Designing a plano-convex aspheric lens for fiber optics collimator

A plano-convex aspheric lens is designed to collimate the emitted light of the fiber optics. In this paper even orders of general aspheres are used to describe the aspheric surfaces sag. To determine the aspheric coefficient, the even asphere polynomial are fitted on the computed sag data. The surface sag data is determined using genetic algorithm method. The surface sag was analyzed by the commercial optical software package ZEMAX. For typical fiber optics, the numerical aperture (NA) of 0.22 was assumed. With this specification, the expected output spot diagram of 20 mm and the maximum aperture of 25.4 mm have been obtained. A comparison between here presented lens and the similar type of conventional lens has been carried out; the proposed aspheric lens corrected the spherical aberration, which led to increase in the collimated distance.     

Aberration correction of a single aspheric lens with particle swarm algorithm

In order to design a single aspheric lens to meet the requirements of spherical aberration, the particle swarm algorithm is applied to the aberration correction for a single aspheric lens. A mathematical model is constructed, and a program code is developed. Merit functions in an optical system are employed as fitness functions, which combined coefficients of a higher order polynomial equation, a reciprocal of radius of curvature, the conic constant, thicknesses among lens surfaces and refractive indices regarding an optical system. By using this function, the automatic correction of spherical aberration is carried out. The example for a single aspheric lens design using particle swarm algorithm shows that PSO as a tool of the spherical aberration correction for a single aspheric lens is simple and effective, and easy to find a series of good design results. The asphere's more complex surface profile can reduce or eliminate easily spherical aberration at different incidence heights at one time. The automatic design and analysis of a single aspheric lens using this method from the view of a particular optical design problem are presented.     

用粒子群算法进行单个非球面透镜的球差校正

为设计出符合球差要求的单个非球面透镜,把粒子群算法应用到单个非球面透镜的球差校正中,构造相应的数学模型,并编程实现算法.设计关于非球面高次多项式的顶点曲率半径,高次多项式各项系数,透镜面之间的距离和玻璃折射率等光学系统结构参数的适应度函数,用这个函数作为评价函数,实现对球差的自动校正.给出用粒子群算法进行单个非球面透镜设计的实例,结果证明:粒子群算法用于非球面透镜的球差校正简单有效,能同时校正不同入射高处的球差,且容易发现一系列好的设计结果.从实际光学设计角度呈现使用这种方法进行单个非球面透镜的自动设计分析.     

Error compensation in reflection type centering error testing

The error compensation for an error caused from unwanted surfaces when using single autocollimator reflection type centering error testing. And compare the result with commercial equipment like OptiCentric built by TRIOPTICS GmbH using a concave lens and a convex lens.     

基于Wassermann-Wolf方程的共形光学系统设计研究

提出了基于多项式拟合Wassermann-Wolf曲面设计共形光学系统的设计方法，并给出了完整的设计结果.共形光学系统要求导弹整流罩具有流线型几何外观以减少空气阻力，其次考虑导引头的光学系统设计，所以共形整流罩引入的像差通常高达几十甚至一百个波长量级，为导引头光学系统的设计带来了极大的困难.通过多项式拟合Wassermann-Wolf曲面提供共形光学系统初始结构，建立Zernike多项式特殊优化函数取代传统的光学系统评价函数，克服了用传统光学设计方法设计共形光学系统时系统评价函数收敛缓慢的问题，实现了共形光学系统的设计.设计结果表明，系统的调制传递函数在整个目标视场范围内达到了衍射极限.     

球形透镜表面特性数值分析

球形透镜表面在一些高精度的光学系统变得越来越重要,它们和其他透镜表面一样必须满足一样的质量标准。本文采用数值计算方法分析了球形透镜的表面特性,并以Snell定律为基础,建立了用于计算球形表面特性的公式。通过与已有的球面特性公式进行比较,采用该方法计算球形透镜表面特性的拟合误差小于1μm。     

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.     

椭圆平顶高斯光束的聚焦特性

利用级数分解法把椭圆平顶高斯光束(EFGB)分解成多个椭圆厄密-高斯模的叠加形式,利用椭圆厄密-高斯模的传输公式导出了EFGB通过非轴对称光学系统的传输公式,该公式和直接用矢量积分得出的结果是等效的.利用导出的公式,我们计算分析了EFGB通过轴对称透镜和非轴对称透镜的聚焦特性.结果表明,EFGB聚焦后,近场光强分布变化很快,特别是焦点前后,光强分布会快速旋转.另外,EFGB的聚焦特性与阶次有关.     

Aspherical lens shapes for focusing synchrotron beams

Aspherical surfaces required for focusing collimated and divergent synchrotron beams using a single refractive element (lens) are reviewed. The Cartesian oval, a lens shape that produces perfect point‐to‐point focusing for monochromatic radiation, is studied in the context of X‐ray beamlines. Optical surfaces that approximate ideal shapes are compared. Results are supported by ray‐tracing simulations. Elliptical lenses, rather than parabolic, are preferred for nanofocusing X‐rays because of the higher peak and lower tails in the intensity distribution. Cartesian ovals will improve the gain when using high‐demagnification lenses of high numerical aperture.     

Effect of crystalline lens surfaces and refractive index on image quality by model simulation analysis

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye.On the basis of two eye models,which are widely applied at present,the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co.,San Diego,USA).The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution.It has great potential in the design of intraocular lens (IOL).The eye models with an intraocular implantation are presented.     

基于多次平移的平面绝对检测仿真

将待测面形表示为多项式的和,通过分别沿x,y向多次平移待检光学元件得到移动前后待测元件面形差,采用最小二乘法拟合多项式系数,得到待检光学元件的绝对面形。推导了多次平移法的理论公式,并进行了仿真实验,模拟了移动次数、移动间隔和采样点数对测量精度的影响。仿真结果表明:待测平面与初始平面残差图的均方根值为5.118×10~(-13)λ,理论误差达到高精度平面面形检测要求。     

Dynamic pulsed-beam shaping using a TAG lens in the near UV

The ability to dynamically shape the spatial intensity profile of an incident laser beam enables new ways to modify and structure surfaces through pulsed laser processing. Here we describe a method to generate doughnut-shaped beams from an input Gaussian source using a tunable acoustic gradient index (TAG) lens. The TAG lens is capable of modulating between focused beams and annular rings of variable size, using sinusoidal driving frequencies. Laser micromachining is accomplished by synchronizing the TAG lens to a 355 nm pulsed nanosecond laser. Results in polyimide demonstrate the ability to generate adjacent surface features with different shapes and sizes.     

双变量正交多项式描述光学自由曲面

推导了单位圆域和单位方域内的双变量正交多项式曲面的数学模型,详细分析了将不同正交多项式曲面应用于自由曲面拟合的精度问题。采用均匀随机、阵列分布和环状辐射三种采样方式,并选择具有代表性的普通非球面、自由曲面以及Peaks自由曲面进行了大量的拟合实验。实验结果表明:三种采样方法中,阵列采样的拟合适应度最高;XY多项式和正交XY多项式的拟合适应度最高;方域和圆域内正交的泽尼克多项式在曲面拟合中优势显著;双变量正交切比雪夫多项式在方域内、阵列采样的情况下曲面拟合优势明显。     

A catadioptric magnifier with two magnifications for microfiche reading

We have considered the possibility of using four internal reflections in a single lens to reduce its effective focal length by a very large factor. Hence, by using very shallow curvatures on the lens surfaces, it is possible to obtain very high visual magnification for viewing transmission objects such as microfiche. Some details of such a system are presented here, where a lower magnification is obtained for two internal reflections and a higher magnification for four internal reflections.     

ASAP模拟变焦系统中鬼像的研究

 非成像光束在光学系统内表面的多次折射反射容易在像面附近形成光晕或鬼像,变焦系统由于镜片多,机构复杂等往往难以进行全面的分析模拟。利用ASAP软件模拟每个透射面作为部分透射、部分反射的表面,对变焦光学系统非轴上光进行分析,模拟出变焦系统的光学元件表面和光机内壁,实行实际光线追迹,然后以像面为研究对象,进一步实施实际光线追迹,模拟出全部散射光在像面上的能量分布,找出鬼像形成的原因,并在此基础上通过改变二次反射所在面的曲率或改变所在面的折射率两种方法对变焦光学系统进行优化,减小鬼点数目,以提高系统的成像质量。     

泽尼克多项式曲面投影显示系统

采用调制传递函数和波前像差分析方法,设计了基于三片泽尼克多项式曲面反射镜的反射投影成像系统.其中第一片反射镜表面为凹面,用于减小第二片反射镜的尺寸和获得高对比度,而另外两片反射镜表面为凸面,用于校正主要的像差和获得更短的投影距离.利用ZEMAX软件分析了所设计的基于泽尼克多项式曲面反射镜成像系统的光学性能.结果表明,设...     

激光等倾干涉法

本文介绍一种新的基于两点光源干涉原理的精确检测透镜中心偏的方法。利用由静止参考面和位于空气轴承转台上的被检透镜表面之间产生的非定域干涉条纹,可以把透镜的面倾角误差大大放大并加以检测。这种方法与现有的透镜中心偏检测方法相比具有精度高、操作简便、并与透镜形状无关等明显优点。理论与实践证明,如果参考面的曲率半径和参考面与被检面之间的空气间隔选得合适,那么即使用肉眼也能检测出约1″大小的透镜面倾角误差。     

液滴透镜在电场中的变形研究

利用电场作用操控液滴面形获得非球面液滴透镜,并实时检测其光学性能,利用紫外光固化技术使液滴透镜固化得到固体非球面透镜.实验测量了液滴透镜的面形并经过图像处理提取面形轮廓,经多项式拟合得出液滴透镜的面形表达式.比较了不同强度电场作用下的液滴透镜面形,计算了主曲率随电场的变化规律,讨论了液滴透镜在电场中的变形机制|根据透镜面形表达式,采用光线追迹法得出了液滴透镜的焦距随电场的变化规律,结合ZEMAX软件计算了3 550 V时液滴透镜的最大波像差为0.32个波长,Strehl Ratio为0.74,及光学传递函数等参数,计算了所制作的非球面透镜的像差,为低像差非球面透镜的研制提供了依据.     

液滴透镜在电场中的变形研究

利用电场作用操控液滴面形获得非球面液滴透镜,并实时检测其光学性能,利用紫外光固化技术使液滴透镜固化得到固体非球面透镜.实验测量了液滴透镜的面形并经过图像处理提取面形轮廓,经多项式拟合得出液滴透镜的面形表达式.比较了不同强度电场作用下的液滴透镜面形,计算了主曲率随电场的变化规律,讨论了液滴透镜在电场中的变形机制;根据透镜面形表达式,采用光线追迹法得出了液滴透镜的焦距随电场的变化规律,结合ZEMAX软件计算了3 550 V时液滴透镜的最大波像差为0.32个波长,Strehl Ratio为0.74,及光学传递函数等参数,计算了所制作的非球面透镜的像差,为低像差非球面透镜的研制提供了依据.     

N=2 topological Yang-Mills theory on compact Kähler surfaces

We study a topological Yang-Mills theory withN=2 fermionic symmetry. Our formalism is a field theoretical interpretation of the Donaldson polynomial invariants on compact Kähler surfaces. We also study an analogous theory on compact oriented Riemann surfaces and briefly discuss a possible application of Witten's non-Abelian localization formula to the problems in the case of compact Kähler surfaces.This article was typeset by the author using Pjour1