面向经济公差应用的波像差拟合研究

利用二阶泰勒形式表示公差与波像差的函数关系，依据差分光线追迹法，通过光线追迹理论推导完善了偏心和倾斜两种公差关于波像差的一阶导数计算公式，利用依次求导和公式移项两种方法建立波像差的二阶导数模型。结果表明：依次求导法的求解过程复杂，应用范围受到限制，只可用于光学后截距分析；公式移项法所需的追迹像质次数少，且拟合效果良好，残差平方和处于10^-7～10^-6量级；所提方法可对光学系统进行有效的经济公差分配。     

用于空间相机设计的高精度光线追迹方法

空间光学系统在应用需求牵引下,向着大尺度、高精度、复杂化等方向发展,像差随着焦距与口径的增大呈幂指数增长,微小的误差扰动就会引起像质的大幅退化,因此对光线追迹算法的精度和稳定性提出了更严苛要求.本文从误差分析理论出发,提出了光线追迹精度表示模型,依据模型分析了计算过程误差来源,并设计了高精度光线追迹算法.数值仿真实验和典型空间相机设计案例结果表明,本文方法在精度上较原有方法提高了5—6个数量级,残差平均比Zemax小近3个数量级,数值稳定性也得到了极大提升.     

应用场光线传递方程计算鱼眼镜头像场像差

应用场光线传递方程,从鱼眼镜头的孔径光阑处,逆向追迹场光线传递方程,确定任意视场角场光线的初始位置,即光阑球差.正向追迹场光线计算鱼眼镜头系统物、像空间视场角之间的关系曲线;用多项式拟合求出关系曲线的解析表达式.通过反演运算,根据畸变图像复原物的图像分布,达到消除鱼眼镜头成像系统畸变的目的.最后,计算了一个160°鱼眼镜头光学系统的光阑球差和图像的畸变,并应用本文方法复原物的图像分布.计算结果表明:光阑球差的计算结果与真值的相对误差小于1%;复原的物方图像径向高度相对误差小于0.25%,说明本文计算鱼眼镜头像场像差的方法是可行的.     

使用辅助光栅的平面变间距全息光栅加工理论研究

变间距全息光栅具有自聚焦和消像差功能,是高分辨率光谱仪与同步辐射单色器中的重要元件。研究了使用平面等间距光栅产生非球面波,记录平面变间距全息光栅的方法。根据几何光学的光线追迹理论,推导了光栅参量的四阶解析表达式。并基于费马原理,提出了记录光路的光线追迹数值算法。应用所推导的光栅参量四阶表达式,仿真设计了变间距全息光栅。通过合理选择记录参量,可以避免光栅基底受到零级及高阶衍射光场的影响。设计结果表明,理论光栅线密度与要求值相当符合;经光线追迹数值算法验证,解析表达式的展开误差在整个记录区域内小于1.5线;考虑到实际加工工艺允许误差,使用辅助光栅的记录光路对记录参量的误差并不敏感;设计实例证明了解析表达式的有效性,以及使用辅助光栅的记录光路的优越性。     

LASIK手术对人眼波前像差的影响

采用主观光线追迹的像差仪测量人眼波前像差,比较3mm和6mm 瞳孔直径下,LASIK手术前与术后四个月的29只人眼波像差情况.数据比较分析表明,手术后人眼高阶像差一般会大于术前,且像差增大量随术前屈光度数的增大和瞳孔直径的增大而增加,如3 mm瞳孔直径下86%的人眼高阶像差的RMSH<0.12 μ,>0.4μ.比较人眼波像差的Zernik展开式中各项发现球差Z04无论在3 mm还是6 mm孔径下术后改变都最大;其中,当比较3阶,4阶和5至7阶时可看出对于3 mm孔径第三阶术后改变比例较大,为1.87,6 mm时第四阶改变较大,比例为2.21.     

基于相位测量偏折术的透镜波像差检测方法

根据逆哈特曼检测原理建立了逆光线追迹模型,对透射相位测量偏折术系统进行了分析,并提出了可适用于透镜或成像镜头波像差测量的计算方法。在波像差定义的基础上,通过计算正逆模型光程差的对比在原理上验证了此方法的可行性,通过模拟计算验证了本方法的有效性。结合实际光线标定、系统模型追迹和N步相移算法得到了实际透镜的波像差。在实验中测量一个平凸透镜的波像差,并与干涉仪的测量结果进行对比,两者测得的波像差的RMS差仅为0.03μm,验证了此方法能够精确地测量透镜的波像差。结果表明,本方法具有装置简单、成本低、计算原理简单等优点。在无需干涉仪的前提下,为测量透镜的波像差提供了一种新的离线或在线/在位检测手段。     

反射式转镜干涉光谱仪光程差计算

高分辨率反射式转镜干涉光谱仪是一种新型傅里叶变换光谱仪,它利用倾斜旋转镜的转动产生非线性的光程差(OPD).光程差的研究对于干涉光谱仪的性能指标分析、设计和研制具有重要意义.在介绍反射式转镜干涉光谱仪的原理基础上,描述了利用基于马吕斯定律的光线追迹法和基于镜面成像原理的像点法分析其光程差的方法.利用光线追迹法导出了任意...     

基于元胞自动机的气动光学光线追迹算法

对于含激波等大密度脉动结构气动光学流场,沿着直线路径对折射率积分会带来较大的光程误差.因此,数值求解光线方程进行光线追迹是必要的.与数值求解光线方程不同,元胞自动机(cellular automata,CA)通过给定光线位置和方向变换规则来模拟光线在介质中传输路径.本文基于已有的实验测量、数值仿真所获得的高超声速流场密度场数据,分别采用数值求解光线方程法和CA光线追迹算法进行光线追迹,进而得到光线出射流场后的光程差.结果表明, CA算法对于二维气动光学流场中光线追迹的适用性,且较数值求解光线方程方法具有更高的效率.     

奇对称型相位板波前编码成像系统的点列图分析

基于几何光学理论利用光线追迹方法得到了适用于任意面型相位板的大视场平行光入射情况下的光线像差近似表达式,并在此基础之上分析了奇对称型相位板波前编码系统的点列图的大小、边界以及光线结构等特性,研究了大视场角平行光入射下的光线像差增强及点列图形变等现象,并且给出了相应的近似数学解析式来描述这些特性。通过对奇对称型相位板波前编码成像系统的点列图特性分析,有助于进一步的理解波前编码技术并且指导实际系统的设计。     

啁啾脉冲放大系统展宽压缩器各阶色散分析

 通过在光程差中增加相位校正项,重新推导了更为完善的压缩器各阶色散解析式。并对压缩器的各阶色散作了光线追迹的模拟计算,得到与解析式完全一致的计算结果,从而验证了解析式的正确性。基于解析式和光线追迹的方法,更加系统完善地对比较常用的Offner展宽器的各阶色散进行了研究,分析了入射角、光栅与凹面镜距离对其各阶色散及剩余各阶色散的影响。同时,还对非匹配的展宽压缩系统的剩余色散的影响因素进行了讨论。     

基于Buchadhl象差系数和解析偏导数的光学优化设计

本文以基于 Buchadhl 象差系数得到的点列图为目标函数,只需追迹少许光线就可得到近似点列图,大大减少了计算量;同时采用了目标函数对结构参数偏导数解析求导原理并应用于光学自动设计,这样得到的解析偏导数不仅不存在原理误差,同时极大地减少了求得所需的时间;最后给出了使用 DFP-BFGS 优化方法设计一个双高斯物镜的实例.     

Analytical calculation of cathode spot parameters on the electrode surface in arc discharge

The model of a heat transfer in the cathode spot on an electrode in the arc discharge is developed and analytical expressions for the spot radius and temperature as the functions of basic characteristics of the discharge and the electrode material are obtained. The dependence of the spot radius on the voltage drop of the cathodic discharge, which is consistent with results of numerical simulation, is calculated.     

Dynamics of a Second-Order Digital Recursive System with Binary Quantization

We analyze free oscillations and dynamical regimes of a second-order recursive system under constant or periodic binary forcing. Based on the technique developed in this paper, we find the parameter regions corresponding to certain forms and periods of motion in the system and analytical expressions for motion trajectories. The bifurcation diagrams are plotted.     

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams for the massless ϕ ³ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of the Lipatov integrable chain model. The text was submitted by the authors in English.     

基于成像清晰度函数的非球面反射镜位置校正实验研究

在具有双曲面、抛物面或椭圆面反射镜的成像光学系统中,反射镜的位置误差通常具有对成像质量影响灵敏的特点.因此,在该类光学系统装调或工作过程中反射镜位置存在误差时需要对该反射镜进行精确调整.目前,反射镜位置校正的方法多基于对系统波前误差的测量,从而判断其位置误差.然而在系统工作过程中可能无法进行光学系统的波前测量,或者需要复杂的光学系统才能实现波前误差的测量.本文以焦平面图像清晰度作为评价函数,采用随机并行梯度下降算法对反射镜位置进行调整,使系统成像质量达到最佳.针对迭代过程中反射镜位置发生变化时图像偏离探测器靶面而无法探测的问题,本文采用了一种反射镜垂直光轴平移和旋转相结合的调整方法.在保证图像位置不变化的条件下对系统像差进行校正.室内实验验证了该方法具有可行性,校正后的成像质量达到衍射极限.     

Isolating vacuum amplitudes in quantum field calculations at finite temperature

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. However, at least with the regularization used in this paper, this simple analytical structure does not hold for arbitrary diagrams, as revealed by counter-examples. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture for a relation, in the imaginary time formalism, between the expressions of a Feynman diagram at zero and finite temperature.     

Stability Diagrams of a Bose-Einstein Condensate in a Periodic Array of Quantum Wells

With the help of a set of exact closed-form solutions to the stationary Gross Pitaevskii equation, we compre-hensively investigate Landau and dynamical instabilities of a Bose-Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the anaiyticai expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.     

Field-induced spin-orientational phase transitions in Néel ferrimagnets. I

The breakdown of the aligned states of Néel ferrimagnets in an applied magnetic field is considered. The behaviour of isotropic two-and three-sublattice ferrimagnets is treated in the framework of the mean-field approximation. A phenomenological method also limited by the mean-field approximation is used to analyse the behaviour of the anisotropic ferrimagnet. Particular emphasis is placed on the vicinity of the compensation temperature. Approximate analytical expressions which are valid near the compensation temperature are given for the phase-boundary positions, typical magnetic fields, and temperature ranges of the phase diagrams.     

Rigorous Treatment of the Liquid-Vapor Transition in a Polydisperse System with Kac Interaction

Within the canonical formalism, we consider a polydisperse lattice-gas model and a polydisperse continuous system interacting with the Kac potential. We obtain rigorous expressions for free energy densities. We also exhibit phase diagrams of the bidisperse lattice-gas model.