板条增益介质波前畸变诊断方法

对波前重构算法中的区域法进行了改进,使其能够应用于板条增益介质的波前畸变诊断。利用该方法对47块Nd: YAG板条增益介质沿厚度方向波前畸变进行测量,指出镀膜和加工等环节对增益介质的波前畸变可能造成的影响。按照波前畸变峰谷（PV）值对测量结果进行了统计,结果表明:增益介质造成的静态波前畸变参差不齐,测量样本中静态畸变PV值最多可达5 m以上,且仅有4.1%的增益介质静态畸变PV值小于1 m。通过选取某些增益介质使之级联,测量其组合波前畸变,发现在系统中使用两块波面互补的增益介质有助于减小系统的静态波前畸变。     

数字全息用于光波衍射传播理论教学研究

数字全息技术是基于传统光学全息原理,借助于光电探测和数字处理技术,通过单次曝光记录和再现物光场的振幅和相位信息,近年来被广泛研究和应用.将数字全息应用于光波衍射传播理论教学中,不仅能够使学生在学习过程中形象、直观的理解光波衍射传播理论,而且能够通过编程计算完成数字全息图的数值再现,锻炼他们的知识运用能力,从而拓宽专业知识面、了解科学的发展前沿.     

High precision Zernike modal gray map reconstruction for liquid crystal corrector

This paper proposes a new Zernike modal gray map reconstruction algorithm used in the nematic liquid crystal adaptive optics system. Firstly, the new modal algorithm is described. Secondly, a single loop correction experiment was conducted, and it showed that the modal method has a higher precision in gray map reconstruction than the widely used slope method. Finally, the contrast close-loop correction experiment was conducted to correct static aberration in the laboratory. The experimental results showed that the average peak to valley (PV) and root mean square (RMS) of the wavefront corrected by mode method were reduced from 2.501\lambda (\lambda =633~nm) and 0.610\lambda to 0.0334\lambda and 0.00845\lambda , respectively. The corrected PV and RMS were much smaller than those of 0.173\lambda and 0.048\lambda by slope method. The Strehl ratio and modulation transfer function of the system corrected by mode method were much closer to diffraction limit than with slope method. These results indicate that the mode method can take good advantage of the large number of pixels of the liquid crystal corrector to realize high correction precision.     

Low dimensional chaos in the AT and GC skew profiles of DNA sequences

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.     

A numerical method for reconstructing the coefficient in a wave equation

We present a numerical method for reconstructing the coefficient in a wave equation from a single measurement of partial Dirichlet boundary data. The original inverse problem is converted to a nonlinear integral differential equation, which is solved by an iterative method. At each iteration, one linear second‐order elliptic problem is solved to update the reconstruction of the coefficient, then the reconstructed coefficient is used to solve the forward problem to obtain the new data for the next iteration. The initial guess of the iterative method is provided by an approximate model. This model extends the approximate globally convergent method proposed by Beilina and Klibanov, which has been well developed for the determination of the coefficient in a special wave equation. Numerical experiments are presented to demonstrate the stability and robustness of the proposed method with noisy data.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 289–307, 2015     

三种降采样成像策略的性能优化以及与传统傅里叶望远镜的比较

为了获得成像质量较好且成像时间较少的新型傅里叶望远镜成像策略,本文比较了三种降采样成像策略(压缩感知方法 (CS)、低频全采样方法 (LF)和变密度随机采样方法 (VD))与传统傅里叶望远镜(FT)在图像质量和成像时间上的差异.分析方法如下:利用传统FT外场实验所获得的目标频谱数据作为基础,三种降采样方法 (LF, VD和CS)分别按照各自的采样模式和重构方法实现目标图像的重构;通过直观观察和Strehl比两种方法比较三种降采样方法与传统FT在图像质量上的差异;通过分析成像时间的组成要素,初步比较三种降采样方法与传统FT在成像时间上的差异.分析表明:1)压缩感知方法的图像质量优于其他两种降采样方法 (LF和VD),但略低于传统成像结果; 2)压缩感知方法在成像质量上略低于传统FT,但在成像时间上却明显小于传统FT; 3)分析中采用的外场数据均含噪声,这说明上述三种降采样重构过程对噪声有较好的鲁棒性.综合上述分析结果可以看出,基于压缩感知的傅里叶望远镜(CS-FT)是在实际含噪情况下可大幅减少成像时间的优良成像策略.     

3DSEM++: Adaptive and intelligent 3D SEM surface reconstruction

Structural analysis of microscopic objects is a longstanding topic in several scientific disciplines, such as biological, mechanical, and materials sciences. The scanning electron microscope (SEM), as a promising imaging equipment has been around for decades to determine the surface properties (e.g., compositions or geometries) of specimens by achieving increased magnification, contrast, and resolution greater than one nanometer. Whereas SEM micrographs still remain two-dimensional (2D), many research and educational questions truly require knowledge and facts about their three-dimensional (3D) structures. 3D surface reconstruction from SEM images leads to remarkable understanding of microscopic surfaces, allowing informative and qualitative visualization of the samples being investigated. In this contribution, we integrate several computational technologies including machine learning, contrario methodology, and epipolar geometry to design and develop a novel and efficient method called 3DSEM++ for multi-view 3D SEM surface reconstruction in an adaptive and intelligent fashion. The experiments which have been performed on real and synthetic data assert the approach is able to reach a significant precision to both SEM extrinsic calibration and its 3D surface modeling.     

Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Jiittler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.AMS subject classifications: 65D17     

Comparison of two-dimensional integration methods for shape reconstruction from gradient data

As a requisite and key step in some gradient-based measurement techniques, the reconstruction of the shape, more generally the scalar potential, from the measured gradient data has been studied for many years. In this work, three types of two-dimensional integration methods are compared under various conditions. The merits and drawbacks of each integration method are consequently revealed to provide suggestions in selection of a proper integration method for a particular application.