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.     

基于随机数据元扩张的大气湍流相位屏数值模拟

准确模拟大气湍流相位屏是建立大气湍流数值模型的核心问题。从大气湍流的统计学特性入手,利用大气湍流波前相位结构函数建立了一种新的大气湍流相位屏数值模拟方法,通过随机数据元扩张对大气湍流波前畸变相位分布的尺度随机性和高频分量随机性进行了模拟,并以此为基础通过相位屏近似构建了满足Kolmogorov统计规律的大气湍流数值模型。计算结果表明,随机数据元扩张法生成的相位屏在统计特性上与理论值基本吻合,在低频部分相对于功率谱反演法有明显的提升。同时,随着相位屏网格数的增加,计算结果的高频特性逐渐呈现并逼近理论值。对于由相位屏构建的大气湍流数值模型,在此通过光强闪烁率作为判据进行了验证,结果表明对于弱湍流和中等强度的湍流,模拟结果与理论计算基本相同;对于强湍流则误差较为明显,相对误差最大可达40%。     

无限长湍流相位屏产生方法

在考虑时间特性的激光大气湍流数值模拟中,构造满足要求的湍流相位屏对大气湍流的模拟尤为重要,为此提出基于多点预测的相位协方差插值方法产生湍流相位屏,由多个已知点的相位值对新插值点的相位值进行预测,推导出了插值点的预测矩阵及其残余方差的表达式,并对插值后生成的相位屏的空间统计特性进行了验证。数值模拟结果表明:该方法产生的湍流相位屏与大气湍流的统计特性符合得较好,随着用于预测的已知点数的增加,模拟生成的湍流相位屏的精度提高,并可以进行连续插值生成无限长的湍流相位屏。     

自适应光学系统测试中大气湍流的时域模拟

建立了大气湍流模拟的时域模型,用于在自适应光学系统的测试中模拟大气湍流的时域变化。讨论了时域模型下随机相位屏平滑帧数和刷新频率与平均风速的关系。结果表明：对表征随机波前的随机相位屏进行时域平滑可使随机波前的变化更符合大气湍流对入射波前连续平滑渐变的影响;随机相位屏的平滑帧数仅与系统口径和大气相干长度相关,而与风速无关;随机相位屏的刷新频率与平均风速成正比,平滑后的刷新频率还与平滑帧数成正比。最后,构造了一套大气湍流模拟装置,应用功率谱分析法对时域模型的有效性进行了验证。     

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.     

一种改进的次谐波大气湍流相位屏模拟方法

提出了一种改进的次谐波大气湍流相位屏模拟方法,通过对低频相位屏的采样方式进行设计,能够充分地补偿相位屏中的低频信息.利用该方法对符合Kolmogorov理论的大气湍流相位屏进行数值模拟,并结合相位结构函数和相对误差函数对所提方法的准确性进行验证,分析谐波次数和采样点数对模拟相位屏的影响.此外,还将改进后的次谐波法与经典的功率谱反演法、Zernike多项式法、分形法及改进前的次谐波法进行了对比,结果表明:改进后的次谐波法对应的相位结构函数与Kolmogorov湍流理论值最符合,即利用此方法生成的相位屏最准确.     

采用分区法生成稀疏谱湍流相位屏

为了更好地研究光束在大气湍流中的传播特性,提出了基于稀疏谱模型的湍流相位屏模拟方法,对生成相位屏的灰度图、结构函数和光束漂移量进行了研究分析。首先采用数学方法分析光波的方向、大小和振幅,并由此得到稀疏谱相位屏;然后分别在不同相干半径下,与功率谱反演法生成的相位屏灰度图进行对比,并分析稀疏谱模型下的结构函数和光斑位置拟合度。仿真和实验测试结果表明,实验结构函数的平均误差为6.1%,该模拟方法下的相位屏细节信息更为丰富,大气湍流光斑质心的均方根误差为1.013×10?7 m,具有精度高、运行速度快、模拟周期长等优点,能够较好地模拟真实大气湍流。     

大气湍流下合成孔径激光雷达成像数值模拟及PGA补偿

为研究大气湍流对合成孔径激光雷达(SAL)的成像影响,采用谱反演法对符合Kolmogorov谱的大气随机相位屏进行了数值模拟,给出了单层及多层叠加的随机相位屏图像;然后以多层随机相位屏叠加方式模拟实际大气湍流,计算了无湍流、弱湍流、中等湍流和强湍流等情况下理想机载单站聚束式SAL对点目标以及扩展目标的成像,模拟成像表明大气湍流对SAL成像的方位分辨率有严重影响,湍流越强,图像方位向分辨率越差;针对湍流造成的SAL图像方位向分辨率降低,采用相位梯度自聚焦(PGA)算法对SAL图像进行了方位向补偿,结果有效地改善了图像的聚焦效果,提高了成像质量。     

基于修正大气谱的湍流相位屏高精度生成方法

为了更准确地反映湍流的实际特征,在光波的大气传输模拟中应采用修正大气折射率谱模型.本文针对该谱模型提出了一种高精度湍流相位屏生成方法.通过改变模型在低频区的采样设置,实现了基于修正大气谱的湍流相位屏高精度生成.通过与原始FFT法、次谐波法以及改进前的优化方法相比发现,本文提出的改进后的优化方法能将相位屏低频区域的最大相对误差从改进前的6.75%减小到1%,作为比较,原始FFT法在低频区的最大相对误差为22.99%,次谐波法为16.81%.利用该方法所生成的相位屏对高斯光束在湍流中的传输进行了模拟并对光束扩展和光束漂移等二阶统计特性进行了估计.结果表明,在弱扰动条件下,模拟结果和理论预测的结果是一致的;在强扰动条件下,随着距离的增加,模拟结果与理论结果偏差越来越大,其中光束扩展与理论预测的偏差最大可达6cm,而光束漂移可达1cm,这是由于理论模型无法预测漂移饱和现象而导致的.在与Von-Karman谱的模拟结果比较时发现,修正大气谱估计的光束扩展大于Von-Karman谱的估计且在光束漂移的预测中比Von-Karman谱更快的达到饱和,这正是修正大气谱高波数处存在"凸起"的结果.本文提出的方法生成的相位屏能够有效的表征实际大气的折射率扰动特性.     

大气风速对大气传输光束相位特性的影响

采用功率谱反演法构建湍流相位屏,通过横向平移相位屏的方法模拟大气风速引起的湍流时间变化,进而模拟分析了包括时间进程的激光大气传输特性,从波前相位功率谱密度的角度,定量分析了大气风速引起的激光束在大气湍流中传输时的相位特性变化。在此基础上,采用影响函数模拟变形镜对畸变波前的校正作用,对激光束经大气湍流传输后的自适应校正效果进行了预估,分析了大气风速对校正效果的影响。结果表明,大气风速对边界层湍流中光束相位特性的影响很小,然而,对于自由大气湍流中的传输光束,大气风速越大,波前相位畸变程度越大,畸变波前中高频相位比例也越大;环状光束的校正效果受大气风速的影响比平顶光束更小,并且,随着环状光束阶数的增大,校正效果所受影响逐渐减小;在一定相位畸变范围内,畸变程度越大的环状光束的相位校正效果受大气风速的影响越小。     

天文望远镜像差对斑点成像技术的影响

着重研究了采用斑点成像技术处理天文望远镜图像时,光学系统固定像差对图像恢复结果的影响。在详细研究各种恢复天文图像振幅和相位的理论和方法的基础上,建立了一个包括Labeyrie振幅恢复方法和KnoxThompson相位重构方法的恢复扩展目标的斑点成像处理模型,分析了光学系统固定像差对系统传递函数相位分布和目标相位重构的影响：天文目标通过大气成像,固定像差将会被淹没在大气湍流随机起伏中,像差对相位重构没有显著影响。处理图像结果表明,斑点成像技术能同时消除大气湍流和望远镜系统固定像差的影响,得到高分辨力的扩展目标图像。还提出了一种消除光学系统像差的方法。     

Simulation of anisoplanatism of adaptive optical system in inhomogeneous turbulent atmosphere

The goal of this study was to analyse anisoplanatism of adaptive optics under an inhomogeneous turbulent atmosphere over a pupil of finite size. By means of a numerical model with layers of turbulence software was proposed by which point spread function (PSF), optical transfer function (OTF) as well as system isoplanatic angle can be calculated. Atmospheric turbulence was simulated with the aid of a set of moving random phase screens with arbitrary statistics. Both reference and target are assumed to be the point light sources. To simulate atmospheric turbulence we applied the concept of a number of moving random phase screens with Kolmogorov spectrum. In my investigation I used the model of the Shack-Hartmann wave front sensor and the ideal model of a wave front adaptive mirror that is assumed to reproduce a given number of Zernike polynomials without time delays. The designed software allows calculation of instantaneous and average values of phase correction errors at different angles between a reference beacon and target source. Simulations can be made with a broad range of parameters of an adaptive system and atmospheric turbulence. The system of the model allows changing of the control algorithm of phase correction. Both common phase conjugation and weighted phase conjugation algorithm have been tested. This program is capable of calculating the effects of beam diffraction during propagation in the atmosphere.     

A three-dimensional refractive index model for simulation of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed with using the so-called “split”-operator method, when the influence of the propagation medium’s refractive index inhomogeneities is accounted for only within a system of infinitely narrow layers (phase screens) where phase is distorted. Commonly, under certain assumptions, such phase screens are considered as mutually statistically uncorrelated. However, in several important applications including laser target tracking, remote sensing, and atmospheric imaging, accurate optical field propagation modeling assumes upper limitations on interscreen spacing. The latter situation can be observed, for instance, in the presence of large-scale turbulent inhomogeneities or in deep turbulence conditions, where interscreen distances become comparable with turbulence outer scale and, hence, corresponding phase screens cannot be statistically uncorrelated. In this paper, we discuss correlated phase screens. The statistical characteristics of screens are calculated based on a representation of turbulent fluctuations of three-dimensional (3D) refractive index random field as a set of sequentially correlated 3D layers displaced in the wave propagation direction. The statistical characteristics of refractive index fluctuations are described in terms of the von Karman power spectrum density. In the representation of these 3D layers by corresponding phase screens, the geometrical optics approximation is used.     

高斯谢尔光束通过湍流大气漫射目标的散射统计

基于广义惠更斯菲涅耳原理分析了高斯谢尔光束通过湍流大气漫射目标的散射统计特性。假定相位结构函数起主导作用,根据高斯谢尔光束的交叉密度函数,推导了散斑场的互相干函数表达式,进而得出接收面处的散斑尺寸大小和强湍流起伏的时延协方差函数表达式。数值分析了源相干长度、波长、湍流强度对互相干函数的影响。对理想漫射目标,接收面的散斑尺寸大小由束腰宽度、源相干长度和湍流强度确定,随着湍流强度的增加,散斑尺寸变小;在弱湍流区,散斑尺寸由源相干长度决定,当湍流增强时,散斑尺寸大小逐渐趋于一致。     

Generation of infinitely long phase screens for modeling of optical wave propagation in atmospheric turbulence

Numerical modeling of optical wave propagation in atmospheric turbulence is traditionally performed by using the so-called 'split'-operator method, where the influence of the propagation medium's refractive index inhomogeneities is accounted for only within a set of infinitely narrow phase distorting layers (phase screens). These phase screens are generated on a numerical grid of finite size, which corresponds to a rather narrow slice (spatial area) of atmospheric turbulence. In several important applications including laser target tracking, remote sensing, adaptive optics, and atmospheric imaging, optical system performance depends on atmospheric turbulence within an extended area that significantly exceeds the area associated with the numerical grid.

In this paper we discuss methods that allow the generation of a family of long (including infinitely long) phase screens representing an extended (in one direction) area of atmospheric turbulence-induced phase distortions. This technique also allows the generation of long phase screens with spatially inhomogeneous statistical characteristics.     

Simulation of extended phase screens in problems of optical wave propagation through the atmosphere

Turbulent medium in problems of optical wave propagation through the atmosphere is usually nodeled as a set of statistically independent plane screens with a random two-dimensional field of phase progress. In this paper, we develop methods for the formation of nonperiodic phase screens infinitely extended in a certain direction, which are required in problems of dynamic simulation of wave propagation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 1, pp. 21–34, January 2006.     

Diffractive optical elements with a double identical microstructure for determination of statistical parameters of random phase objects

Physical processes of interference pattern formation in partially coherent and coherent optical systems containing special diffractive optical elements with a double identical microstructure are studied in the case when a thin scattering object is present in the optical system. Methods for determining the spatial coherence function of the light field, the autocorrelation function of transmission of random phase screens, and the statistical parameters of the screens are considered.     

The angle-of-arrival variance of optical waves propagating through turbulent atmosphere in the presence of random jitter

Dynamic wind loads, thermal expansion and other mechanical reasons cause optical platform mounts to sway. The sway distorts the alignment between transmitters and receivers, causing random pointing jitter, the outcome of which is the phase fluctuation of optical waves from the transmitter. Furthermore, atmospheric turbulence causes fluctuations in the phase of those optical waves. By using the extended Huygens-Fresnel principle, both phase fluctuations are considered and an analytic formulation for the angle-of-arrival variance of optical waves propagating through turbulent atmosphere in the presence of motion-induced pointing jitter is derived. The result shows that the angle-of-arrival variance of optical waves under the combined impact of motion-induced pointing jitter and atmospheric turbulence is the sum of the angle-of-arrival variances induced by them independently.