the theory frame and the solution method of analytical solution, the fourth and eighth moment are obtained when wave propagation in the turbulent atmosphere.The equation for higher-order moment has been treated without restrictions on both the scattering regimes and incident wave sources, thus the analytical solution is general. Finally, the relation of the plane wave scinllation index with turbulent intensity, zenith angle and propagation distance are discussed.
Third, on slant paths, by applying a modification of the Rytov method, a tractable model is developed for the scintillation index of a Gaussian optical beam wave that is valid under moderate-to-strong irradiance fluctuations considering inner- and outer- scales effects of turbulence. The results agree with experimental scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on slant paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C n2. According to Huygens-Fresnel and Mellin transform techniques, spreading radius and wander with outer scale effect on the slant path, and applying the ITU-R C_n~2 model which is altitude dependent to calculate the spreading radius and wander covariance with different height of drone in the slant path. These results can be reduced to a Gaussian beam wave model on horizontal sight paths of invariable C_n~2.
Fourth, the extended Huygens-Fresnel principle is utilized to make analysis of the backscattering of a target in the turbulent atmosphere. The treatment includes the effects of the atmospheric turbulence both on the laser beam as it propagates to the target and on the scattered field as it propagates back to the receiver. The covariance function and variance of the scattering intensity are derived with considering the fluctuation of the log-amplitude and phase, and the numerical results are given. The influence of wavelength and propagating distance on the covariance function and normalized variance of the scattering is discussed. The statistical effects of the atmospheric turbulence on coherent radiation scattering from a diffused target are extended to the target with multiple glint (the glint is small compared with the illuminating beam). The influence of radius of the glint and the distance off the incident beam on these parameters is discussed.
Finally, based on the Rytov theory and rotationally symmetric ABCD ray matrices, this paper educed the mutual coherence function, mean intensity and scintillation of retuned waves by plane mirror and retroreflector in the turbulent on the slant path, and can be reduced to model on the horizontal path of invariable C n2. The results of Gaussian beam, spherical wave and plane wave incident on plane mirror and retroreflector are discussed respectively.
本文围绕斜程湍流大气中激光波束传输与目标回波特性开展研究,主要成果如下:
第一、讨论了斜程路径高斯波束的对数振幅方差随无量纲参量–发射和接收参数的变化关系,分析了高斯波束的光学湍流效应,当大气结构常数为定值时可以退化到水平传输情形的结果。数值计算了不同类型入射波的对数振幅方差随不同接收机高度、Fresnel比及接收机参数的变化关系。
第二、通过在完全饱和情况高斯解的基础上添加非高斯修正项的方法推导了波在湍流大气中传输时强起伏情况场的(m + m)阶对称矩的解析解。其中高斯项部分可以由二阶矩的乘积和求得;非高斯修正项部分通过求其Rytov近似解得出。利用上述理论框架和解析求解方法导出了波在湍流介质中传播的四阶矩和八阶矩的解析解。高阶对称矩求解过程没有对湍流强度和入射波源作任何限定,所以所得解析解具有通用性。最后给出了平面波入射时的闪烁指数随湍流强度、天顶角以及传输距离的变化关系。
第三、讨论了从弱到强大气湍流中光波传播闪烁和修正Rytov理论,给出了考虑湍流内、外尺度效应时斜路径高斯波束从弱起伏到强起伏区的闪烁指数统一理论模型。根据ITU-R大气结构常数C n2模型,分析了光波的斜径闪烁指数随Rytov方差的变化关系,其结果和实验的结果相符。该模型可退化到斜路径平面波和球面波的闪烁指数模型,也能在C n2为定值的条件下,简化到均匀湍流的水平传输波束闪烁模型。基于广义Huygens-Fresnel原理,利用Mellin变换技术,推导了激光波束的扩展半径和考虑外尺度效应时的漂移方差,并利用ITU-R湍流大气结构常数模型数值分析了不同接收机高度波束的扩展半径和漂移方差随传输距离的变化关系。
第四、利用Huygens-Fresnel原理,考虑大气湍流对激光束从发射机到目标和从目标到接收机双程路径的影响,研究了斜程湍流大气中漫射目标和目标上含一个或多个镜反射点(该镜反射点半径远小于束宽)的散射统计特性。导出了考虑对数振幅和相位起伏影响,激光波束在湍流大气中斜程传输时其散射场的互相关函数、强度协方差和强度方差的计算公式,讨论了不同湍流强度、波长、目标高度和传播距离对它们的影响,以及镜反射点的半径和离轴远近对归一化强度方差的影响。
第五、根据Rytov近似和ABCD传输矩阵表示法,应用Kolmogorov功率谱推导了双程斜路径湍流大气中平面镜和后向反射器回波的互相关函数、平均强度以及闪烁指数。当大气结构常数为一定值时均可以退化到水平传输情况,与以前文献中的结果一致。给出了高斯波束、球面波,平面波入射到平面镜和后向反射器上,反射波的数值计算结果。
Laser propagation in the turbulent atmosphere is one of important research topics of latter-day optics and its engineering application, and is significant for laser satellite-Earth communication, target characteristic extracting and calibrating, laser tracking, controlling and guiding.
The topic of laser beam propagation on the slant path through the atmospheric turbulence and the characteristics of returned waves by targets have great value.The main topics and results are as follows:
First, the transmitter and receiver parameters become apparent in the derived analytical expressions for the log-amplitude variance of the Gaussian beam propagation on the slant path. The expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam wave analysis and can be reduced to a Gaussian beam wave model on horizontal sight paths of invariable C_n~2. The numerical results of different form beam log-amplitude variance with the height of receiver, Fresnel zone size and receiver parameters are given.
Second, by adding a non-Gaussian correction to the Gaussian solution to the m + mth order moment equation under complete saturation case, an analytical solution is deriveded for general strong scattering regime. The Gaussian term is the sum of the product of the second order moment, while the equation for the non-Gaussian part can be treated by Rytov approximate method. Based on the theory frame and the solution method of analytical solution, the fourth and eighth moment are obtained when wave propagation in the turbulent atmosphere.The equation for higher-order moment has been treated without restrictions on both the scattering regimes and incident wave sources, thus the analytical solution is general. Finally, the relation of the plane wave scinllation index with turbulent intensity, zenith angle and propagation distance are discussed.
Third, on slant paths, by applying a modification of the Rytov method, a tractable model is developed for the scintillation index of a Gaussian optical beam wave that is valid under moderate-to-strong irradiance fluctuations considering inner- and outer- scales effects of turbulence. The results agree with experimental scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on slant paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C n2. According to Huygens-Fresnel and Mellin transform techniques, spreading radius and wander with outer scale effect on the slant path, and applying the ITU-R C_n~2 model which is altitude dependent to calculate the spreading radius and wander covariance with different height of drone in the slant path. These results can be reduced to a Gaussian beam wave model on horizontal sight paths of invariable C_n~2.
Fourth, the extended Huygens-Fresnel principle is utilized to make analysis of the backscattering of a target in the turbulent atmosphere. The treatment includes the effects of the atmospheric turbulence both on the laser beam as it propagates to the target and on the scattered field as it propagates back to the receiver. The covariance function and variance of the scattering intensity are derived with considering the fluctuation of the log-amplitude and phase, and the numerical results are given. The influence of wavelength and propagating distance on the covariance function and normalized variance of the scattering is discussed. The statistical effects of the atmospheric turbulence on coherent radiation scattering from a diffused target are extended to the target with multiple glint (the glint is small compared with the illuminating beam). The influence of radius of the glint and the distance off the incident beam on these parameters is discussed.
Finally, based on the Rytov theory and rotationally symmetric ABCD ray matrices, this paper educed the mutual coherence function, mean intensity and scintillation of retuned waves by plane mirror and retroreflector in the turbulent on the slant path, and can be reduced to model on the horizontal path of invariable C n2. The results of Gaussian beam, spherical wave and plane wave incident on plane mirror and retroreflector are discussed respectively.
引文
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