大气湍流随机相位屏的数值模拟和验证

本文使用傅立叶变换法对符合Kolmogorov谱的大气随机相位屏进行了数值模拟,采用三层随机相位屏叠加模拟大气湍流.通过比较模拟相位屏的相位结构函数和理论值的符合度对相位屏的统计特性进行了验证,利用长曝光传递函数和相位结构函数计算大气相干长度r0.结果表明,用傅立叶变换法模拟的随机相位屏是正确的,但相位结构函数存在明显的低频空间频率成分不足,采用三层随机相位屏叠加对相位结构函数和理论值的符合度有所改善,实际r0值比设计值偏大.     

大气湍流随机相位屏的数值模拟和验证大气湍流随机相位屏的数值模拟和验证

本文使用傅立叶变换法对符合Kolmogorov谱的大气随机相位屏进行了数值模拟，采用三层随机相位屏叠加模拟大气湍流。通过比较模拟相位屏的相位结构函数和理论值的符合度对相位屏的统计特性进行了验证，利用长曝光传递函数和相位结构函数计算大气相干长度r0。结果表明，用傅立叶变换法模拟的随机相位屏是正确的，但相位结构函数存在明显的低频空间频率成分不足，采用三层随机相位屏叠加对相位结构函数和理论值的符合度有所改善，实际r0值比设计值偏大。     

大气湍流畸变相位屏的数值模拟方法研究

利用功率谱反演法和Zernike多项式展开法对符合Kolmogonov统计规律的大气湍流畸变波前相位屏进行了数值模拟研究。通过对比模拟相位屏的相位结构函数与理论结果的差异分析模拟相位屏的准确性。结果表明,功率谱反演法产生的相位屏在高空间频率部分与理论相符,在低空间频率部分明显偏离理论值,通过次谐波补偿有效改善低频不足,次谐波级数达到4级足够;Zernike多项式展开法产生的相位屏的低空间频率成分与理论相符,而高空间频率成分不足随着所用Zernike阶数的增加而有所改善,但同时也带来计算量增大的问题。     

天文学自适应光学成像望远镜的模拟

为分析天文学自适应光学(AO)望远镜中AO系统的校正性能,利用Matlab仿真其成像过程。采用正交基为Zernike多项式的自相关法产生符合大气统计特性的大气相位屏,仿真平行光通过大气后的瞬时畸变波前相位;采用快速傅里叶变换仿真哈特曼-夏克波前传感器的成像光斑,根据实际成像与参考平面波成像的质心坐标之差,计算波前传感器子孔径内的平均波前斜率。模拟比较了1.2m望远镜两种AO系统布局的校正性能,结果表明,子孔径为正六边形AO系统的校正性能略优于子孔径为正方形AO系统的校正性能,两种AO系统的SR比(StrechlRatio)分别为0.872和0.859。     

重轨InSAR干涉测量中的大气信号特征分析

给出了干涉测量中大气相位延迟与单次雷达测量时大气相位延迟的关系,并利用ERS Tandem数据对重轨干涉测量中的大气信号进行了定量的分析研究.实验数据的结果表明,干涉测量中大气相位延迟信号与地面高程有关,随高度增高干涉测量中的大气相位延迟信号变小;在重轨干涉测量中大气信号的结构函数和功率谱函数均呈现指数分布规律,并且在山区和平地,在不同的尺度呈现出不同的指数分布特性.该研究结果有助于建立重轨hSAR干涉测量中的大气信号模型.     

基于相位差异的图像复原方法

相位差异法利用焦面和离焦通道图像存在的固定离焦相位差为先验信息,联合估计波前相位和目标.本文设计了相位差异图像复原实验,利用变形镜模拟大气湍流扰动,通过Offner反射镜搭建反射式成像系统,消除了色差影响和简化了实验光路.实验结果表明,恢复后图像的分辨率提高了12%,验证了相位差异法提高图像分辨率和解算波前相位的能力.因此该方法是大口径光电成像系统克服波前畸变较为理想的图像恢复技术.     

一种基于时空瞬时稳定性的方位谱估计方法

针对基于子空间分解的空间方位谱估计方法稳健性问题,提出了一种基于时空瞬时稳定的方位谱估计方法。该方法首先依据空间目标信号时域瞬时稳定性,将协方差矩阵频域求取过程转换为经相参补偿的复域求取,降低空间数据稳定性对协方差矩阵估计的影响;然后依据各子空间输出方位谱峰值索引离散度差异,提取各子空间方位谱加权因子;最后根据加权因子实现对各子空间方位谱加权处理,降低背景噪声对最终合成空间方位谱影响。数值仿真及实测数据处理结果表明,相比子空间分解方法,在不损失空间分辨率情况下,能够有效降低空间数据稳定性对协方差矩阵估计产生的影响,在无目标先验信息情况下,对最低信噪比的需求得到了6 dB以上的降低。     

两种正交多项式模拟湍流波前的比较

针对Zemike多项式仅在连续单位圆上正交,用于在离散点上构造光学波前必然会引起误差的问题,本文提出用能够在离散点上正交的多项式来模拟经过大气湍流的光学波前.该方法根据湍流的统计理论,采用Gram-Schmidt正交化方法,构造了Malacara多项式表示的湍流波前,并进行了数值模拟.将模拟结果与直接用Zemike多项式模拟的结果进行了比较分析,结果表明:在相同的条件下,该方法的模拟结果更接近统计理论值.     

基于协方差矩阵Toeplitz重构的MUSIC算法的波达方位估计方法

针对传统波达方向（Direction of Arrival, DOA）估计方法通过空间平滑对相干信号进行处理损失阵列孔径的问题，文章提出了一种基于协方差矩阵托普利兹（Toeplitz）矩阵重构的多重信号分类（Multiple Signal Classification, MUSIC）算法的波达方位估计方法。该方法首先根据阵列接收数据的协方差矩阵及其翻转矩阵来构造新协方差矩阵，并利用新协方差矩阵构造Toeplitz矩阵，然后对其进行特征值分解，得到Toeplitz矩阵的噪声子空间，利用噪声子空间求出信号空间谱，通过谱峰搜索估计入射信号的方位角。文中方法拓展了阵列孔径，增加了可估计相干信号的数量，提升了方位估计的性能，提高了阵列的空间分辨率。仿真和湖上实验数据处理结果表明，文中方法可估计出更多的相干信号，而且在低信噪比、少快拍以及信号入射角度间隔较小时仍然具有良好的方位估计性能。     

基于相位差法的波前检测技术

基于相位差法的波前检测技术,主要是利用在焦面和离焦位置上同时采集的一对图像,对光瞳上的波前相位分布进行恢复,同时也可以对目标进行恢复。与哈特曼波前传感器和剪切干涉仪等波前检测技术相比,相位差法具有光路简单、易于实现的特点,同时可以采用扩展目标作为参考源,主要适用于对实时性要求不高的领域。在计算机模拟大气湍流和成像系统的基础上,我们使用有限内存拟牛顿法对波前相位和目标进行了恢复。模拟研究结果表明,相位差法可以较准确的恢复出波前相位,并且最优化的离焦波面差为一个波长。     

Fast simulation of a kolmogorov phase screen

A previously presented method for modeling Kolmogorov phase fluctuations over a finite aperture is both formalized and improved on. The method relies on forming an initial low-resolution Kolmogorov phase screen from direct factorization of a covariance. The resolution of the screen is then increased by a randomized interpolation to produce a Kolmogorov phase screen of the desired size. The computational requirement is asymptotically proportional to the number of points in the phase screen.     

Wind-induced deformations in a segmented mirror

A Zernike expansion of wind-induced deformations in a segmented mirror is described. The wind model is a frozen turbulent field with a Kolmogorov spectrum for scales smaller than the outer scale and a flat spectrum for scales larger than the outer scale. The approach allows a mode-by-mode comparison of the wave-front error contributions from atmospheric phase distortions, wind-induced deformations, and the mirror control system noise. This is used to design a controller that minimizes the mirror surface errors by application of corrections based on edge sensor measurements and wave-front measurements on a guide star.     

Wave-front sensing by use of a Green's function solution to the intensity transport equation

A method for reconstructing an unknown wave front from measurements of its intensity distribution on two planes along the direction of propagation is described. The method solves the intensity transport equation by use of Neumann boundary conditions, leading to a solution that requires only matrix multiplication. The method provides real-time wave-front reconstruction with high accuracy and is easily reposed to permit reconstruction of the wave front in any orthonormal basis set.     

Adaptive optics with advanced phase-contrast techniques. I. High-resolution wave-front sensing

High-resolution phase-contrast wave-front sensors based on phase spatial light modulators and micromirror/ liquid-crystal arrays are introduced. Wave-front sensor performance is analyzed for atmospheric-turbulence-induced phase distortions described by the Kolmogorov and the Andrews models. A high-resolution phase-contrast wave-front sensor (nonlinear Zernike filter) based on an optically controlled liquid-crystal phase spatial light modulator is experimentally demonstrated. The results demonstrate high-resolution visualization of dynamically changing phase distortions within the sensor time response of approximately 10 ms.     

Extruding Kolmogorov-type phase screen ribbons

A phase screen ribbon extrusion process is presented that allows a phase screen ribbon of any specified width to be extruded, one column at a time, producing a ribbon of any desired length, with Kolmogorov statistics (i.e., having a five-thirds power-law-dependent structure function) for all separations up to some selected upper limit--which upper limit can be as large as desired. The method is an adaptation of the method described by [Assémat et al. Opt. Express 14, 988 (2006)].     

Inversion of light-scattering measurements for particle size and optical constants: theoretical study

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt-Hilbert eigenfunctions and a set of supplemental basis functions, which have been orthogonalized with respect to the Schmidt-Hilbert eigenfunctions by using the Gram-Schmidt orthogonalization procedure. We use the orthogonality properties of the basis functions and of the eigenvectors of the kernel covariance matrix to obtain the solution that minimizes the residual errors subject to a trial function constraint. The inversion process is described, and results from the inversion of several simulated data sets are presented.     

Breadboard testing of a phase-conjugate engine with an interferometric wave-front sensor and a microelectromechanical systems-based spatial light modulator

Laboratory breadboard results of a high-speed adaptive-optics system are presented. The wave-front sensor for the adaptive-optics system is based on a quadrature interferometer, which directly measures the turbulence-induced phase aberrations. The spatial light modulator used in the phase-conjugate engine was a microelectromechanical systems-based piston-only correction device with 1024 actuators. Laboratory experiments were conducted with this system utilizing Kolmogorov phase screens to simulate atmospheric phase distortions. The adaptive-optics system achieved correction speeds in excess of 800 Hz and Strehl ratios greater than 0.5 with the Kolmogorov phase screens.     

Wave-front design algorithm for shaping a quasi-far-field pattern

To design a fully continuous wave-front distribution suitable for focused beam shaping by a deformable mirror, we modify the phase-retrieval algorithm by employing a uniformly distributed phase as a starting phase screen and spatial filtering for the near-field phase retrieved during the iteration process. A special phase unwrapping algorithm is not required to obtain a continuous phase distribution from the retrieved phase since the boundary of the 2pi-phase-jumped region in the designed phase distribution is perfectly closed. From the computational result producing a uniform square beam transformation from a circular defocused beam, this algorithm has provided a fully continuous wave-front distribution with a lower spatial frequency for a deformable mirror. The transformed square beam has a normalized intensity nonuniformity of varsigma(rms) = 0.14 with respect to a desired flat-topped square beam pattern. This beam-shaping method also provides a high energy-concentration rate of more than 98%.