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.     

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。     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

Fourth moments of acoustic waves forward scattered by a rough ocean surface

Abstract

Three types of statistical fourth moments of acoustic waves forward scattered by a randomly rough ocean surface are derived and numerically evaluated. The first one is related to the scintillation index which characterizes intensity fluctuations. The second one is the two-position intensity correlation function which describes the spatial correlation of wave intensity. The third is the fourth-moment two-position coherence function which carries information on the phase fluctuations of the scattered wave. In the range of weak scattering, the ratio of the absolute value of the fourth-moment two-position coherence function over the two-position intensity correlation exactly describes the mean-square fluctuation of the relative phase between the two positions. The acoustic frequency is high so that the Kirchhoff approximation can be used. Two types of spectral functions for surface-height fluctuations are considered: a Gaussian spectrum and the Donelan-Pierson spectrum. The latter is obtained from a model for the fluctuations of the ocean surface height which are controlled by the wind speed at the ocean surface.     

南海北部浅海声场起伏及统计特性

水下声场的时间积分声强和峰值声强是声呐检测中的重要物理量,而海洋中的内波等动力学过程会造成声场强度的起伏。对南海北部浅海内波环境下定点声起伏实验数据分析,结合数值仿真,总结了试验海域近海底发射和近海底接收条件下内波引起接收信号强度起伏的统计特性.分析结果表明:接收信号的时间积分声强起伏小于峰值声强起伏;时间积分声强与峰值声强起伏的概率分布与对数正态分布较为接近.时间积分声强和峰值声强起伏大小与信号的频率有关,同一收发距离,中心频率650 Hz信号的声强起伏较中心频率310 Hz和375 Hz信号的声强起伏更为剧烈。对于同一频率,当海底较平坦时,声强起伏的闪烁指数随传播距离的增加而增大;当水深随传播距离逐渐变深时,声强起伏规律受内波和水深变化共同影响而更为复杂,闪烁指数先随传播距离增加而增大,之后又随传播距离的增加而逐渐变小.      

湍流特征光学测试对比

在10℃～230℃温差下,对大气相干长度r0分别采用夏克-哈特曼的到达角起伏法、差分像运动法、波面法三种测量法和四象限探测器进行了测试和对比;对折射率结构常量Cn2及闪烁功率谱分别采用夏克-哈特曼和光电倍增管进行对比.实验结果表明:对于r0,在强湍流时四象限探测器比夏克-哈特曼的稳定性明显降低,且对夏克-哈特曼三种方法,差分像运动法可克服设备抖动等问题,但引入了方向上不一致的问题,波面法可有效避免该问题;对于Cn2,夏克-哈特曼比光电倍增管测量更稳定,拟合相关系数高达0.96;对于闪烁功率谱,由于噪音影响,在200℃时夏克-哈特曼比光电倍增管测得的最大频率高15Hz;最后,通过对夏克-哈特曼子孔径的闪烁功率谱分析得出,若同一子孔径入射光强不在CCD响应的线性区间时无法准确测量闪烁功率谱,否则可通过不同子孔径可完成湍流均匀性的测量.这将为湍流池提供最优的测试方法及理论依据.     

畸形波电磁散射特性分析及其特征识别标识的研究

针对弱非线性的Longuet-Higgins模型在模拟强非线性畸形波海面时所存在的问题,采用修正的相位调制法模拟一维畸形波时间、空间波面,该方法能够实现畸形波的定时定点生成,并且其波形既能保持目标谱的频谱结构,又能较大程度地满足波浪序列的统计特性.同时,基于改进的双尺度(TSM)法及时域有限差分法建立畸形波的电磁散射模型,经过相对平均偏差和均方根偏差误差分析后,基于TSM法研究分析了畸形波及其背景海面波的归一化雷达散射截面(NRCS)的计算结果.实验表明,合成孔径雷达成像中畸形波的NRCS比背景波要小,即畸形波的合成孔径雷达图像成像比背景波要灰暗,因此可以将NRCS作为畸形波的特征识别标识.通过分析研究不同极化方式、入射角、入射频率条件下畸形波与背景波面的电磁散射特性实验数据得出:当二者的NRCS差值大于-11.8 dB及以上时,即认为产生畸形波,这为实际的工程应用提供了参照标准.     

湍流等离子体鞘套中高斯光束的传播特性分析

为了研究高斯光束在湍流等离子体鞘套中的传输特性,根据广义惠更斯-菲涅耳原理,采用基于快速傅里叶变换的功率谱反演法,用多随机相位屏来模拟湍流带来的影响.根据超声速飞行器绕流等离子体流场厚度在厘米级别的特点,光束在两个相位屏之间的传输过程中采用菲涅耳衍射积分的两次快速傅里叶变换算法(double fast Fourier transform algorithm),利用多随机相位屏模拟等离子体鞘套湍流对光束传输产生的影响,解决了多随机相位屏模拟湍流研究中的超短距离传输问题.当飞行高度为45 km,飞行速度为18马赫时,通过对超声速飞行器绕流等离子体流场的统计分析,发现在此飞行条件下折射率起伏方差的强度范围10~(–11)—10~(–14).对高斯光束在湍流等离子体流场中的传输特性进行了数值仿真.结果表明:在等离子体鞘套湍流中折射率起伏强度、波长、传输距离等都是影响高斯光束质量的重要因素.折射率方差越大,传输距离越长,光斑弥散越严重,光强起伏越大,光强减弱也越明显.光束的波长越长,高斯光束抑制湍流的能力越强,光斑弥散程度越小,光强起伏也越小.     

超声纵波在孔隙砂岩中的传播特性实验*

为了深入研究不同入射频率下超声波纵波在砂岩中的传播特性,以灰、红、褐砂岩为研究对象,开展了基于50 k Hz、100 kHz、200 kHz、500 kHz和1000 kHz入射频率的超声波纵波测试。提取纵波波速、幅值衰减系数、主频幅值、波形能量这些声学参数,结合入射频率和砂岩孔隙率进行传播特性的相关性分析。结果表明,在3种砂岩中,纵波波速随入射频率增大呈非线性增长趋势,砂岩种类不同,波速增长规律也不同;波形能量和主频幅值随入射频率呈指数关系降低;灰、红砂岩纵波波速随孔隙率越大,下降速率越大,褐砂岩在同级孔隙率下波速差异性明显。建立了基于3种砂岩的入射频率和幅值衰减系数的回归方程;基于200 kHz的入射频率,建立了砂岩孔隙率于波形能量的回归方程,实际测试中建议采用200 kHz作为入射频率,可较好兼顾检测的灵敏度和探测距离。研究成果为建立声学参数与砂岩抗压强度之间的内在联系提供了更多数据支撑,为实际物探测试中超声波入射频率的选择提供参考。     

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.     

椭圆涡旋光束在海洋湍流中的传输特性

本文采用分步相位屏方法来仿真椭圆涡旋光束在海洋中的实际传输情况,并对椭圆涡旋光束在海洋湍流中的传输光强和闪烁因子进行了仿真。研究发现,椭圆涡旋光束在海洋传输过程中,光斑会发生明显的旋转,同时光斑会产生暗核且暗核个数与光束的拓扑荷数相等。一个拓扑荷数为m的相位奇点会分裂成m个拓扑荷数为1的相位奇点,并且海洋湍流越强,光斑受到的干扰越严重。研究还发现,在较弱的海洋湍流中,随着传输距离的增加,椭圆涡旋光束的闪烁因子会低于高斯光束和涡旋光束的闪烁因子,而且在远距离处拓扑荷数越大闪烁因子降低越明显,同时也发现,传播一段距离后涡旋光束的闪烁因子会低于高斯光束的闪烁因子。在较强湍流中,椭圆涡旋光束的闪烁因子会交叠在一起。对于不同强度的海洋湍流,随着均方温度耗散率的增大,椭圆涡旋光束的轴上点闪烁因子也增大。在同一传输距离处,束腰宽度越小的椭圆涡旋光束闪烁因子越小。     

部分相干光在大气湍流中传输的闪烁指数

实验测量了不同空间相干度的部分相干光在实际大气湍流中传输的闪烁指数。结果表明:随着入射光空间相干度的降低,闪烁随光传输距离增长而增加的趋势变得缓慢,甚至出现减小的情况。此外,与完全相干光的闪烁指数随着径向距离的增加而增加不同,部分相干光的闪烁指数沿着光斑径向距离的增加不一定增加,而有可能出现降低。相干度越低,该效应越明显。     

Pulsed digital micro-holography of femto-second order by wavelength division multiplexing

Wavelength division multiplexing (WDM) used in a pulsed digital micro-holographic system to record ultra-fast processing of the order of femto-second is reported for the first time, where a BBO crystal is used to generate harmonic wave of the incident laser wave, and both of the basic and the frequency doubled waves are time-delayed and introduced to a Michelson’s interferometer to record two sub-holograms with different spatial frequencies on a single frame of a CCD by WDM. In the experiment, an ultra-fast dynamic process of air ionization induced by a single femto-second laser pulse is holographic recorded by this system, and both of intensity and phase difference images digitally reconstructed are obtained through Fourier transformation and digital filtering, which shows clearly the dynamic process of formation and propagation of the plasma, with a time resolution of the order of femto-second.     

光纤布喇格光栅器件应力疲劳评价理论研究

在10℃~230℃温差下,对大气相干长度r₀分别采用夏克-哈特曼的到达角起伏法、差分像运动法、波面法三种测量法和四象限探测器进行了测试和对比;对折射率结构常量C_n²及闪烁功率谱分别采用夏克-哈特曼和光电倍增管进行对比.实验结果表明:对于r₀,在强湍流时四象限探测器比夏克-哈特曼的稳定性明显降低,且对夏克-哈特曼三种方法,差分像运动法可克服设备抖动等问题,但引入了方向上不一致的问题,波面法可有效避免该问题;对于C_n²,夏克-哈特曼比光电倍增管测量更稳定,拟合相关系数高达0.96;对于闪烁功率谱,由于噪音影响,在200℃时夏克-哈特曼比光电倍增管测得的最大频率高15 Hz;最后,通过对夏克-哈特曼子孔径的闪烁功率谱分析得出,若同一子孔径入射光强不在CCD响应的线性区间时无法准确测量闪烁功率谱,否则可通过不同子孔径可完成湍流均匀性的测量.这将为湍流池提供最优的测试方法及理论依据.     

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.     

Shack-Hartmann波前传感器用于闪烁和相位起伏效应的同时测量

将每一个子孔径及相应的CCD面元作为一个光强探测系统,可以将Shack-Hartmann波前传感器用于湍流大气闪烁效应的测量.分析了该测量方法的基本原理,并结合其波前探测的功能.在近地面水平1km的湍流大气中,同时进行了闪烁和相位起伏的实验研究.将闪烁测量得到的Cn2与大口径闪烁仪测量的结果进行对比,发现两者的相关系数达0.838,验证了Shack-Hartmann波前传感器用于闪烁效应测量的可靠性.对闪烁和相位起伏效应得到的Cn2的日变化进行了对比.结果表明,两者在变化趋势上具有较好的一致性;采用双对数坐标对两种结果进行相关性分析,发现两者的相关系数达0.798.这表明将Shack-Hartmann波前传感器用于闪烁和相位起伏效应的同时测量是可行的,拓展了该传感器的使用功能.     

伪部分相干高斯-谢尔模型光束在湍流大气中传播的闪烁孔径平滑效应

采用光传播的数值模拟方法, 对伪部分相干高斯-谢尔模型光束大气传播过程进行数值模拟, 统计分析不同接收口径内的光强起伏特性,计算闪烁的孔径平滑因子, 讨论了表征伪部分相干光的调制相位屏的相对变化频率对闪烁指数的影响, 并将其与充分发展的部分相干高斯-谢尔模型光束及完全相干光的闪烁指数对比. 结果表明: 降低光源相干性可大幅度降低闪烁指数, 但同时其闪烁指数的孔径平滑效应减弱, 在相同接收孔径下, 伪部分相干光闪烁指数的孔径平滑效果要比完全相干光差; 增大调制相位屏的相对变化频率可在一定程度上降低闪烁指数, 随着其相对频率的增大, 伪部分相干光的闪烁指数与部分相干光的结果趋于一致. 关键词： 伪部分相干高斯-谢尔模型光束 湍流大气 孔径平滑闪烁指数 数值模拟     

湍流中漫射目标偏振部分相干激光的闪烁特性

采用广义惠更斯-菲涅耳原理和矩阵光学理论,研究了湍流大气中偏振部分相干激光波束从发射机到目标和从目标到接收机双程路径的闪烁特性。将产生任意偏振光束的琼斯矩阵和ABCD传输矩阵进行结合,围绕接收机处波场四阶矩展开推导,得出双程路径下偏振部分相干激光波束在接收机处的闪烁指数表达式,数值分析了大气折射率结构常数、激光波束的波长、束宽、相干长度对接收机处光强闪烁指数的影响。结果表明:偏振部分相干激光波束的闪烁指数随着目标与发射机之间距离呈现先增大、到达峰值后逐渐减小的变化趋势;相干性差的光束产生的闪烁指数小,相干长度微小的变化将会产生较大的闪烁指数变化,相干性好的光束产生较大的闪烁指数,但是相干长度的变化对闪烁指数的影响很小。     

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.     

相位连续变化型太赫兹波带片

通过对太赫兹波段相位连续变化型波带片的系统研究,分析了特征尺寸与焦距、F数、预设频率、材料折射率等设计参数之间的关系,讨论了影响相位连续变化型波带片效率的几个主要因素。选取太赫兹透过率较高的泡沫聚乙烯和高密度聚乙烯材料,提出了设计方案,对所设计的波带片沿光轴方向太赫兹波强度变化以及焦平面太赫兹波强度变化给出了计算机模拟结果,并给出一组不同频率的波带片的特征参数。