Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.     

实际大气中闪烁指数测量的数据处理

在闪烁指数定义的基础上,综合考虑背景光噪声、探测器固有噪声和散粒噪声等影响闪烁指数测量精确度的因素,修改了测量系统的数学模型,并对现有数据处理方法做出改进。在1 km距离上进行了激光水平传输实验,分别采用了现有方法和改进方法处理实验数据,并对获取的3种闪烁指数进行了比较。实验结果显示：修改后数学模型相比现有模型更符合实测值;相比系统本底噪声,探测器散粒噪声要高出一个数量级,将会严重影响测量准确度;在信噪比有较大波动的条件下,改进方法受到的影响小于现有方法;在信噪比较低时,改进方法的准确度优于现有方法。     

实际大气中闪烁指数测量的数据处理

在闪烁指数定义的基础上,综合考虑背景光噪声、探测器固有噪声和散粒噪声等影响闪烁指数测量精确度的因素,修改了测量系统的数学模型,并对现有数据处理方法做出改进。在1 km距离上进行了激光水平传输实验,分别采用了现有方法和改进方法处理实验数据,并对获取的3种闪烁指数进行了比较。实验结果显示:修改后数学模型相比现有模型更符合实测值;相比系统本底噪声,探测器散粒噪声要高出一个数量级,将会严重影响测量准确度;在信噪比有较大波动的条件下,改进方法受到的影响小于现有方法;在信噪比较低时,改进方法的准确度优于现有方法。     

Theoretical expressions of temporal power spectra of irradiance fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

The temporal power spectra of irradiance fluctuations reflect the frequency distribution of temporal statistical property of irradiance fluctuation. In this paper, new analytical expressions of the temporal power spectral models of irradiance fluctuations are developed for optical waves propagating through weak non-Kolmogorov turbulence with horizontal path. They are derived with the general modified atmospheric spectral model, and they consider the finite turbulence inner and outer scales, and have a general spectral power law value in the range of 3 to 4 instead of the standard power law value of 11/3. Numerical calculations are conducted to analyze the influence of non-Kolmogorov weak turbulence on the temporal power spectra of irradiance fluctuations.     

Analysis of the temporal power spectral models of angel of arrival fluctuations for optical waves propagating through weak non-Kolmogorov turbulence

New analytical expressions for the temporal power spectral models of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak non-Kolmogorov turbulence. They consider the finite turbulence inner and outer scales, and have a general power law value in the range of 3–4 instead of the standard power law value of 11/3. The results derived in this work can reduce correctly to the previously published analytic expressions for the case of plane and spherical waves propagation through Kolmogorov turbulence case. These results are useful for the understanding the potential impact of derivations from the standard Kolmogorov spectrum.     

探测大气湍流的光强闪烁激光雷达

基于残余光强闪烁理论,分析了与大气湍流探测有关的激光雷达各项硬件参数并获得参数的优化范围,据此研制了一台用于大气湍流探测的光强闪烁激光雷达。背景基线、线性特征等性能测试表明,激光雷达各硬件工作正常,数据获取可靠。实验测量中获得了水平方向上闪烁指数和大气折射率结构常数随探测距离和时间的变化趋势,其中闪烁指数在450~2000 m探测距离范围内由0.001逐渐增大至0.350左右;大气折射率结构常数基本保持水平均匀性,在1.010-16~1.010-15m-2/3范围之内;大气折射率结构常数在10:00~21:00时间内大致呈现上午上升、下午下降、晚上上升的变化趋势,具有较明显的日变化特征。实验结果与理论和常规测量较为相符,表明光强闪烁激光雷达能够获取大气湍流的探测距离变化和日变化特征信息。     

Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation

This paper evaluates the performance of a point-diffraction interferometer for closed-loop adaptive optics. A point-diffraction interferometer was built using a modified Mach-Zehnder set-up. The system was used in closed-loop using a SLM to implement a square, 12 × 12, piston-only segmented corrector with a stroke of ±π. Its performance was tested for the case of atmospheric turbulence aberrations. The investigation showed, through simulation and experiment, that the point-diffraction interferometer worked in closed-loop operation in both uniform intensity and scintillated aberrations. Its robustness in the presence of phase discontinuities makes it a promising option for wavefront sensing in strong scintillation.     

大气湍流对部分相干平顶高斯光束的影响

采用相屏近似处理方法对激光通过湍流大气的传输进行了数值模拟。从数值模拟的结果拟合出两个公式:一是通过湍流前后部分相干平顶高斯光束的束宽平方比随阶数、传输距离和湍流强度的变化关系式;一是通过湍流后的相干长度随初始光束相干长度、湍流相干长度的变化关系式。研究发现:部分相干平顶高斯光束分解为相互独立的厄米-高斯光束的叠加;相干性越差的光束受到湍流的影响程度就越小;湍流对光束传输的影响与光束自身相干特性对其传输的影响之间是不相关的。     

利用闪烁和漂移效应测量大气折射率结构常数的对比分析

 在近海面大气边界层中进行了1 km路径的水平光传输实验,结果表明：利用闪烁和漂移效应推导的大气折射率结构常数之间存在着较大的差异。定量的理论分析揭示了两者不一致的原因在于：闪烁效应主要对路径中部的小尺度湍涡敏感,漂移效应则对发射端附近的大尺度湍涡敏感;随着内尺度变大,漂移效应测量的折射率结构常数将大于闪烁效应测量的折射率结构常数,当内尺度达到20 mm时,前者的测量结果是后者的3倍;当外尺度变小时,漂移效应的测量结果小于闪烁效应的测量结果,当外尺度仅为1 m时,前者的测量结果为后者的1/2;大气折射率3维功率谱的幂律的变化对测量结果的影响非常大,当幂律大于-11/3时,闪烁效应测量的折射率结构常数大于漂移效应测量的折射率结构常数, 最大差异接近于25倍, 当幂律小于-11/3时,漂移效应的测量结果大于闪烁效应的测量结果,两者的差异甚至可达两个量级。     

利用闪烁和漂移效应测量大气折射率结构常数的对比分析

在近海面大气边界层中进行了1 km路径的水平光传输实验,结果表明：利用闪烁和漂移效应推导的大气折射率结构常数之间存在着较大的差异。定量的理论分析揭示了两者不一致的原因在于：闪烁效应主要对路径中部的小尺度湍涡敏感,漂移效应则对发射端附近的大尺度湍涡敏感;随着内尺度变大,漂移效应测量的折射率结构常数将大于闪烁效应测量的折射率结构常数,当内尺度达到20 mm时,前者的测量结果是后者的3倍;当外尺度变小时,漂移效应的测量结果小于闪烁效应的测量结果,当外尺度仅为1 m时,前者的测量结果为后者的1/2;大气折射率3维功率谱的幂律的变化对测量结果的影响非常大,当幂律大于-11/3时,闪烁效应测量的折射率结构常数大于漂移效应测量的折射率结构常数, 最大差异接近于25倍, 当幂律小于-11/3时,漂移效应的测量结果大于闪烁效应的测量结果,两者的差异甚至可达两个量级。     

大气湍流对部分相干平顶高斯光束的影响

采用相屏近似处理方法对激光通过湍流大气的传输进行了数值模拟。从数值模拟的结果拟合出两个公式：一是通过湍流前后部分相干平顶高斯光束的束宽平方比随阶数、传输距离和湍流强度的变化关系式;一是通过湍流后的相干长度随初始光束相干长度、湍流相干长度的变化关系式。研究发现：部分相干平顶高斯光束分解为相互独立的厄米-高斯光束的叠加;相干性越差的光束受到湍流的影响程度就越小;湍流对光束传输的影响与光束自身相干特性对其传输的影响之间是不相关的。     

非Kolmogorov湍流相位屏仿真及对光束传输模拟的影响

采用正态分布模型来描述传播路径上功率谱幂值的非均匀性,利用功率谱反演法构建了基于等效结构常数的非Kolmogorov湍流相位屏,并利用多重相位屏法进行了高斯光束在均匀各向同性湍流与非Kolmogorov湍流两种模型下的传输模拟。通过观察模拟光束的光强均匀度、光束漂移以及闪烁指数等,研究了非Kolmogorov湍流对光束传输模拟的影响。结果发现,当光束通过单个非Kolmogorov相位屏时,光强最大值与光强均匀度随着幂值先增大后减小,光束漂移随幂值在一定范围内单调变化。当光束通过多重相位屏时,发现模拟光束的光强闪烁指数会受到相位屏数量以及湍流模型的影响,当相位屏数量较多时,均匀各向同性湍流模型下模拟得到的光强闪烁指数会大于非K湍流模型下的结果,且非K湍流模拟的光束漂移与均匀各项同性湍流模拟得到的光束漂移的相对误差会随着相位屏数量增多而趋于0。     

湍流折射率谱型对大气闪烁和相位起伏功率谱的影响

基于Taylor湍流冻结假设理论,在不同湍流折射率谱型条件下,推导得出了光波闪烁和相位起伏频谱的表达式;数值计算了湍流谱型中折射率标度指数、内尺度以及外尺度变化时对光波频谱的影响。结果表明：随着折射率起伏标度指数的增大,闪烁频谱的低频段不再仅为常数,高频段下降的幂率逐渐增大,同时相位频谱在整个起伏频率段下降的幂率越来越大;湍流内尺度的增加将引起光波频谱的高频段下降的幂率越来越大;而随外尺度的减小,闪烁频谱低频段的振幅减小,这种影响在大口径接收时较为明显,相位谱的低频段幂率减小。     

Speckle statistical properties of Gaussian beam from a semi-rough target in the atmospheric turbulence

Based on extended Huygens–Fresnel principle and Goodman model for target surface, analytic expression is developed for the mutual coherent function (MCF) of a reflected Gaussian-beam from a semi-rough target in single-pass atmospheric turbulence. Then according to the MCF we derive expression about the mean intensity and average speckle size at the receiver. The analysis indicates that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length; in addition, the speckle size is associated with turbulence strength and roughness of target. Our results agree with well-known the limiting cases of perfectly smooth and Lambertian target.     

湍流大气中激光上行和下行传输时相位奇点的演化

利用激光大气传输四维程序数值模拟了激光在湍流大气中上行和下行传输时产生的相位奇点的变化过程。由模拟结果可知,当光束自地面向空中垂直上行传输时,相位奇点数密度随传输高度的变化有一个从无到有、从快速增加到缓慢增加、达到峰值后又减小的过程;湍流越强,畸变光场中产生的相位奇点数密度越大,达到的峰值越高,且达到峰值后减小的幅度也越大,但达到峰值时对应的传输高度越低;当激光自空中某一位置垂直下行传输时,相位奇点数密度随传输距离的增加有一个从无到有、从缓慢增加到快速增加且在接近地平面处急剧增加的过程。另外,通过对模拟结果的曲线拟合发现,激光在湍流大气中上行传输时产生的相位奇点数密度与传输高度的关系符合黑体辐射公式;当激光在湍流大气中下行传输时,相位奇点数密度随传输距离的增加呈指数增加。     

The effect of tilt aberration and astigmatism of turbulent atmosphere on the intensity distribution of a vortex carrying Gaussian beam

The effect of tilt and astigmatism aberration of the turbulent atmosphere on the intensity distribution of a focused vortex carrying Gaussian beam was investigated based on the extended Fresnel-Kirchhoff diffraction integral and the quadratic approximation of phase structure function. Our results have shown that the intensity distribution on the focal plane in the effect of tilt aberration changes with the turbulent strength, the propagation distance and the topological charge of the initial beam. The propagation distance is larger, the focal spot size will be larger, and the central dip will be less deep. It is also noticed that the intensity distribution of a beam with single topological charge is affected more by tilt aberration in comparison to the beam with double topological charge. The effect of astigmatism on the intensity distribution is quite less than that of tilt aberration. For focused beam propagation in atmosphere, the effect of the tilt aberration on the intensity distribution of optical vortex beam is the main effect of total turbulent aberration.     

间歇性大气湍流中光传播问题的近Gauss极限分析

间歇性是湍流的重要特征，多年来一直是湍流研究的核心内容之一.考虑大气湍流中的光传播问题，一般回避其间歇性，假设大气介电起伏满足Gauss统计.考虑大气湍流（内）间歇性 对光波传播的影响.考虑到大气介电起伏方差较小的事实，将光场统计矩方程在Gauss场附近 展开到四阶累计量，分析其近似解.进一步，以层次结构模型为基础，着重研究了光场二阶 统计矩的间歇性效应.研究表明，大气湍流间歇性对光场的影响很小. 关键词： 光波传播 大气湍流 间歇性     

Statistic of a Gaussian beam from an arbitrary rough target in the single passage atmospheric turbulence

The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function (MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.     

基于多阶频率栅格的湍流相位屏低频补偿

提出一种基于多阶频率栅格划分的子谐波方法用于湍流相位屏的构造.通过对相位屏频域空间划分多阶频率栅格,并将每一阶的频率栅格进行更进一步精细子划分,补偿对湍流谱贡献最多的低频范围频率分量.采用大气湍流的相位结构函数和功率谱分析所构造相位屏的准确度.仿真结果表明:由所构造相位屏得到的相位结构函数与由湍流谱直接计算得到的理论值之间的偏差随着频率栅格总阶数M、每一阶的频率栅格点数目N＇x和N＇y的增大而减小,对每一组M、N＇x、N＇y的取值,子划分前的频率间隔△f1有一最佳值;当选取M=3、N＇x=N＇y=3、△f1=2 m-1时,所构造的相位屏的相位结构函数和功率谱与理论十分接近;所产生的随机相位屏的整体倾斜反映了低频成分的准确采样.