直角棱镜平面反射衰减在激光光束诊断中的应用研究

论述了普通光学元件-直角平面反射镜在激光光束诊断中的应用,提出了利用直角棱镜的直角面反射进行光能衰减,详细论述了采用该方法进行光能衰减的可行性,分析了平面反射衰减法在激光束诊断中对测光束的影响,讨论了激光束发散角在直角面反射中的影响,结合半导体光束诊断进行了应用分析.实验证明,该方法结构简单,误差小,调整方便,利用普通反射棱镜直角面衰减即可满足激光强度的匹配要求,实现了待测激光束的无失真取样,达到了很好的测试效果.     

直角棱镜棱脊倾斜对方位瞄准的影响

火箭制导系统中惯性器件的方位敏感轴方向通常是借助于直角棱镜来确定的,因而直角棱镜的棱脊倾斜对方位瞄准精度有影响.本文推导了直角棱镜的棱脊倾斜造成的反射光矢量的精确表达式,并在此基础上讨论了棱脊倾斜对线阵CCD测角的影响.     

内反射法快速准确检测等腰直角棱镜三个内角

以一单角45°±1′,90°±1′的等腰直角棱镜为例,详细介绍了利用内反射法快速准确检测三个内角的方法.利用等腰直角棱镜既可做一次反射,又可做二次反射的基本特性,通过检测两次光学平行差来快速准确地进行三个内角的判断.实践证明该方法很好地解决了等腰直角棱镜在单角检验时精度、速度和准确度的关系,大大提高了检测效率,适用于批量检验时推广使用.     

直角棱镜的特性研究

推导直角棱镜的偏向角与入射角的关系式,得到恒偏向角的条件和结果,并讨论了直角棱镜的最大入射角和最小入射角与折射率的变化关系.     

从反射面检测锥体棱镜直角误差的方法

介绍了一种使用平面干涉仪检测锥体棱镜直角误差的方法。使用这一检测方法时需要制做一个角度为24.4°的夹具,将被测棱镜放置在夹具之上。这个夹具的作用是,可以使来自干涉仪的标准平行光束(测试光束)由反射面折射入棱镜内,并且垂直于被测直角棱线,经被测直角两个面的反射光仍按原光路返回。当出射光束与干涉仪的标准平行光束(参考光束)重合时产生干涉,实现在平面干涉仪上对锥体棱镜直角误差的测量。与传统的测量方法相比较,该方法具有测量准确、计算精度高的特点。适合于对高精度锥体棱镜(α≤3″)直角误差的测量。     

从入射面检测锥体棱镜直角误差的方法

介绍了一种应用激光平面干涉仪从入射面检测锥体棱镜直角误差的方法。棱镜被测角通过一个夹具被预置一个初始角,使射入棱镜内的测试平行光垂直于被测角棱,经被测直角的两个面反射后形成全反射光路,当射出的光与测试平行光重合时产生干涉,实现对锥体棱镜直角误差的测量。介绍了测量、干涉条纹图形分析和直角误差计算的方法,并与传统检测方法进行了比较。结果表明,该方法具有操作简单、测量准确、计算精度高等特点,适合于高精度锥体棱镜(α≤3″)的直角误差测量。     

角锥棱镜的直角面面形问题

从一个侧面论述了角锥棱镜直角面面形误差所导致的出射波面像差及两面直角误差之间的定量关系 ,因而可以分别从后两者的精度要求提出对面形误差的要求。对于高精度的角锥棱镜 ,直角面面形问题应如同两面直角误差一样受到重视和关注     

基于等腰棱镜单摄像机立体视觉系统误差分析

基于等腰棱镜和单摄像机设计了一款小型化工业内窥镜系统,它能够同时获取同一场景的两个视图并在单帧CCD图像上显示。通过建立系统结构参数模型,分析测量范围对系统测量误差的影响,结果表明：近距离测量时,测量范围小系统误差小,随着测量范围变大测量误差也会变大,并且在沿着直线ω₁=ω₂方向,误差变化平缓。利用该系统测量高精度标定板的方格尺寸,测量误差达到微米量级,平均误差为2.06%,符合工业应用需求。文章系统结构紧凑,系统参数相对较少,对工业内窥镜的结构设计与应用具有一定的指导意义。     

用直角棱镜校正迈克尔逊干涉仪的分光板

在观察迈克尔逊干涉仪产生的干涉图样的时候 ,有时会发现干涉图样是椭圆形干涉环 ,而不是圆形干涉环 ,这是因为干涉仪分光板的方位已经不是原来的“与两臂轴各成 45°角”的方位了 ,必须校正分光板才能使干涉仪产生正常的同心圆形干涉环。在普通物理实验室的条件下 ,用直角棱镜可以帮助校正分光板的方位。     

Baxterization of Solutions to Reflection Equation with Hecke R-matrix

Let R be a Hecke solution to the Yang–Baxter equation and K be a reflection equation matrix with coefficients in an associative algebra . Let R(x) be the baxterization of R and suppose that K satisfies a polynomial equation with coefficients in the center of . We construct solutions to the reflection equation with spectral parameter relative to R(x), in the form of polynomials in K.     

19顶角模型反射方程的常数解

通过直接解反射方程,给出了19顶角模型A2(2)模型反射方程的所有矩阵元非零形式以及其它几种非对角形式的常数解.     

15顶角模型反射方程的常数解

得到了15顶角模型A2(1)模型和超对称t–J模型反射方程的非对角解,结果发现,A2(1)模型具有三种形式的非对角解,超对称t–J模型具有一种形式的非对角解,每种形式的非对角解均含有两个解,每个非对角解中均含有三个任意参数.关于对角解也得到了一些新的形式的解.     

Zn Belavin模型反射方程的多参数解

利用A_(n－1)⁽¹⁾面模型反射方程的对角解,得到了ZnBelavin模型反射方程的含有n+1个参数的解.当n=2时,其结果与侯伯宇等人给出的8项角反射方程的解是一致的.     

Derivation of Dirac's Equation from the Evans Wave Equation

The Evans wave equation [1] of general relativity is expressed in spinor form, thus producing the Dirac equation in general relativity. The Dirac equation in special relativity is recovered in the limit of Euclidean or flat spacetime. By deriving the Dirac equation from the Evans equation it is demonstrated that the former originates in a novel metric compatibility condition, a geometrical constraint on the metric vector qused to define the Einstein metric tensor. Contrary to some claims by Ryder, it is shown that the Dirac equation cannot be deduced unequivocally from a Lorentz boost in special relativity. It is shown that the usually accepted method in Clifford algebra and special relativity of equating the outer product of two Pauli spinors to a three-vector in the Pauli basis leads to the paradoxical result X = Y = Z = 0. The method devised in this paper for deriving the Dirac equation from the Evans equation does not use this paradoxical result.     

不匹配介质三层漫射方程的时间分辨漫反射

生物体的表面组织是一个不匹配的多层介质,大多数研究人员研究匹配介质的漫射方程,将组织表面看作折射率相同的介质。为更好的理解光在生物体内的传播,建立了不匹配条件的三层半无限厚频域方程的解;并对频域进行傅里叶变换,计算出时域的时间分辨漫反射。为了验证此的理论,使用蒙特卡罗方法进行仿真研究,结果表明该理论研究不仅和蒙特卡罗方法高度一致,而且还可以解决两层不匹配介质模型。     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f（ξ）, is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f(ξ), is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

Invertibility of Infinite-Dimensional Hamiltonian Operators and Its Application to Plate Bending Equation

The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.