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.     

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。     

Study on the Scintillation for Optical Wave Propagation in the Slant Path Through the Atmospheric Turbulence

Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is altitude dependent, the modified Rytov method, which is applicable to the optical wave propagation in the horizontal path, is extended to the propagation in the slant path. According to the spectrum model with non-zero inner scale, the scintillation index as a function of the Rytov variance is obtained from weak to strong fluctuation regions with plane wave and sphere wave incidence, respectively. Finally, the scintillation index with different zenith angles is analyzed, and comparison between the results of the modified method and experimental measurements is given and discussed in detail.     

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)     

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.     

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.     

湍流大气中星载角反射器阵列回波的闪烁指数

利用Rytov方法结合ABCD传输矩阵理论, 推导了地-空-地双程湍流大气路径中单个角反射器回波在接收孔径平面上的强度协方差函数及闪烁指数公式. 根据角反射器阵列的各角反射器单元回波相位相互独立假设, 计算了接收孔径平面上的强度协方差函数、孔径平滑因子和闪烁指数, 比较分析了单个角反射器与角反射器阵列回波闪烁指数. 证明角反射器阵列不改变闪烁指数, 但大气湍流会引起光强起伏放大两倍的规律. 关键词： 大气光学 角反射器阵列 闪烁指数     

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.     

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.     

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.     

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.     

INNER AND OUTER SCALE EFFECTS ON SCINTILLATION INDEX FOR AN INFRARED LASER PROPAGATING ON EARTH-SPACE PATHS

The effects of the inner-and outer-scale of turbulent atmosphere on the scintillation index for an infrared laser beam propagating through atmospheric turbulence are discussed under the assumption that small-scale irradiance fluctuation is modulated by large-scale irradiance fluctuation on Earth-space paths. A model about the scintillation index with the inner-and outer-scale is developed. A numerical analysis is done by using this model. It is shown that the effect of the inner scale on scintillation index is larger than the outer scale effect for the lesser wavelength wave at visible and infrared band. From moderate to saturation regime, the inner scale effect becomes gradually small; however, the outer scale effect becomes gradually obvious. Under moderate to strong regime, therefore, the effects of the inner-and outer-scale on scintillation index must be considered for theoretical prediction scintillation of an infrared laser beam propagating through turbulent atmosphere on Earth-space paths.     

Irradiance scintillation index for Gaussian beam based on the generalized anisotropic von Karman spectrum

Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3–4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.     

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。     

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。     

湍流大气中光束的相位不连续点数密度

基于Rytov近似和几何光学近似条件下,导出了对数振幅导数方差的解析表达式,证明了该参量主要取决于湍流内尺度、Rytov方差以及Fresnel尺寸大小.在此基础上,给出了光束相位不连续点数密度的修正表达式,分析了相位不连续点数密度随上述湍流参量变化的情况.分析表明在Rytov方差小于1的湍流条件下,不连续点数密度数随Rytov方差的增大而增大,而随湍流内尺度和Fresnel尺寸的增大而减小.     

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。     

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.     

湍流内尺度对光波起伏频谱的影响

在不同湍流内尺度情况下,对大气湍流引起的光波光强闪烁和到达角起伏的时间频谱特征进行了实验研究。由于实际大气湍流的复杂性和不可控性,利用大气湍流模拟箱来生成具有不同内尺度的大气湍流实验环境。利用位置敏感探测器对光波的光强闪烁和到达角起伏进行了同时测量,并反演得到了光传输路径上的湍流内尺度。实验结果显示:湍流内尺度为2.7~5.0 mm,对应同一湍流内尺度,闪烁频谱和到达角起伏频谱在高频段以相同的幂指数关系下降,幂指数的绝对值与湍流内尺度的大小呈线性关系,随着内尺度的增大,频谱指数变化区间逐渐向低频方向移动。     

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.