Phase compensation in non-Kolmogorov atmospheric turbulence

Zernike polynomial decompositions are used for investigating phase distortion induced by atmospheric turbulence in optical systems. Closed-form expression of the Zernike-coefficient variances is derived. The finite size of the receiver aperture is analyzed using the filter function which is also particularly effective in the theoretical analysis of lower-order aberrations like tilt terms and piston-removed phase variance. The outer scale of the non-Kolmogorov turbulence is considered. The result shows that the effect of finite outer scale attenuates low-order Zernike mode of optical distortion and longer outer scale can lead to more energy in the tilt terms. The generalized exponent can only enhance tilt terms and attenuate other Zernike modes of optical distortion. Further, for different outer scale and generalized exponent, the residual phase variance decreases with more modes of phase compensation.     

Performance of phase compensated coherent free space optical communications through non-Kolmogorov turbulence

The bit-error-rate (BER) performance of coherent free-space optical (FSO) links employing phase compensation techniques is investigated in weak non-Kolmogorov turbulence. Assuming that the amplitude fading and phase fluctuation follow lognormal model and Gaussian distribution respectively and using the expression of non-Kolmogorov turbulence in terms of Zernike polynomials, the signal-to-noise ratio (SNR) at the coherent receiver is analyzed and as a special case, a new closed-form expression using chi-square distribution is obtained. Thus, the influence of different compensation modes and normalized receiver diameter on BER performance is evaluated and an optimum normalized receiver diameter is suggested to achieve the minimum BER. Moreover, the impact of outer scale L₀ and the exponent value α in non-Kolmogorov spectrum is studied with the optimum diameter, which reveals that the BER has an obvious decrease with larger values of L₀ and α.     

部分相干光与相干光在湍流中的传输特性实验研究

相干光经湍流传输引起光强闪烁效应,理论研究表明利用部分相干光可降低该影响,而相关的实验验证鲜有报道。利用水介质的对流湍流池模拟产生了Rytov方差为0.04~0.16的湍流,进行了弱起伏区湍流中部分相干光及相干光的传输实验,由接收光强计算出其光强闪烁指数随湍流Rytov方差的变化关系。实验结果表明：随着湍流强度的增加,部分相干光与相干光的闪烁效应均增强,但部分相干光的闪烁指数小于相干光。将实验数据与Andrews等人建立的闪烁指数理论模型进行比较,得出了较为一致的结论。     

部分相干光与相干光在湍流中的传输特性实验研究

相干光经湍流传输引起光强闪烁效应,理论研究表明利用部分相干光可降低该影响,而相关的实验验证鲜有报道。利用水介质的对流湍流池模拟产生了Rytov方差为0.04~0.16的湍流,进行了弱起伏区湍流中部分相干光及相干光的传输实验,由接收光强计算出其光强闪烁指数随湍流Rytov方差的变化关系。实验结果表明:随着湍流强度的增加,部分相干光与相干光的闪烁效应均增强,但部分相干光的闪烁指数小于相干光。将实验数据与Andrews等人建立的闪烁指数理论模型进行比较,得出了较为一致的结论。     

非均匀采样的功率谱反演大气湍流相位屏的快速模拟

对大气湍流功率谱非均匀采样可以有效改善传统功率谱反演法低频采样严重不足的缺陷, 实现高精度的大气湍流相位屏的模拟. 但采用的直接求和运算计算复杂度高, 相位屏的模拟速度极慢. 将非均匀快速傅里叶变换(NUFFT)引入到大气湍流相位屏的模拟, 可以实现相位屏的快速模拟. 从随机过程的谱分解出发, 将大气湍流相位随机过程表示为有限谐波分量叠加和的均方极限. 通过一个高斯核函数的卷积, 将非均匀分布的谐波复振幅映射到均匀网格空间, 进而利用快速傅里叶变换, 降低计算复杂度, 加快大气湍流相位屏的模拟速度. 以大气湍流的Kolmogorov 谱为例, 利用NUFFT仿真得到大气湍流相位屏, 并对相位屏的模拟精度、模拟速度和误差进行统计分析. 结果表明, NUFFT的引入可以实现快速、高精度的大气湍流相位屏的模拟.     

功率谱反演大气湍流随机相位屏采样方法的研究

从产生大气湍流随机相位屏的功率谱反演法原理出发,分析了均匀采样造成的随机相位屏大量低频信息泄漏的不足,提出利用非均匀采样方法对功率谱进行滤波产生随机相位屏.建立了非均匀采样模型,并分析比较了两种采样方法覆盖的采样频率范围和单边采样频率区域的湍流功率,理论证明了非均匀采样功率谱反演产生大气湍流随机相位屏的可行性和有效性.针对大气湍流的Kolmogorov谱,分别仿真计算了两种采样模型下功率谱反演生成的大气湍流随机相位屏.仿真结果表明,在不增加采样点和计算量条件下,非均匀采样方法生成的大气湍流随机相位屏具有丰富的低频和高频信息,有效改善了传统功率谱反演大气湍流随机相位屏时低频信息严重不足的缺陷.     

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration.     

Capacity of wander and spread beams in log-normal distribution non-Kolmogorov turbulence optical links

We model the average channel capacity of optical wireless communication systems in weak turbulence horizontal channels, using the log-normal distribution models. The effects of beam wander and spread, pointing errors, turbulence inner scale, turbulence outer scale and the spectral index of non-Kolmogorov turbulence on system's performance are included. The model can evaluate the influence of the atmospheric turbulence conditions in the performance of a ground-to-train optical wireless communication system.     

The influence of high-frequency phase distortion on the phase correction effect in atmospheric turbulence

By using the method of the power-spectrum inversion, the turbulence phase screen has been built up, and the propagation characteristics of high-frequency phase of laser beam in atmospheric turbulence have been analyzed; in addition, the phase correction effect of laser beams by using the adaptive deformable mirror has been simulated, and its affecting factors in turbulence have also been analyzed quantitatively. The results show that the phase correction effect of laser beams in turbulence is mostly determined by the percent of high-frequency phase in distorted wavefront. With the increase of the intensity of atmospheric turbulence and the propagation distance in turbulence, the percent of high-frequency phase in distorted wavefront increases, resulting in the degradation of the phase correction effect.     

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。     

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。     

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.     

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。     

Characteristics of scintillations and bit error rate of partially coherent rectangular array beams in turbulence

According to the paraxial form of the extended Huygens-Fresnel principle, the analytical formulas of the on-axis average irradiance and the on-axis scintillation index for a rectangular array Gaussian Schell-model (RAGSM) beams in atmospheric turbulence have been derived. The on-axis bit error rate has been analyzed quantitatively. Their effects of the turbulence intensity, the initial correlation length, and the array parameters including the beamlet number (M and N) and the array separation distance (x₀ and y₀) have been discussed. The results show that the correlated and uncorrelated superposition RAGSM beams exhibit the different on-axis intensity distribution, the similar variation of the on-axis scintillation and the bit error rate. At the nearer propagation distance the on-axis scintillation rises against propagation distance with the increasing beamlet number and the decreasing array separation distance, whereas the situation is reversed at the farther propagation distance. The effects of array parameters on the bit error rate are similar to that on the scintillation. For a given propagation distance the scintillation index increases with the stronger coherence and the larger waist width of the array beam.     

倾斜离轴高斯-谢尔模型光束在大气湍流中通过猫眼光学镜头反射光的光强特性

本文研究了大气湍流和探测光空间相干性对倾斜离轴激光束通过猫眼光学 镜头反射光光强特性的影响. 研究表明: 由于光阑效应以及光束倾斜或离轴, 反射光光强出现振荡和非对称分布现象. 大气湍流不会改变其非对称性, 但湍流中其光强不再振荡. 当猫眼光学镜头存在微弱正离焦δ_max情况下, 轴上光强可达到最大值. 猫眼光学镜头焦距越大, 所需δ_max越大. 但是, 大气湍流和探测光相干性好坏都不会改变所需δ_max值. 在大气湍流中传输距离足够远时, 反射光强会成为离轴类高斯分布. 随着传输距离的增大, 相干性越差的探测光的反射光束扩展可以更小, 这与部分相干光自由空间传输规律完全不同. 探测光相干性越好, 其反射光强受湍流的影响越大, 但差异不大. 本文所得结果对激光主动探测的应用具有意义. 关键词： 猫眼光学镜头 大气湍流 部分相干光 光强     

大气湍流中部分相干光束上行和下行传输偏振特性的比较

以部分相干的电磁高斯-谢尔模型(electromagnetic Gaussian-Schell model, EGSM) 光束为研究对象, 根据相干和偏振的统一理论以及随机光束的Stokes参量, 推导出EGSM光束在大气湍流中斜程传输时的偏振度(degree of polarization, DoP)和偏振方向角的表达式, 研究了大气湍流中上行和下行传输时EGSM光束偏振特性的不同. 研究结果表明: 在相同条件下, EGSM 光束下行传输时整个光场DoP的分布比上行传输要集中; 下行传输时轴上点的DoP达到最大值所对应的传输距离长于上行传输. 可以看出, EGSM光束沿下行路径传输时, 探测器可以接收更远距离处的波束传输信息.