用液晶电视控制激光束小尺度波前畸变研究

 将两块液晶电视(LCTV)通过中继成像方式级联，一块用于模拟小尺度畸变波前，另一块用于控制和衰减前面的小尺度畸变，通过环路径向剪切干涉(CRSI)装置对畸变波前的控制结果进行检测，从实验上实现了LCTV对激光光束小尺度波前畸变的控制。从理论上对实验原理进行了分析，给出了补偿后波前存在剩余波前起伏的合理解释。     

基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法

横向剪切干涉术是一种自参考干涉计量技术,其原理是被检测波前与其自身被剪开的波前之间在重叠范围内相干涉,由干涉图得到两相互剪切波前的波前差,通过波面重建算法得到待测波面.在波面重建算法中,泽尼克待定系数法是其中的一种.分析了横向剪切干涉技术的测量原理;提出了一种新的基于解耦差分泽尼克待定系数法的二维横向剪切波面重建算法....     

含中心遮拦剪切干涉图的波前重建新方法

在利用剪切干涉测量共轴折返式光学系统波像差时,会得到含中心遮拦的环形剪切干涉图。但是,目前的剪切干涉波前重建方法大多适用于圆形或矩形区域。提出了一种适用于含中心遮拦环形剪切干涉图的波前重建方法。该方法是一种基于Zernike环多项式的模式法。仿真和分析了不同剪切比、单项像差、噪声对重建精度的影响,结果表明:该算法具有较高的重建精度,剪切比小于6%时,相对重建误差小于10%;对像散的重建精度较高,对球差和慧差的重建精度相对较低;具有较好的抗噪性。该方法已应用于实验室开发的交叉光栅横向剪切干涉仪的干涉图像波前重建中。     

二维剪切干涉波前的最小二乘法重建

提出了一种可以快捷地重建原始的二维波前的新算法。对于分别在相互垂直方向上横向切干涉获得的两个差分波前,用快速傅里叶变换首先计算出待测原始波前存x和y方向的估计分布,然后利用误差计算的最小二乘法进行二维拟合,可以恢复出待测波前的二维分布。提出的理论可以应用于剪切量大于1个采样间隔的二维波前重建问题,解决了已有的二维剪切干涉波前重建技术中要求剪切量等于采样间隔的限制。研究了剪切量和噪声对重建精度的影响．和其它算法进行了比较．给出了数值实验结果和分析讨沦。结果表明该算法速度快,对噪声有较强的抵抗力．有望在实际的剪切干涉测量中获得应用。     

中心不重合径向剪切干涉迭代波前重构算法仿真分析

径向剪切干涉测量时经常会出现扩束与缩束光波中心不重合情况,传统波前重构算法会导致较大重构误差,其应用受到挑战。推导了中心不重合径向剪切干涉迭代波前重构算法,仿真分析了组合像差、单阶Zernike像差、中心偏移量大小及其计算误差对重构算法的影响。结果表明,在剪切光波中心不重合情况下,该文算法能够准确进行波前重构,重构效果显著优于传统算法;在论文仿真条件下,随着中心偏移量的增大,本文算法重构波面均方根误差（RMS）不高于0.05λ,而传统算法重构误差RMS值达1.6λ且与偏移量近似线性相关。     

基于偏振移相的环路径向剪切干涉

只需要一幅干涉图就能得到被检波面信息的径向剪切干涉,适于动态波前的测量。将便于干涉图像处理的同步移相技术引入径向剪切干涉中,基于环路径向剪切干涉,利用一个正交的二维光栅分光,采用偏振移相法,能同时得到相移间隔π/2的四幅移相干涉图。运用传统的四步移相算法,结合波面迭代算法复原波面。通过理论公式的推导、计算机的模拟分析,以及初步的实验测试,验证了偏振移相应用于径向剪切干涉的可行性,模拟结果显示均方根精度优于λ/100。具有抗振特点的光栅分光偏振移相的同步移相方案,不仅能够克服剪切干涉的单幅干涉图处理复杂的缺点,更有利于提高剪切干涉的抗干扰能力。     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

剪切干涉测量电缆枪等离子体电子密度

用剪切干涉仪测量了电缆枪产生的等离子体电子密度分布.在实验中获得了激光波前通过等离子体后的干涉图样,测出等离子体沿轴向的平均运动速度约为2 cm/μs.对干涉图进行了二维波前重建,计算了电子线积分密度,给出了直观的等离子体分布图像,并计算了自由电子总数.根据等离子体的圆柱对称关系,利用Abel积分变换算出了局部电子密度沿径向的分布曲线.     

二维横向剪切干涉中采样点的选取

为了使相移式横向剪切干涉法能够广泛应用于大口径非球面的在线检测,通过计算机仿真研究横向剪切干涉测量的非球面面形,实现其二维波面的重建.分别对仿真中获得的被测非球面在x方向和y方向的两个差分波前中剪切量大小和采样点个数的选取进行分析,利用最小二乘法求取波差值,采用Zernike多项式拟合法进行波前重建,在保证高准确度测量情况下,对一被测抛物面面形进行计算机仿真实验,结果表明:最适合的剪切量是其被测口径的十分之一大小,此时只需要对其选取49个离散数据采样点,采用泽尼克多项式拟合就可得到二维波面的形貌.该结论为相移式横向剪切干涉的二维波前重建提供了理论指导,同时,也为大口径非球面在线测量的实际应用提供了技术支撑.     

波前延拓剪切干涉的数学原理与数值模拟

从数值方法的角度分析了常规剪切干涉存在的缺陷,通过数学原理和数值分析方法提出波前延拓剪切干涉,并证明了它的可行性及其对常规剪切干涉缺陷的克服。最后用数值方法模拟了波前恢复过程。     

A novel wavefront reconstruction algorithm based on interpolation coefficient matrix for radial shearing interferometry

A novel wavefront reconstruction algorithm for radial shearing interferometer (RSI) is proposed in this paper. Based on the shearing relationship of RSI, an interpolation coefficient matrix is established by the radial shearing ratio and the number of discrete points of test wavefront. Accordingly, the expanded wavefront is characterized by the interpolation coefficient matrix and the test wavefront. Consequently the test wavefront can be calculated from the phase difference wavefront. The numerical simulation is conducted to confirm the correctness of the proposed algorithm. Compared with the previous wavefront reconstruction methods, the proposed algorithm is more accurate and stable.     

自基准哈特曼波前测量装置的研制

采用自基准哈特曼径向斜率测量原理,设计了旋转加摩擦线性移动扫描机构,对被测波前进行连续极坐标扫描采样;用CCD相机采集光斑图像,经波面径向斜率计算和泽尼克径向斜率多项式最小二乘拟合,求出被测波面的泽尼克系数和波前畸变值。与干涉仪测量结果进行了比较,所以研制的波前测量装置可满足大口径光学系统的像质测量。     

Improved formula of wavefront reconstruction from a radial shearing interferogram

A radial shearing (RS) interferogram obtained by the carrier fringe method is essentially the combination of radial and lateral shearing. The previous phase reconstruction algorithm neglects the effect of lateral shearing on the obtained RS interferogram. A mathematical formula for wavefront reconstruction from an RS interferogram is deduced. If the phase difference of the tested wavefront phase, the RS ratio s, and the laterally sheared amount x(0) in the x direction and y(0) in the y direction, respectively, have been determined, the tested wavefront phase can be precisely reconstructed using this formula. The result of simulation analysis and experiment shows that the formula is correct and more accurate.     

Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique

The transient radial shearing interferometry technique based on fast Fourier transform (FFT) provides a means for the measurement of the wavefront phase of transient light field. However, which factors affect the spatial bandwidth of the wavefront phase measurement of this technology and how to achieve high-precision measurement of the broad-band transient wavefront phase are problems that need to be studied further. To this end, a theoretical model of phase-retrieved bandwidth of radial shearing interferometry is established in this paper. The influence of the spatial carrier frequency and the calculation window on phase-retrieved bandwidth is analyzed, and the optimal carrier frequency and calculation window are obtained. On this basis, a broad-band transient radial shearing interference phase-retrieval method based on chirp Z transform (CZT) is proposed, and the corresponding algorithm is given. Through theoretical simulation, a known phase is used to generate the interferogram and it is retrieved by the traditional method and the proposed method respectively. The residual wavefront RMS of the traditional method is 0.146λ, and it is 0.037λ for the proposed method, which manifests an improvement of accuracy by an order of magnitude. At the same time, different levels of signal-to-noise ratios (SNRs) from 50 dB to 10 dB of the interferogram are simulated, and the RMS of the residual wavefront is from 0.040λ to 0.066λ. In terms of experiments, an experimental verification device based on a phase-only spatial light modulator is built, and the known phase on the modulator is retrieved from the actual interferogram. The RMS of the residual wavefront retrieved through FFT is 0.112λ, and it decreases to 0.035λ through CZT. The experimental results verify the effectiveness of the method proposed in this paper. Furthermore, the method can be used in other types of spatial carrier frequency interference, such as lateral shearing interference, rotational shearing interference, flipping shearing interference, and four-wave shearing interference.     

基于哈特曼-夏克波前传感器的模糊图像复原方法

离焦模糊图像的清晰度较低,因此必须对其进行复原。传统方法通常采用圆盘或高斯函数来近似离焦造成的点扩散函数,复原效果不够理想。为此,提出利用哈特曼-夏克波前传感器探测离焦波前,根据所得波前计算光学系统的点扩散函数,并采用Richardson-Lucy算法对模糊图像进行复原。搭建了实验用的光学系统,采集了离焦模糊图像以及相应的波前信息,获得了清晰的复原图像,并利用客观图像评价方法对退化图像和复原图像进行了评价,同时与传统方法得到的复原图像进行了比较。实验结果表明,该方法能精确重建点扩散函数,有效提高图像的质量。     

Method of reconstructing wavefront aberrations by use of Zernike polynomials in radial shearing interferometers

A novel method of reconstructing wavefront aberrations by use of Zernike polynomials for radial shearing interferometers is discussed. This method uses matrix formalism to calculate the Zernike coefficients of a wavefront under test and shows the validity of reconstructing an arbitrary wavefront aberration from an interferogram taken by a radial shearing interferometer. We also propose a new interferometer setup to determine the shape and the direction (concave or convex) of wavefront aberration in a single measurement.     

基于模型选择的模式波前重构算法研究

基于Zernike模式的波前重构算法通常忽略实际波前像差构成的差异, 而用一定数量的低阶Zernike模式进行波前重构, 导致模式混淆或耦合等问题, 进而影响波前重构的精度. 根据信息论中的最小描述长度准则对重构模型的阶数进行了选择, 在此基础上应用非线性优化算法计算重构系数, 并最终实现波前重构; 对不同信噪比条件下振幅均匀分布入射光束的波前进行了重构. 结果表明: 该算法不但能够实现相对于现有算法相对较高的波前重构精度, 并且具有优良的噪声适应性, 体现了模型选择在模式法波前重构算法中的意义.     

基于远场信息和卷积神经网络的波前重构方法

探测波前相位信息是实现自适应光学波前补偿的关键,使用卷积神经网络（CNN）代替波前传感器进行波前重构,系统简单易于实现,同时重构过程不依赖迭代运算,快速实时。为准确提取远场中的波前特征,CNN需要事先使用大量样本进行训练。研究中根据4～30阶大气湍流泽尼克像差系数与其远场强度的对应关系,仿真制作样本数据集,训练CNN从输入的一帧远场图像中预测出畸变波前的泽尼克像差系数,重构原始波前。验证结果表明,该方法能快速实时地还原出波前相位信息,重构波前较原始波前具有极高的波面吻合度和较小的残差剩余量,有望实现实际自适应光学系统中的闭环校正。     

Modal wavefront reconstruction for radial shearing interferometer with lateral shear

In a radial shearing interferometer, a portion of the test beam is magnified and used as the reference for the tested wavefront. However, the reference portion is always off center (lateral shear), which complicates the wavefront reconstruction. A modal method for solving this problem is presented here. This method uses orthogonal Zernike polynomials and its matrix formalism to calculate the Zernike coefficient of the wavefront under test. This approach has easier implementation, is better filtering, and has a more adaptive practical situation. The corresponding mathematical formula is deduced, and a computer simulation is also made to verify operation of the algorithm. The result of simulation analysis shows that the proposed method is correct and accurate.