高斯波束在湍流大气斜程传输中的闪烁问题研究

根据光波斜程传输理论以及随高度变化的ITU-R湍流大气结构常数模型,将水平传输的修正里托夫方法推广到了斜程传输问题中。导出了高斯波束入射时,在零内尺度湍流谱模型及考虑湍流内尺度效应和外尺度效应条件下,从弱起伏湍流区到强起伏湍流区闪烁指数随斜程里托夫方差变化的计算公式。讨论了不同传播高度、不同湍流内、外尺度对高斯波束斜程传输闪烁指数的影响。最后将有关数值计算结果与实验测量结果进行了比较和验证。     

Performance of distributed array receivers for optical-wave propagation in the slant path through the turbulent atmosphere

Considering free-space optical communication systems, we analyze the performance of the intensity scintillation of the optical-wave propagation in the slant path under different atmospheric turbulences. Under the zero scale, we derive the log-intensity spatial covariance function of the optical-wave propagation in the slant path through the turbulent atmosphere based on the modified Rytov method. We demonstrate the relationship between the reception performance of the distributed antenna array and the aperture-averaging factor. Furthermore, we also obtain the optimum aperture diameter, number of sub-antennas, and the sub-antenna interval of the array receiver in intermediate turbulence. This study can benefit the design of the receiving system for the optical-wave propagation in the slant path through the turbulent atmosphere in free-space optical communication systems.     

斜程大气湍流中激光回波的闪烁指数

根据光波斜程传输理论以及随高度变化的ITU-R大气折射率结构常数模型,考虑内尺度及从发射机到目标和从目标到接收机双斜程路径影响的条件下,应用修正Hill湍流折射率起伏功率谱,对反射器目标激光回波闪烁指数进行了研究。推导了回波闪烁指数随菲涅耳率的变化关系,数值分析了不同内尺度、传输距离、激光波长以及目标高度对回波闪烁指数的影响。结果表明:内尺度和目标高度对回波闪烁指数的影响要远大于波长和传输距离的影响。     

Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

双孔差分闪烁法测量大气湍流的理论与实验研究

根据cross-path理论, 推导出弱起伏条件下差分孔径光强起伏结构函数的精确表达式, 以此为依据, 从理论上提出测量大气湍流强度的双孔差分闪烁法. 在Kolmogorov湍流谱条件下, 分析了信标光直径和信标光高度对该方法中路径权重函数的影响. 在近地面开展了2 km路径的水平光单程传输实验, 将双孔差分闪烁法和单孔闪烁法的测量结果进行了对比. 实验结果表明: 在不同的天气条件和大气湍流状况下, 两种方法测量的折射率结构常数具有高度的一致性; 通过对折射率结构常数积分得到的球面波大气相干长度进行相关性分析, 发现两者的线性相关系数达0.96; 由此验证了双孔差分闪烁法的可行性和有效性. 该方法能够分离出主动信标双程传输的后向闪烁信息, 为主动信标准确探测大气湍流提供了一种新方法.     

Scintillation index of optical wave propagating in turbulent atmosphere

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.     

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.

(Some figures in this article are in colour only in the electronic version)     

大气环境下用于瞄准的激光波束传播特性研究

针对激光瞄准过程中的光斑偏移现象,结合修正的Von Karman谱的折射指数起伏和Hufnagel-Vally湍流模型上的近似积分,研究了高斯脉冲光束在湍流大气中远场水平以及斜程传播时的脉冲展宽和闪烁指数,分析了强湍流条件下1.06 μm准单色光斜程大气传输光强分布与脉冲展宽的关系,对数值结果进行比较,发现远距离传输中波长和距离对波束瞄准偏差影响较大.从理论和实验上对大气环境下激光光斑瞄准偏差进行了分析研究,研究结果表明:将激光光斑全场数据及分析结果应用到现有偏差补偿算法中,可以实现激光瞄准偏差的有效补偿,在大气能见度1 km～3 km范围内,激光瞄准偏差测量误差σA≤0.1 mrad.     

Aperture-averaging effects for weak to strong scintillations in turbulent atmosphere

Under the approximations of (1) the received irradiance fluctuations of an optical wave caused by small scale turbulent eddies are multiplicatively modulated by the fluctuations caused by large scale turbulent eddies;(2) the scintillations caused by small- and large-scale eddies, respectively, are statistically independent; (3)the Rytov method for optical scintillation collected by the finite-diameter receiving aperture is valid for light wave propagation under weak to saturation fluctuation regime, we develop the applicable apertureaveraging analytic formulas in the week-to-strong-fluctuation for the scintillations of plane and spherical waves, which include the outer- and inner-scale rules of turbulence.     

Laguerre-Gaussian beam scintillation on slant paths

Scintillation evaluations for Laguerre-Gaussian (LG) beams for slant paths are made using Rytov approximation. On- and off-axis scintillation is formulated and calculated up to several tens of kilometers of slant distances for different zenith angles. Scintillation index variations against radial receiver point and different source sizes are also investigated. In all cases evaluated, it is found that LG beams with higher radial mode numbers result in less scintillation than Gaussian beam. Kolmogorov spectrum function is utilized in the scintillation calculations.     

大气闪烁对自适应光学校正的影响

 激光在大气湍流中长距离近水平传输时，闪烁加强，限制了常规自适应光学的校正能力。数值研究了大气闪烁对自适应光学校正的影响，拟合得到了在Fresnel数一定时，Strehl比与Rytov方差的表达式，以及Rytov方差一定时，Strehl比与Fresnel数的表达式。结果表明，在Rytov方差较小时，纯相位校正Ｓtrehl比只与Rytov方差有关；随着Rytov方差的增加，Strehl比不仅与Rytov方差有关，还与Fresnel数有关，Fresnel数越大，校正Strehl比越大；大发射和接收孔径有利于提高校正Strehl比；在一定的Rytov方差下，Stregl比随Fresnel数增大而增加，逐步趋于饱和，达到纯相位校正的极限。     

General optical scintillation in turbulent atmosphere

A general expression of the scintillation index is proposed for optical wave propagating in turbulent atmosphere under arbitrary fluctuation conditions. The expression depends on extreme behaviors of the scintillation indices under both weak and strong fluctuations. The maximum scintillation index in the onset region and the corresponding Rytov index can be evaluated from the general expression. Plane and spherical waves in the cases of zero and non-zero turbulence inner scale are given as examples for illustration of the general behaviors of scintillation indices.     

Study of Scintillation for Infrared Laser Beam Propagating in Atmospheric Turbulence on Earth-Space Paths

On earth-space paths, by applying a modification of the Rytov method that incorporates spatial frequency filter function under strong atmosphere fluctuation conditions, a tractable model is developed for the scintillation index of infrared laser Gaussian beam wave that is valid under moderate-to-strong irradiance fluctuations. At Infrared band, based on ITU-R C ² _n model, the scintillation indexes for collimation laser beam are predicted by this analytic model. The results agree with theoretic expected scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on earth-space paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C ² _n.     

漂移对聚焦高斯光束闪烁影响的数值模拟

 采用非自适应坐标变换对聚焦高斯光束在湍流大气中的传输进行了数值模拟，结果显示轴闪烁指数并没有出现如Rytov理论所预言的随初始光束半径的增大而明显减小的现象，其原因在于Rytov近似理论未考虑大尺度湍涡产生的漂移效应对闪烁的贡献。对比数值模拟结果与漂移理论结果以及相关实验结果，三者相吻合,表明未考虑漂移效应的Rytov近似理论不能完全准确地描述聚焦光束的闪烁特征，在研究聚焦光束的闪烁时，应当考虑漂移的影响。     

部分相干光束经过湍流大气传输研究进展

相较于相干光束,部分相干光束经过湍流大气传输能够有效地抑制湍流引起的光束展宽、光斑漂移及光强闪烁等扰动效应,在自由空间光通信、激光雷达和激光遥感等方面有重要的应用前景.近年来,部分相干光束湍流大气传输研究受到越来越多学者的关注.本文回顾了部分相干光束在湍流大气中传输特性研究的发展历程、理论基础及常用的理论方法,介绍了处理光束经过湍流大气传输的相位屏数值模拟方法,以及如何把该方法运用到处理部分相干光束传输.     

Analysis of Inner-Scale Effect on Atmosphere Scintillation for Infrared Laser Beam Propagating on Earth-Space Paths

On Earth-space paths, based on ITU-R C_n² (h) model, by means of a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, considering atmospheric turbulence inner-scale, an expression is developed for the scintillation index of a visible or a near and middle infrared laser beam wave that is valid under moderate to strong irradiance fluctuations. The quantitative analyses of scintillation index are done by this analytic model for laser Gaussian collimated beam wave at visible or near and middle infrared wave band. The results agree with theoretic analysis scintillation. This scintillation model can be converted into a Gaussian beam wave model with finite inner-scale on horizontal sight paths of invariable C_n².     

Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.     

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.     

Expressions of the scintillation index for optical waves propagating through weak non-Kolmogorov turbulence based on the generalized atmospheric spectral model

The high frequency “bump” which occurs in the turbulence spectral model just prior to the turbulence cell dissipation is important for the analysis of the irradiance scintillation for optical wave propagating through atmospheric turbulence. In this study, expressions of the irradiance scintillation index are developed from the generalized modified atmospheric spectral model for optical waves propagating through weak non-Kolmogorov turbulence. Compared with the expressions of the irradiance scintillation index derived from the general non-Kolmogorov spectral model, the new expressions can consider the influences of finite turbulence inner and outer scales and the influence of finite diameter aperture receiver. As the irradiance scintillation is caused mainly by the small scale turbulence cells' diffractive effects for weak turbulence, the turbulence outer scale's influence can be ignored. Numerical simulations show that variable inner scale values produce obvious effects on the irradiance scintillation for non-Kolmogorov turbulence.     

非均匀湍流路径光传播数值模拟中相位屏间C_n~2的选取

针对非均匀湍流路径光传播的数值模拟,为减小相位屏间湍流强度均匀的假设所引起的模拟误差,数值分析了五种选择相位屏间折射率结构常数Cn2的可能方案。通过计算平面波和球面波的Rytov指数和Fried参数,对比五种方案得到的Rytov指数和Fried参数与理论结果的相对误差。结果表明,当相位屏间C2n选择为相位屏间湍流大气实际的折射率结构常数的路径平均值时,模拟误差最小,该选择方案为相位屏间C2n选取的最佳方案;当根据相位屏间湍流大气的Rytov指数相等的原则来设置相位屏分布时,选择相位屏间C2n为两相邻相位屏处折射率结构常数的几何平均值时,在一定的误差允许范围内,该选择方案具有可取性。