球面端面的锥形梯度折射率透镜的近轴成像特性

本文根据光线在球面上的折射公式及光线微分方程,研究了光线经两端面为球面的锥形梯度折射率透镜的传播和变换,基于光线传递ABCD矩阵,提出了球面端面的锥形梯度折射率透镜的一种等效光学系统.文中给出了该透镜的主平面、焦平面和焦距计算公式,以及近轴成像高斯公式.当锥度为零时即得到球面端面的柱形或径向梯度折射率透镜的相应结果.     

薄透镜反射成像研究

从薄透镜反射成像的实验现象出发，运用光学系统中变换矩阵的有关理论，研究了薄透镜的反射成像规律，并对双凸透镜及平凸透镜的反射成像进行了定量分析。     

Cивухин的“等效”薄透镜并不等效

本文根据等效光学系统理论和光心的概念，指出只有在一定条件下，两共轴薄透镜系统才可以用一个等效薄透镜来代替，使对任何物所成的象的大小和位置都完全相同．     

薄透镜组的光心

根据等效光学系统理论和光心的概念及其性质，讨论薄透镜组的光心     

基于望远镜原理测量薄透镜焦距

当标准凸透镜与待测薄透镜(凸透镜和凹透镜)的焦点重合时会形成一个典型的望远系统。根据望远镜成像原理可知平行光入射时出射光线为平行光,利用这一特殊成像性质可以快速测定薄透镜的焦距。此实验方法原理简单、操作方便是一种实用的薄透镜焦距测量方法。     

旋转抛物透镜的ABCD矩阵

通过傍轴近似及相位匹配技术,推导得到了旋转抛物透镜的反射矩阵及其相应的折射矩阵.利用推导出的反射、折射矩阵,得到了入射光束经旋转抛物透镜作矩阵变换后,其光斑及光波波前曲率半径的变换关系式.为设计具有旋转抛物透镜的特殊光学系统提供了便利.     

光学系统实现热补偿的通用条件

运用光学系统的近轴成像公式，推导出微分形式的物面位于任意位置时热补偿的通用条件，包括薄单透镜、密接薄透镜组和分离薄透镜组等不同情况。推导过程中假设物面位置不随温度发生变化，并且忽略分离薄透镜组中各组分上光线入射高度随温度的变化。利用推导的条件建立了像距的归一化温度变化率与各透镜光热膨胀系数之间的关系，指出所得到的条件具有更加普遍的意义，能够指导机械和伺服控制系统的工程设计，并且在物面位于无穷远时与目前普遍采用的热补偿条件相吻合，即光学系统的光热膨胀系数等于壳体的热膨胀系数。     

无限薄透镜组的基本参数

斯留莎列夫研究了在Ⅲ级象差范围内,利用光学系统薄透镜模型计算光学系统的理论,变量分离法在这种理论中占有重要位置,并且运用所谓基本参数P、W、π只与光学系统的内部原件有关。如果透镜焦距为正,确定无限薄透镜组的基本参数就用于物体处于无穷大时,并     

光学透镜边缘杂散光的消除

<正> 一、光学透镜边缘杂散光在现代精密光学仪器制造工业中,要想进一步提高各种光学仪器的成象质量,就必须考虑光学系统的杂散光。然而,光学透镜边缘毛面所产生的杂散光是一个很特殊的问题。国内对此常常不够重视,国外则十分注意这一问题。大家知道,一台光学仪器在成象的光学系统中,形成物体的实象时除了成象光线外,还有非成象光线在象面上扩散,这些非成象光线(即杂散光)非常有害。其中很大一部分来自光学透镜边缘毛面,因为光学透镜边缘毛面是用磨料经机械加工形成的一个粗糙表面,当不同波长的光线经过光学仪器的透镜系统时,就会在光学透镜组的毛面发生反射、散射,形成所谓二次和高次杂散光,透镜数目越多,杂散光量也越大,致使象质变坏。如果散杂光严重到足够程度的话,将使光学仪器的鉴别率降低,以致不能有效观察,从而降低了仪器使用效能。有时在实际检验和测量透镜质量时也会     

部分偏振高斯－谢尔模光束在准直和失调光学系统中的传输

利用张量方法导出了部分偏振高斯－谢尔模光束在准直和失调光学系统中的相干－偏振矩阵的传输公式，并以经过失调薄透镜为例，详细讨论了部分偏振GSM光束的传输特性。导出的公式提供了一个研究部分偏振GSM光束在准直和失调光学系统中传输的简便方法。     

一维大气边界层光学折射率结构常数数值模式的实验检验

提出了一种大气光学折射率结构常数的数值模式。一次输入日期、时间、经纬度、温度、湿度、风速、粗糙度、土壤参数，云量等相关参数，可得到24h内的温度、湿度、风场、折射率结构常数等量。通过与实测对比表明，无论是月平均折射率结构常数还是某天的折射率结构常数，模式计算与实测数据都符合得很好。模式计算的向下总辐射通量与实测数据基本一致。     

Alternative representation of the linear canonical integral transform

Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulting decomposition of the entire first-order optical system then shows a physically attractive representation of the linear canonical integral transformation, which, in contrast to Collins integral, is valid for any ray transformation matrix.     

A novel ray refraction matrix for curved interface

A problem in fundamental 2 × 2 ray matrix for refraction at curved interface proposed by A. E. Siegman was found out and a novel one was derived in this paper. An experiment is introduced in detail to verify the reasonability of the novel ray matrix. Using the novel 2 × 2 ray matrix, augmented 5 × 5 ray matrix of refraction at misaligned curved interface between media of different refractive indices was deduced. With the refraction matrix, it is easy to characterize the effect of an astigmatic thick lens. The augmented ray matrix approach was applied to model and estimate the performance of an optical alignment system. Utilizing these matrices, one can readily design and evaluate optical systems, where contain astigmatic elements such as tilted spherical or cylindrical lenses, mirrors and so on. These results are also useful for cavity design, alignment, ray tracing and beam position control in 3D optical systems.     

The representation of waist-to-waist transformation of Gaussian beams by the scaled fractional Fourier transform

The beam waist-to-waist transformation of Gaussian beams between input and output reference planes described by the scaled fractional Fourier transform is analyzed in this paper. We obtain the transfer matrix of ABCD optical system that corresponds to the scaled fractional Fourier transform. The results show that the beam waist-to-waist transformation of Gaussian beams can be described by the scaled fractional Fourier transform when the ABCD optical system has a suitable transfer matrix. The relationship between the input and output waist planes and some particular cases when a Gaussian beam passes through a thin lens is also discussed.     

Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

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Wigner Transforms and Fractional Fourier Transforms of the First Order Optical Systems

Based on the Collins formula, the relationship between the coordinate transform matrix (WCTM) of the Wigner distribution function (WDF) and the ray transfer matrix (RTM) of an arbitrary first-order optical system has been derived. By using this relation and the definition of fractional Fourier transform (FRT) in terms of WDF rotation, it is concluded that an arbitrary first-order optical system can be generally decomposed into a thin lens and a FRT sub-system whose order is not unique and depends on two concrete decomposing operations on the system. And when the system is reciprocally symmetric, a FRT can be implemented by it. In addition, the composition, that is also the decomposition condition of the complicated FRT optical system by cascading a series of FRT subsystems has also been derived by using the operations of RTM.     

Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators

The propagation of a non-monochromatic (polychromatic) TEM₀₀ Gaussian beam in vacuum, its passage through a thin plate and its transformation by a thin lens are studied in the case of a non-dispersive laser resonator. The basic assumptions of the model are as follows: optical fields are stationary and plane-polarized, the paraxial wave equation is valid, an equivalent non-dispersive hemiconfocal resonator represents the lasing medium and its stable resonator, the laser emits in a single mode. It is also assumed that the plate and the lens have large transverse dimensions. Mathematical expressions, for beam radius, divergence, radius of curvature and beam parameter product, are obtained. A beam quality factor for polychromatic Gaussian beams is defined and its value calculated in each case of interest. It is proposed to simulate a dispersive laser resonator by a non-dispersive resonator complemented with a plate and/or a thin lens.     

运用阿贝成像原理进行平面密铺结构的频谱分析

运用阿贝成像原理分析了平面密铺结构的频谱.使用AutoCAD绘制密铺图样作为物,用透过液晶光阀的扩束激光作为物光,经F透镜变换后形成频谱和物像.当物面的精细度和其构成线段的分布规律发生改变时,频谱面上相应的频谱也发生变化.通过分析形成密铺图形的结构基元和密铺图形本身的傅里叶变换之间的关系,确定当密铺图形的结构基元尺度介于可见图形和光栅网格之间时频谱的结构特征及此特征的可能应用.     

Orthonormal mode sets for the two-dimensional fractional Fourier transformation

A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied.