Monte-Carlo analysis of centroid detected accuracy for wavefront sensor

By utilizing Monte-Carlo simulation technology, the centroid algorithms have been compared in detail. The factors such as the detected window size, threshold and weighting power factor, which affect the detected accuracy of the wavefront sensor, have been studied and the optimal parameters for each algorithm have been found. The numerical results will be helpful for further improving the measurement accuracy of the wavefront sensor.     

Noise reduction in the Fourier spectrum of Hartmann patterns for phase demodulation

A simple method to reduce the noise in the Fourier spectrum of Hartmann patterns for filtering the fundamental sidelobes (first harmonics) is presented. The method consists on replacing the Hartmann pattern by a fringe pattern within a circular pupil. The fringes are cosine square type and the pupil is apodized with a Gaussian function. These fringes follow the centroid spots of the Hartmann pattern along the horizontal and vertical directions. The width of the fringes in each direction is constant and it is determined according to the distortion of the Hartmann pattern. In this way, it is possible to obtain the wavefront’s slopes more accurate in comparison with the traditional method. We present experimental results to show the advantages of our method.     

基于哈特曼法球差自动测量系统的图像处理

从基于哈特曼法自动测量球差所需解决的CCD图像传感和数字图像处理技术出发，提出将哈特曼光阑图像用于存储器中的目标识别与测量时，图像映像区搜索算法和哈特曼光阑图像中测量光斑距离的中心重叠算法，解决了在一维图像存储器中准确寻找二维图像目标，随后进行相关目标计算的技术。其中利用所有光斑的质心求解哈特曼光阑图像的中心,再由光斑质心关于光阑图像中心的对称性确定光斑质心距离的中心重叠算法可减少计算次数，大大降低了算法的时间复杂度和计算复杂度。     

Encircled energy measurement for focusing lens based on scanning Hartmann test

The encircled energy of a focusing lens is one of the parameters directly affecting the target efficiency in high-power laser facilities. The direct measurement method of the encircled energy for the focusing lens based on the scanning Hartmann test is proposed in this paper. With the scanning Hartmann test setup, the information in the whole aperture of the focusing lens can be achieved. The encircled energy can be obtained by analyzing the spot diagram on the focal plane of the focusing lens. In experiments, the encircled energy of an aspheric focusing lens is measured using this method. The measurement result is in good agreement with that derived from measurement data by an interferometer and the difference is 7.7%.     

基于改进哈特曼法的眼镜片全孔径屈光度测量

自由曲面镜片的发展和普及,对现有的屈光度测量方法提出了挑战,也要求新的测量方法具有更高的精度以及更好的可靠性。因此,介绍了传统哈特曼检测法测量眼镜片屈光度的测量原理并提出了一种改进方法,对球面单焦点镜片和散光镜片进行仿真测量的屈光度误差均在1%以内。对改进方法与传统方法测量所得到的渐进多焦点自由曲面镜片屈光度分布图的分析结果表明,改进哈特曼检测法相比于传统哈特曼检测法具有测量范围大,精度高的特点,能够准确反映眼镜片的屈光度分布特征。     

Hartmann test of small F/# convex mirrors

A modified Hartmann test for testing aspherical convex surfaces of F/# ∼ 1 is analyzed. We present the main differences of this test in comparison to the usual Hartmann test. Theoretical results show that the transverse aberrations yielded by a testing surface have to be measured with respect to its mean sphere. A method to determine the mean sphere is also presented. Experimental results show the feasibility of this method.     

基于优化探测窗口的光斑质心探测方法

 哈特曼-夏克波前传感器进行波前探测时，用子孔径光斑强度的一阶矩来计算光斑质心位置，子孔径窗口作为探测窗口，但探测时子孔径窗口内噪声对一阶矩有很大的影响，会使质心探测精度产生很大的误差。因此在计算质心位置时探测窗口的选取对探测精度有重要影响，必须选取合适的探测窗口来提高光斑质心探测精度。为此，在传统算法的基础上提出优化探测窗口的方法来提高质心探测精度,仿真和实验结果表明新方法提高了质心探测的精度，未经处理的高噪声恢复波前的波前残差峰谷值是2.851 4λ，均方根值是0.606 3λ，优化探测窗口后波前残差的峰谷值是1.636 2 λ，均方根值是0.367 1 λ，重构误差减小了40％。证明了算法的可行性和稳定性。     

基于FW-H方程的Hartmann哨辐射声场数值研究*

该文基于声类比法,通过求解FW-H方程,对不同喷口与谐振腔位置关系的Hartmann哨的声场分布进行了分析,计算了不同位置关系的Hartmann哨的声指向性。得到了以下结论:喷口与谐振腔位置关系对Hartmann哨的发声基频几乎不产生影响。对称位置关系的Hartmann哨的声场呈对称趋势,且在垂直于喷流方向上达到最大;非对称位置关系的Hartmann哨不再呈现对称趋势。Hartmann哨的最大声压级随着偏离对称位置的距离的增加有小幅增加,最大声压级出现的方向向着谐振腔方向移动。     

Centroids analysis for circle of confusion in reverse Hartmann test

The point spread function(PSF) is investigated in order to study the centroids algorithm in a reverse Hartmann test(RHT) system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion(CoC) and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional(2D) Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional(1D) Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson's correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error(RMSE) by nearly one order of magnitude, thus achieving an accuracy of ~ 0.01 pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method.     

Figure Measurement of Concave Mirror by Fiber-Grating Hartmann Test

A new type of Hartmann test was developed using an optical fiber grating instead of the traditional Hartmann screen with multiple holes. A fiber-grating is made of short optical fibers arranged in single layers with no gaps between them. On illumination with laser light, the fiber-grating generates fan-like diverging multiple rays of almost equivalent intensities. Two gratings are overlapped at right angles to make multiple beams diverging in two directions. Rays reflected from test mirror surfaces converge to make a point focus provinding the sulface is free from aberrations. A CCD camera detects a spot pattern of beams near but out of focus, and a personal computer analyzes the spot patterns and calculates the figure error from a ideal surface. A few concave mirrors were analyzed by this method and the results compared with those obtained with a Fizeau interferometer. The data using the two systems were consistent with each other to within 1/10A.     

基于三维离散元方法研究热点的位置和温度对奥克托今颗粒点火燃烧的影响

炸药的点火燃烧特性与炸药的安全和使用密切相关,其一直是研究者重点关注的问题之一.普遍认为,凝聚炸药起爆的关键是热点.基于此,本文采用三维离散元方法,以奥克托今(HMX)颗粒为研究对象,探究了HMX颗粒中不同位置和初始温度的热点对其燃烧过程的影响.结果发现,热点的不同初始温度和位置都会对HMX炸药颗粒的燃烧特性造成影响.由于处于炸药内部分散位置的热点表面积较大,其相比集中的热点更有利于HMX炸药颗粒的起爆.并且研究发现,并不是热点的温度越高越有利于炸药的起爆,这也取决于炸药颗粒的含量.本文的研究工作对炸药的实验研究以及军事应用提供了一定的参考.     

Limitations of the Shack–Hartmann sensor for testing optical aspherics

Aspheric lenses and surfaces are increasingly used in modern high-quality optics. Therefore, new measuring methods for an accurate quantification of these aspheres are also necessary. The current approach to quantify aspheres is to apply null systems such as computer-generated holograms as a part of a null lens in a interferometer. An alternative to this method is the Shack–Hartmann wavefront sensor. The dynamic range of this sensor can be adjusted by the optical parameters of the applied microlens array. Hence, large wavefront aberrations can be measured directly without a null lens. However, there are basic limitations in the dynamic range of a Shack–Hartmann sensor (SHS) depending on the curvature of the incident wavefront. In this paper, an analytical expression to determine the strongest wavefront curvature which can be measured with a defined microlens array of an SHS is derived. It allows to calculate the microlens parameters required to measure the wavefront of a test lens. Particularly, the influence of rotational symmetric aspherical wavefront shapes to the dynamic range of an SHS has been studied. A comparison between interferometry and the SHS has been accomplished. Numerical solutions using scalar diffraction theory illustrate the analytical predictions.     

Numerical simulation of Shack–Hartmann wavefront sensor to characterize the turbulence phase statistics

Shack–Hartmann wavefront sensor (SHWS) is one of the important parts in an adaptive optics system and its detection accuracy has considerable influences on the performances of the whole system. In this paper, a simulator of such type of wavefront sensor is built and tested by measuring the slope structure function of Kolmogorov turbulence simulated by random phase screens. The numerical results show that it works well to characterize the turbulence phase statistics. In combination with the noise simulation, this simulator will be a very useful tool to further investigate and optimize the system parameters to improve the detection accuracy and the performance of the whole system.     

A method to calculate Boltzmann entropy

A method is proposed to calculate the Boltzmann non equilibrium entropy as a Taylor series expansion in terms of the successive moments of the velocity distribution function. As a first application, the entropy of the BKW solution of the Boltzmann equation is calculated for both even and odd dimensions. The properties of the entropy of the Tjon Wu modeld=2) are studied and a quantitative condition is derived, showing that the McKean conjecture is incorrect. As a second application of the method, the entropy of one of the solutions of the very hard particle model for the Boltzmann equation is also derived.     

基于数字图像处理的蚕茧表面积计算方法

介绍了基于数字图像处理的蚕茧质量无损智能检测方法,通过对被检茧进行图像采集、数据分析处理和计算,应用软件自动推算出各项评级指标并综合评级,最后得出评级结果。根据蚕茧质量无损智能检测方案,主要论述了其中重要参数的测量方法——基于图像处理技术的蚕茧表面积测量计算方法,介绍了建立蚕茧茧壳表面积计算的数学模型和测量方法。并对测量结果进行分析,本检测方法误差小,简便可靠,有很好的实际应用价值。     

Hartmann势的Klein-Gordon方程束缚态解及递推关系

给出了在Hartmann型标量势与矢量势相等的条件下其Klein-Gordon方程束缚态解.结果表明 ，径向波函数可用广义Laguerre多项式表示，其角向波函数可用Legendre多项式表示.另外 ，给出了径向波函数关于角量子数l和量子数n的二类新递推关系. 关键词： Hartmann势 Klein-Gorgon方程 束缚态 递推关系     

中阶梯光栅光谱仪信号光斑位置的质心提取算法

中阶梯光栅光谱仪二维谱图中,信号光斑位置的提取精度直接影响光谱分析精度,是中阶梯光栅光谱仪研制中的关键问题之一。为保证中阶梯光栅光谱仪的高分辨率特征(其分辨率一般为几千以上,本仪器光谱分辨率为15 000),信号光斑的位置提取误差应小于0.03mm(小于2个像素)。在分析中阶梯光栅光谱仪谱图特征的基础上,提出了一种基于质心法的信号光斑位置提取算法,即通过搜索信号光斑探测窗口进行光斑判读以及信号光斑质心计算,实现了信号光斑位置的精确读取。实验结果表明,采用该算法可以有效地去除噪声光斑的干扰,实现信号光斑位置的快速精确读取,位置提取误差小于2个像素,波长误差小于0.02nm,满足本仪器要求。     

An off-axis Hartmann sensor for the measurement of absorption-induced wavefront distortion in advanced gravitational wave interferometers

We describe a novel off-axis Hartmann wavefront sensor, developed for the measurement of wavefront distortions induced in the mirrors (test masses) of advanced gravitational wave interferometers by residual absorption of the circulating laser power.     

A study on a fast measuring technique of wavefront using a Shack–Hartmann sensor

The measuring resolution and speed for wavefront are important to improve the performance of an adaptive optics system. In this paper, we propose a fast measuring technique with high resolution in the Shack–Hartmann wavefront sensor. The proposed measuring technique of wavefront combines the conventional center of mass algorithm with an estimated weighting factor. The estimated weighting factor is a real value anticipating the real center of mass in a wavefront spot image. This estimated weighting factor can be calculated at the initialization step of an adaptive optics system. We designed a robust adaptive optics system with this proposed measuring algorithm. The measuring accuracy and speed are investigated by using the proposed algorithm compared with the conventional center of mass algorithm in experiments.     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.