子孔径拼接干涉测量的精度估计方法

作为一种高精度的光学镜面测量方法,子孔径拼接干涉测量的精度指标十分重要,必须对其进行定量估计.提出将子孔径拼接十涉的结果与全口径测试结果进行对比实验,将全口径测试结果作为拼接测量结果的参考真值,讨论了拼接测量精度评价指标及其计算方法.全口径测试与子孔径拼接干涉测量的几何参量并不相同,提出将全口径测试结果与子孔径拼接结果进行最优匹配,其原理与子孔径拼接算法的原理相同.在最优匹配后计算拼接测量精度的评价指标,通过测量实验进行了验证,结果表明最优匹配后的误差指标比未经最优匹配的误差指标减小约48%,证明上述方法是一种定量估计子孔径拼接干涉测量精度的有效方法.     

基于虚拟圆柱的曲面拼接方法

圆柱坐标下的多视角(孔径)扫描拼接方法主要针对类似回转物体面形的拼接测量,用该方法在对非单一回转轴,或者近似回转轴位置远离坐标轴形式的一类物体面形的拼接测量时遇到了困难,把拼接方法推广到基于虚拟圆柱可以解决这一难题。为此提出了基于虚拟圆柱原理的曲面拼接方法,给出了如何估计虚拟圆柱的半径,以及轴心坐标的计算方法,推导了基于虚拟圆柱的坐标转换方程,通过计算机模拟验证了其精确性,并通过实验证明这种方法对解决三维复杂物体表面特别是多视角测量获得面形的拼接测量问题是十分有效的。     

基于单数码相机的三维视觉测量数据拼接方法

针对大型物体三维形貌视觉测量,提出了一种新的视觉测量三维数据拼接方法。以一台高分辨率数码相机作为全局测量设备,在测量过程中固定不动,并以数码相机坐标系作为全局坐标系。视觉传感器流动到不同位置对物体各子区域进行测量,获得局部坐标系下的三维数据。以一平面靶标为中介将视觉传感器在各位置的局部坐标系统一到全局坐标系下,从而将三维数据统一到全局坐标系下,完成三维拼接。该方法无需在被测物上贴标记,因此适用于任何材质的被测物,且消除了拼接累积误差。实验结果表明,该方法相对拼接误差为0.076%。以Venus石膏像为被测对象,视觉传感器对其三个局部区域进行测量,给出了局部测量结果及拼接结果。     

双线阵CCD光学拼接与误差分析研究

基于线阵CCD的图像测量技术是当前工程应用中的一个重要领域,针对当前高精度大动态范围测量和标准线阵CCD测量范围及线阵CCD几何结构之间的矛盾,提出了一种高精度大范围的线阵CCD测量拼接方案。利用半反半透镜平面反射原理设计了双线阵CCD高精度拼接的光学拼接系统的光机结构原理,给出了重叠像元的标定原理,对其标定和拼接误差进行了分析。通过拼接系统的实验室长期实验结果表明:方案拼接简单,实用可靠,系统的整体拼接误差约为0.019mm,且拼接不存在漏缝现象,拼接精度满足高精度测量的要求。拼接方案对高精度、大动态范围CCD测量实际应用有一定的参考意义。     

子孔径拼接检测非球面时调整误差的补偿

针对在子孔径拼接测量非球面的过程中干涉仪与待测非球面相对位置存在的对准误差,提出了一种基于模式搜索迭代算法的调整误差补偿方法。该方法可以很好地从测量的子孔径相位数据中消除由拼接测量位置没有对准带来的调整误差,实现多个子孔径的精确拼接。对该方法的基本原理和实现步骤进行了分析和研究,建立了子孔径拼接测量的调整误差补偿模型。对口径为230 mm×141 mm的离轴碳化硅非球面反射镜进行了调整误差补偿和相位数据拼接,得到了精确的全口径面形分布。作为验证,对待测非球面进行了零位补偿检测,结果显示两种测试方法的面形PV值和RMS值的相对偏差仅为0.57%和2.74%。     

相位差波前检测方法应用于平移误差检测的实验研究

相位差波前检测方法由于其结构简单,对环境要求低,测量精度较高等优点,被应用于诸多领域.本文针对拼接型天文望远镜中主镜的共相位检测问题,对相位差波前检测方法在拼接主镜各子镜间平移误差测量进行理论分析,并搭建了实验光路.实验结果表明:相位差波前检测方法对拼接镜平移误差的测量精度高于λ/20(λ为波长),满足系统对拼接平移误差的要求.     

子孔径光学检测拼接准确度实验研究

实验研究了子孔径光学检测的拼接准确度.实验选取9个子孔径进行拼接,同时利用ZYGO干涉仪来测量子孔径和整个被检面的表面面形.实验发现,测量基准子孔径和整个被检面的时间间隔对子孔径拼接准确度的评价存在严重影响.为此,重点研究了产生影响的原因并提出了消除测量基准子孔径和整个被测面时间间隙影响的方法.最后,利用该方法研究了子孔径重叠面积对拼接准确度的影响.结果显示,当重叠面积比为7%时,PV和RMS的拼接误差分别为0.03λ(λ=632.8 nm) 和 0.01λ,并且重叠面积比和拼接准确度呈近似线性关系.     

基于单应性矩阵的大尺寸零件视觉测量图像拼接方法

针对视觉检测技术对大尺寸复杂零件测量精度低的问题,提出一种基于单应性矩阵的大尺寸零件视觉测量图像拼接方法。首先建立世界坐标系→相机坐标系→投影坐标系→图像坐标系之间的归一化模型,提炼出简单易懂的坐标变换表达式H;然后对摄像机进行多次标定,确定像素当量、拍摄视场及焦距;再获取零件图像,利用前面得到的最简坐标表达式H得到拼接图像之间的配准,最后完成若干副图像的拼接,把拼接结果和SURF特征点方法及向后映射模型归一化的拼接结果进行比较。结果表明,该方法可以大大减少大尺寸零件拼接的时间,较SURF特征点方法和向后映射拼接用时分别降低86.55%和67.30%,拼接精度远高于SURF特征点方法和向后映射方法,分别提高了50.95%和25.08%,测量精度满足大尺寸零件检测精度要求。     

基于标志点的三维拼接立体偏折法

立体偏折法作为一种非接触式镜面表面三维测量方法,近年来发展迅速。为了解决传统立体偏折法难以测量较大倾角曲面的问题,提出了一种基于标志点的三维拼接立体偏折法。先利用立体偏折法测量不同视角下的曲面子区域的三维点云,同时通过立体视觉测量样品台上标志点的三维坐标,使用标志点坐标进行粗拼接,再通过迭代最近点算法进行精拼接,最终重构出完整的三维面型。实际搭建了一套三维拼接立体偏折测量系统,测量了一个倾角25.8°的光滑凸球面反射镜,拼接后球面拟合误差在3μm以内。实验结果验证了方法的可行性,对立体偏折法应用于大口径和大倾角的复杂光学曲面三维测量具有借鉴意义。     

基于小波变换的拼接重叠区域融合方法

为了解决大口径光学元件面形高精度测量问题,建立了拼接测量系统,通过测量得到整体表面面形。在拼接测量过程中,需要将待测面形进行划分,按着一定的顺序进行测量,再根据各个子口径之间的相对位置进行拼接。各个子口径存在重叠部分,采用均化的处理方法会导致高频面形数据的丢失。采用小波变换的拼接重叠区域融合方法可以减少高频数据的丢失。首先,对各个子口径的重叠区域分别进行小波变换得到低频和高频系数矩阵;然后,根据不同的方法对低频和高频系数矩阵进行融合得到新的系数矩阵;最后,通过小波逆变换得到整体面形。对尺寸为120 mm×40 mm的长方形反射镜面形进行拼接干涉测量,并用功率谱密度对本文方法和平均融合结果进行客观比较。实验结果表明,该方法可以保留更多的高频面形数据。     

二维三温能量方程的差分格式及平面靶数值模拟

通过统一二维直角坐标与柱坐标下三温能量方程的差分格式,实现了LARED-H(laser radiationelectron dynamic holehurm)程序既可以模拟正入射激光平面靶过程,也可模拟斜入射平面靶问题,从而扩展了LARED-H程序的功能.使用发展后的LARED-H程序进行了直角坐标系下线聚焦打靶耦合过程数值模拟,给出了不同入射角度下靶等离子体的膨胀过程.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

均匀带电圆环的电场强度

求出了均匀带电圆环的电场强度,给出了它在3种坐标系里的表达式.     

A high order ENO conservative Lagrangian type scheme for the compressible Euler equations

We develop a class of Lagrangian type schemes for solving the Euler equations of compressible gas dynamics both in the Cartesian and in the cylindrical coordinates. The schemes are based on high order essentially non-oscillatory (ENO) reconstruction. They are conservative for the density, momentum and total energy, can maintain formal high order accuracy both in space and time and can achieve at least uniformly second-order accuracy with moving and distorted Lagrangian meshes, are essentially non-oscillatory, and have no parameters to be tuned for individual test cases. One and two-dimensional numerical examples in the Cartesian and cylindrical coordinates are presented to demonstrate the performance of the schemes in terms of accuracy, resolution for discontinuities, and non-oscillatory properties.     

POSITIVE DEFINITE PROBLEM OF ENERGY DENSITY AND RADIATIVE ENERGY FLUX FOR PULSE CYLINDRICAL GRAVITATIONAL WAVE

By using the general expressions of energy momentum pseudo-tensor of the cylin-drical gravitational waves (GW) given by Rosen and Virbhadra in Cartesian coor-dinates, the concrete forms of energy density and radiative energy flux of the pulse cylindrical GW are obtained. Their physical properties, suitable range and asymp-totic behaviour are considered. It is found that: For the region in which space radial coordinates to origin are greater than the pulse width of the pulse cylindrical GW, the energy density and radiative energy flux of the outward travelling pulse cylindrical GW propagating along at light-cone are positive definite. However, for the region in which the space radial coordinates are less than the pulse width, there is no guarantee for the positive definite property of the radiative energy flux of the outward travelling wave. Moreover, we show that the asymptotic behaviour of the energy and energy flux densities of the pulse cylindrical GW and that of the Riemann curvature tensor have good self-consistancy in space like, time like and null infinity regions.     

A high order ENO conservative Lagrangian type scheme for the compressible Euler equations

We develop a class of Lagrangian type schemes for solving the Euler equations of compressible gas dynamics both in the Cartesian and in the cylindrical coordinates. The schemes are based on high order essentially non-oscillatory (ENO) reconstruction. They are conservative for the density, momentum and total energy, can maintain formal high order accuracy both in space and time and can achieve at least uniformly second-order accuracy with moving and distorted Lagrangian meshes, are essentially non-oscillatory, and have no parameters to be tuned for individual test cases. One and two-dimensional numerical examples in the Cartesian and cylindrical coordinates are presented to demonstrate the performance of the schemes in terms of accuracy, resolution for discontinuities, and non-oscillatory properties.     

Analysis of curved bends in arbitrary optical devices using cylindrical coordinates

An extension of the beam propagation algorithm based on the method of lines (MoL–BPM) is proposed and substantiated for analysis of curved bends–constituent parts of complicated optical devices, connecting waveguides with different orientation. Cylindrical coordinates are introduced. The formulas are compatible with those in Cartesian coordinates for analysis of straight waveguides. So, in combination concatenations of curved bends and straight waveguides can be examined in a uniform way. For the purpose of analysis in cylindrical coordinates a suitable set of wave equations without any approximation and valid for a general hybrid case is derived. To prove the accuracy of the MoL–BPM in cylindrical coordinates applying the derived formulas, the curvature loss of a rib waveguide was computed and compared with other methods showing very good agreement. As an application of the method two straight waveguides are connected by a curved bend and the power flow is determined.     

Turbiner’s conjecture in three dimensions

We prove a modified version of Turbiner’s conjecture in three dimensions and we give a counter-example to the original conjecture. The Lie algebraic Schrödinger operators corresponding to flat metrics of a certain restricted type are shown to separate partially in Cartesian or cylindrical or spherical coordinates.