A subdivision collocation method for solving two point boundary value problems of order three

In this paper, we propose a method for the numerical solution of self adjoint singularly perturbed third order boundary value problems in which the highest order derivative is multiplied by a small parameter $\varepsilon$. In this method, first we introduce the derivatives of two scale relations satisfied by the subdivision schemes. After that we use these derivatives to construct the subdivision collocation method for the numerical solution of singularly perturbed boundary value problems. Convergence of the subdivision collocation method is also discussed. Numerical examples are presented to illustrate the proposed method.     

Algebraic Properties of Subdivision Operators with Matrix Mask and Their Applications

Subdivision operators play an important role in wavelet analysis. This paper studies the algebraic properties of subdivision operators with matrix mask, especially their action on polynomial sequences and on some of their invariant subspaces. As an application, we characterize, under a mild condition, the approximation order provided by refinable vectors in terms of the eigenvalues and eigenvectors of polynomial sequences of the associated subdivision operator. Moreover, some necessary conditions, in terms of nondegeneracy and simplicity of eigenvalues of a matrix related to the subdivision operator for the refinable vector to be smooth are given. The main results are new even in the scalar case     

干涉测量系统中杂散条纹影响的抑制

 为了抑制杂散条纹的影响，提出了一种简单实用的单幅三表面干涉条纹傅里叶分析法，它根据三表面干涉时各个表面干涉的条纹调制度不同，从三表面干涉图的频谱中提取测试面的频谱，从而准确地恢复测试面的面形。模拟结果证明了该方法的有效性，准确度可以达到l/1 000。实验表明：单幅三表面干涉条纹傅里叶分析法得到的面形形状与波长调谐时域傅里叶变化法和涂消光漆法得到的结果基本一致，PV值和RMS值与波长调谐时域傅里叶变化法相差分别为0.001l和0.004l，与涂消光漆法相差分别为0.042l和0.019l。通过7次单幅三表面干涉条纹傅里叶分析法测量，得到PV和RMS值的重复性分别为0.007 8l和0.002 6l。     

一类与BB型对偶剖分相关的广义差分格式

豆引言考虑二阶椭圆方程的边值问题〔,a.an.a.＆t-。^D一[六（a于）十十…于）」一八x,y）,（x,y）En,（1.1）J“山一而“av”-av”。。、一、。。,\一·。·---,l。。、____（.2）LU一0,（J,y）E厂一go,其中D是多边形区域,厂一JD为0的边界,f（x,y）为o上的已知函数/三L‘（0）,系数a—a（xJ）充分光滑,且存在常数7>O,使得以X,y）>/,对任意（X,y）ED.文[1],[2]已系统地研究了求解口.1）,（l.2）的广义差分法.广义差分法的基本思想是对求解区域0作三角形剖分TA及其对偶剖分T;,然后构造T^上的试探函数空间U。（有限元空间）和耳上的…     

利用三次样条插值提高自准直仪的准确度

为了提高自准直仪的准确度,利用三次样条插值法对CCD像元进行细分,并利用直线边缘拟合法检测图像边缘.实验采取独立的测量手段,将自准直仪的实际转角和算法计算得到的角度值进行比较,分析其准确度.实验结果表明,该方法能明显提高自准直仪的准确度,准确度达到0.1角秒.     

基于FPGA的准直测角系统

为了提高线阵CCD准直测角系统的精度、速度、集成度,以及可靠性,提出一种集成于单片FPGA、光积分时间可自适应调节的片上准直测角系统。以FPGA作为系统处理核心,利用高斯滤波算法对CCD输出信号进行数字滤波,利用边缘自动检测算法获得图像的像元级边界,在此基础上应用多项式插值算法对图像边缘位置进行亚像元细分,最终计算出失准角。利用VHDL语言以及MAX+plus II软件完成了系统设计。系统仿真和实验表明,所设计的片上系统具有高精度、高集成度、高可靠性的特点。     

Second harmonic generation: Effects of the multiple reflections of the fundamental and the second harmonic waves on the Maker fringes

The Maker fringes technique is commonly used for the determination of nonlinear optical coefficients. In this article, we present a new formulation of Maker fringes in parallel-surface samples, using boundary conditions taking into account the anisotropy of the crystal, the refractive-index dispersion, and the reflections of the fundamental and the second harmonic waves inside the material. Complete expressions for the generated second harmonic intensity are given for birefringent crystals for the case of no pump depletion. A comparison between theory and experimental results is made, showing the accuracy of our theoretical expressions.     

A live fringe technique for stress measurements in reflecting thin films, using holography

A simple technique is given for measuring stresses in reflecting thin films, using real-time holography. The technique gives clear real fringes with good visibility which can be easily monitored and photographed. No substrate profile measurement is needed. Thermal stress of 0.49 × 10⁹ dynes cm^-2 is observed for a 200.0 nm thick Ag film in the temperature range of 30 to 55°C. This is in good agreement with reported values.     

Separation of vibration fringe data from rotating object fringes using pulsed ESPI

In industrial and other types of non-controlled environments, an unbalanced rotating object may present characteristic out-of-plane vibration amplitude at a specific frequency. For this type of cases and as a first step towards a complete evaluation, it is only desired to visualize the effect of the vibration on the rotating object, or vice versa, for instance to achieve object balancing. Real time optical non-intrusive measurement techniques such as pulsed electronic speckle pattern interferometry (ESPI), are well suited to study this rotating-vibrating object. The advantage offered by ESPI is that real-time fringe data is qualitatively analyzed while being observed on a TV monitor. The present paper proposes a qualitative method, based on pulsed ESPI, to separate rotation fringes from fringes solely related to vibration. The method relies on a high precision scheme that synchronizes and fixes an object point during rotation, without the use of an optomechanical object derotator.     

Smoothness of Nonlinear Median-Interpolation Subdivision

We give a refined analysis of the Hölder regularity for the limit functions arising from a nonlinear pyramid algorithm for robust removal of non-Gaussian noise proposed by Donoho and Yu [6,7,17]. The synthesis part of this algorithm can be interpreted as a nonlinear triadic subdivision scheme where new points are inserted based on local quadratic polynomial median interpolation and imputation. We introduce the analogon of the Donoho–Yu scheme for dyadic refinement, and show that its limit functions are in C for >log₄(128/31)=1.0229.... In the triadic case, we improve the lower bound of >log₂(135/121)=0.0997... previously obtained in [6] to >log₃(135/53)=0.8510.... These lower bounds are relatively close to the anticipated upper bounds of log₂(16/7)=1.1982... in the dyadic, respectivly 1 in the triadic cases, and have been obtained by deriving recursive inequalities for the norm of second rather than first order differences of the sequences arising in the subdivision process.