标准球面透镜的几何特性与误差分析

标准球面透镜是斐索型干涉仪的核心器件,综述标准球面透镜的几何特性和误差。分析标准球面透镜在干涉照明光路和成像光路中的作用,重点介绍并实验验证了球面干涉成像的R-sinθ几何特性关系模型,给出了采用Q非球面实现非球面分裂的新型设计方法,以及2片式非球面标准球面透镜结构的实例,概述了针对小F数标准球面透镜球面干涉腔中的待测球面调整误差和移相空间非均匀性误差的研究成果,介绍了校正球面干涉腔中误差的波面差分算法,指出在近标准球面透镜焦点位置测量球面时的回程误差影响,从物像共轭关系角度解释了近焦点位置回程误差较大的原因,比对分析了标准球面透镜的透射波前与斜率对回程误差的影响。提出了在设计标准球面透镜时需注意的几何特性关系,以及使用标准球面透镜时易产生的误差和相应的抑制方法。     

On the use of lenses to focus few-cycle pulses with controlled carrier–envelope phase

From a model of focusing with lenses that includes the effects of the lens variable thickness, material dispersion, aperture, spherical and chromatic aberrations, we characterize the conditions under which a lens can focus to few-cycle, transform-limited pulses propagating without distortion along the focal region. A lens also allows to control the carrier?Cenvelope phase shift along the focus. The carrier?Cenvelope phase shift is drastically reduced by focusing with specific focal lengths and input spot sizes, which are of the same order as those typically used in experiments involving focusing for phase-sensitive, light-matter interactions.     

Cylindrical Zone Lens

We present the theory of a cylindrical zone lens. It is shown that the law describing the formation of Fresnel zones on a divergent cylindrical front is very different from the plane and spherical cases. The field configuration of a cylindrical zone lens in a wide range of parameters is described. The near-focus diffraction of a cylindrical zone lens is studied experimentally. Different versions of a cylindrical zone lens are found and analyzed.     

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.     

Third-order design of aspheric spectacle lenses

The theory of third-order aberrations for a system of rotationally symmetric aspheric thin lenses and relations for calculation of the shape of rotationally symmetric aspheric spectacle lenses with zero astigmatism are described. A comparison of aspheric and spherical spectacle lens design is presented. Possible applications of aspheric lens surfaces are proposed including the design of a spectacle lens with two types of primary aberrations corrected, an anastigmatic spectacle lens with minimum weight and a spectacle lens with the desired aesthetic shape. Our work performs a complex analysis of the third-order design of spectacle lenses considering not only astigmatism but all types of primary aberrations and their combinations.     

Multi-directional lateral shearing interferometer based on rotatable prism pairs

The common camera lens usually includes the spherical glass/plastic lens and aspheric glass/plastic lens. However, spherical/aspheric shape measurement is still a key problem in the process of optical lens fabrication. At present, the in-process measurement of spherical/aspheric shape is conducted mainly by the probe-contacting method. But after a long time, its probe could be scratched severely and cause some big errors. Laser shearing interferometry is a good substitute to some degree. Nevertheless, it is not convenient for general shearing interferometer to carry out the in-process measurement because it is only suitable for certain kind of spherical/aspheric with respect to aperture or asperity. Here a new lateral shearing interferometer is proposed to solve the described problems. It is based on two Jamin plates and rotatable prism pairs which are used not only for shearing displacement and direction, but also for fringe period and tilt degree, in order to meet requirements of various spherical/aspheric shapes or asperities. The new interferometer features a simple optical structure and two symmetric light paths, which makes its system with minimal error. The relation between shearing displacement, fringe period and prism angle of rotation is given in this paper. And the error source is primarily from the manufacture errors of prisms and plates. The final experiments show that one can achieve good-quality fringe patterns according to the requirement of measurement, concerning the shearing direction, shearing displacement, fringe period, tilt degree, etc.     

Rotating type miniature camera phone multi-focal-length optical system

We have designed a practical mass produced rotating type miniature camera phone multi-focal-length optical system. The compact and short system, with 3× magnification, 1.3 megapixel sensor elements and total length of less than 10.7 mm, is described and evaluated in detail. Using Zemax lens design software, we start the design with thin lenses first order layout, and then spherical thick lenses, to aspherical lenses. Plastic lens materials are used whenever applicable, and diffractive lens elements are also employed to optimize the design. The beam spot diagrams and modulation transfer function of our design are found appropriate for good optical qualities.     

High aperture focusing through a spherical interface: Application to refractive solid immersion lens (RSIL) for subsurface imaging

The effects of on-axis spherical aberration and defocus on focusing across a spherical interface between two materials of mismatched refractive index are discussed. A vectorial integral representation for high aperture focusing in this configuration is formulated and an analytical expression for the spherical aberration function is derived. Numerical simulations are performed to analyse the effects of the spherical interface on both the transverse and axial intensity profiles. The results from these numerical simulations are important industrially in understanding the resolution enhancements from solid immersion lens technology, as well as being of more fundamental interest in calculating the distribution at the focal plane under different solid immersion lens configurations.     

宽光谱微光准直镜方案设计

介绍宽光谱大视场微光准直镜的光学设计和镜组结构方案,侧重叙述大视场微光准直镜的二级光谱校正方法。根据初级像差理论,由半部系统出发,给出了系统的初始结构。通过理论分析和ZEMAX光学设计软件的优化,结合工程应用给出了工作波长为（0.486～0.863）μm、全视场,相对孔径为1∶7.85的镜头设计实例,其二级光谱为0.01mm。该镜头由6块镜片组成,包括一个标准抛物面,在20lp/mm空间频率处MTF值超过0.8。准直镜的像差满足使用要求。     

Random tilings of spherical 3-manifolds

A set of random tilings for the compact Euclidean 3-manifolds have been considered recently. In this paper, non-deterministic triangulations of spherical 3-manifolds based on recursive procedures are introduced. Simplicial structures for lens, prism and Poincaré spherical dodecahedron spaces are described. The configurational entropies for the random structures depend only on the information in 2D and are consistent with the Bekenstein–Hawking bound.     

Investigation of surface radius variation in design of a lens duct delivery system

In this article a ray tracing method is used to study the variation of the entrance and exit surface shape in the different lens ducts systems. Designs with a variety of plane and spherical first and second surfaces are studied. The optimum geometrical conditions for each design in terms of the aperture, length, and the radius of curvature are reported. A comparison is made between the results obtained for ducts with the spherical and plane surfaces and the more efficient design is described. The effect of second-order aspheric shape factor on the device performance is also investigated. This study shows that each design has some advantages and disadvantages, and considering specific application, the result of this study can lead to a choice of the optimum design in terms of the required lens duct performance.     

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.     

折反射系统中的梯度折射率校正板

本文给出了一种类似于施密特非球面校正板作用的梯度折射率介质平板,这种介质是一种弱径向梯度折射率介质。     

一种球面透镜波前畸变的绝对检测方法

球面透镜的透射波前畸变是影响激光驱动器光束质量的重要参数。采用移相干涉仪检测球面透镜波前畸变时,测量结果的精度受限于标准球面镜头和后置平面反射镜的精度。然而,现有的绝对检测技术仅适用于反射元件。为了满足球面透镜波前畸变的高精度检测需求,提出了一种适用于球面透镜透射波前的绝对检测方法:三位置 平移相减法。详细介绍了三位置 平移相减法的原理,对其进行了模拟仿真和实验验证。仿真结果显示:三位置 平移相减法的仿真误差为10 nm~13 nm,达到高精度测量的理论要求;实验结果表明:三位置 平移相减法可以有效地减小前标准球面镜头和后置平面反射镜对测量结果的影响,该方法对球面透镜的加工和装调具有很好的指导意义。     

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。     

圆锥透镜对偏轴球面波光束的衍射模式

球面波入射圆锥透镜产生的出射光束中心光斑直径较小且焦深长，适合通讯领域长距离测量和准直。针对实际操作中球面波光束入射时很可能与圆锥透镜的中心轴线发生偏移或倾斜，使衍射光场发生变化，着重研究圆锥透镜对偏轴球面波光束的衍射模式，并通过衍射理论和稳相法分析，研究其径向衍射光场的分布特性。使用半径为15mm，底角为1°的圆锥透镜进行计算机仿真和实验，最后将实验结果与理论分析和仿真结果相比较，证明球面波的曲率半径和出射光束的传输距离越小，偏轴对衍射模式的影响越小。该研究结果表明：在激光通讯等长距离通信中，使用曲率半径小的球面波光束代替平面波入射圆锥透镜，不仅可以扩展焦深，还可以降低偏轴对测量的影响。     

Optimization of a long pulse dye laser

The development of the thermal lens in a 60 μs long pulse dye laser is described. The use of a resonator with a spherical mirror permits to obtain reliable output pulses at a conversion efficiency of 0.3%.     

Full correction of spherical aberration for the lens with a spherical refractive index distribution

The potential to create a lens with a spherical gradient of refractive index, transforming a divergent entrance homocentric beam into a convergent output homocentric beam, is shown. The lens has the first and the second spherical surfaces. The second surface is isoindicial. The distribution law of the refraction index for the lens material, and the basic parameters of the lens are obtained in analytical form.     

光束自聚焦的矢量理论研究

基于矢量非傍轴非线性Schr-dinger方程,利用调制理论研究了光束的自聚焦特性,比较了非零电场散度项和非傍轴项在消除自聚焦崩塌方面的贡献。结果表明,引入两项之一都可使光束聚焦到一有限宽度后开始散焦,然后又自聚焦,如此作聚焦-散焦的周期性循环。但是,在光束自聚焦点附近,非零电场散度项的作用要强于非傍轴项。     

Binary space-integrating acousto-optic processor for vector-matrix multiplication

A binary acousto-optic processor for high accuracy vector-matrix multiplication is described. The processor's operation is based on the formation of inner products. Digitsl products are formed via analog convolution. A spherical lens is used to form both the necessary convolution integral as well as the summation of different digital products. The resulting system requires a single detector for inner product detection. The processor's performance and characteristics are discussed along with possible solutions for performance improvements.