李代数在磁偏转系统三级像差计算中的应用

提出了电子光学偏转像差的李代数理论，将这种新型数学工具的应用领域从带电粒子束的聚焦传输系统推广到扫描偏转系统，推导出了磁偏转高斯光学性质主全中三级正则像差（包括在任意观察平面的正则位置像差和正则动量像差），所导出的结果与传统的逐次近似像差理论相同，为将李代数方法用于扫描探针系统的高阶像差的分析计算奠定了理论基础。     

静电偏转器高阶像差的三维微分代数计算

本文研究了静电偏转器高阶像差在三维空间的微分代数计算。利用有限元方法计算了静电偏转器电场的三维分布,通过三维数据拟合方法构造电磁场分布的三维局部解析式,将电场量转化为微分代数扩展数,利用微分代数方法分析计算偏转系统直至五阶的像差。验证了数据拟合方法的精度和可靠性,结果表明该方法具有非常高的精度,完全可以满足工程设计分析的需要。编写了相关的计算软件,具体分析计算了一个八瓣电极偏转器直至五阶的几何像差。     

电子束曝光机的偏转系统

电子束曝光机的偏转系统控制电子束偏转扫描。像差低、偏转灵敏度高、扫描速度快是它的基本要求。对各种偏转器、偏转方式进行分析、比较,从偏转器空间场的数值计算方法、偏转系统的优化、像差校正、偏转器制作工艺、电气参数等方面阐述设计过程和工程实现上一些值得注意的问题。综合考虑偏转器和偏放电路的设计可以得到最优性能的系统。     

基于Trilemma常数调整的偏转像差校正

从多极场像差校正理论出发,根据六极场对三级偏转像差的影响,提出了基于Ｔｒｉｌｅｍｍａ常数调整的偏转像差校正方法,这种方法使偏转像差的校正更方便,更直观,同时可以应用于大偏转角偏转像差的校正。     

基于Trilemma常数调整的偏转像差校正

从多极场像差校正理论出发，根据六极场对三级偏转像差的影响，提出了基于Ｔｒｉｌｅｒｍｍａ常数调整的偏转像差校正方法，这种方法使偏转像差的校正更方便、更直观，同时可以应用于大偏转角偏转像差的校正。     

矩形偏转系统的近似多极场模型

提出了可以应用于矩形偏转系统的近似多极场模型,并给出了应用该模型进行偏转系统优化设计的方法,计算比较了旋转对称多极场模型和矩形近似多极场模型的磁场分布,应用近似多极场模型对矩形偏转系统的偏转像差进行了优化计算,得到了较好的像差校正效果。     

矩形偏转系统的近似多极场模型

提出了可以应用于矩形偏转系统的近似多极场模型,并给出了应用该模型进行偏转系统优化设计的方法,计算比较了旋转对称多极场模型和矩形近似多极场模型的磁场分布,应用近似多极场模型对矩形偏转系统的偏转像差进行了优化计算,得到了较好的像差校正效果。     

偏转像差中束夹角α的高次项研究

通过计算超大偏转角下二极场的偏转像差，对偏转像差中α高次项进行了分析，得出了超大偏转角下α高次项不应忽略的结论。并应用多极场理论，研究了超大偏转角下十四极场对α高次项的校正作用。提出了在超大偏转角下偏转像差的多极场校正方法。     

偏转磁场中HZ分量对偏转像差的影响

对不同张角的一组偏转线圈的Ｈ_z分量对偏转像差的影响进行了计算分析。结果表明,在应用偏转磁场的解析式进行偏转像差分析时,偏转磁场的Ｈ_z分量是必须考虑的,这个分量对偏转像差和Ｔｒｉｌｅｍｍａ常数、偏转像差的校正和优化场分布产生十分大的影响。     

偏转像差中束夹角α的高次项研究

通过超大偏转角下二极场的偏转像差，对偏转像差中α高次项进行了分析，得出了超大偏转角下α高次项不应忽略的结论。并应用多极场理论，研究了超大偏转角下十四极场对α高次项的校下作用。提出了在超大偏角下偏转像差的多极场校正方法。     

The Use of Diffraction-based Criteria of Image Quality in Automatic Optical Design

In automatic optical design it is customary to minimize the mean square value of the aberrations along selected rays. This leads in different cases to different ‘best forms of correction’ of primary and higher-order aberration terms. Image evaluation theory, on the other hand, shows that it is the variances of the wave-aberration and of an aberration difference function which determine the tolerances on aberrations, and the best forms of correction, according to the Strehl intensity ratio and transfer function theory respectively. The consequences of using different criteria of image quality are investigated, and it is shown that significantly poorer image quality can result from using more ‘ad hoc’ criteria instead of those based on diffraction theory. It is then shown how the use of canonical variables makes possible the simple use of the appropriate variances as diffraction-based criteria of image quality for optical systems. To optimise the system using least squares techniques then requires new forms of the normal equations. This procedure is described, it being shown that the method of damped least squares, and the Lagrange method of undetermined multipliers, may still be applied to the problem.     

Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry

Many authors, dating back to at least the 1950s, have presented mathematical expansions of the wave-front aberration function for optical systems without symmetry, typically based on limiting assumptions and simplifications, with some of the most recent work being done by Howard and Stone [Appl. Opt. 39, 3232 (2000)]. This paper reveals that in fact there are no new aberrations in imaging optical systems with near-circular aperture stops but otherwise without symmetry. What does occur is that the field dependence of an aberration often changes when symmetry is abandoned. Each aberration type develops a characteristic field behavior in a system without symmetry. Specifically, for example, astigmatism, develops a binodal field dependence; e.g., there are typically two points in the field with zero astigmatism, and typically neither point is on axis. This construct, nodal aberration theory, for understanding the aberrations in systems without symmetry becomes a direct extension of an optical designer's knowledge base. Through the use of real ray-based analysis methods, such as Zernike coefficients, it is possible to understand completely the aberrations of optical systems without symmetry in terms of rotationally symmetric aberration theory with the simple addition of the concept of field nodes.     

复合静电-磁浸没透镜的宽束曲轴聚焦性质及像差理论

研究了新型的复合静电 磁浸没透镜的曲光轴高斯电子光学性质及像差特性。应用宽束曲轴理论 ,导出了三维局部正交坐标系中的电子运动的中心轨迹方程和曲光轴的近轴轨迹方程 ;利用数学软件Mathematica推导出了复合静电 磁浸没透镜全部曲轴二级像差系数。作为实例 ,文中针对轴上磁场和电场具有某种解析表达式的旋转对称的静电 磁浸没透镜系数 ,计算了它的曲轴高斯聚焦特性和二级像差 ,并给出了二级像差分布图形     

Modelling the primary chromatic aberrations and secondary spectrum of conceptual thick-lens modules

A virtual thick-lens module comprising three air-spaced thin lenses is proposed, which is able to have the identical primary chromatic aberrations and secondary spectrum for just real thick lenses, or groups or components within any thick lens, hence it is capable of studying the chromatic aberration behaviours of conceptual lenses without their detailed structures. The three thin-lens powers are first evaluated to match the required first-order quantities. Then the chromatic aberration coefficients of each thin lens are solved to satisfy the given system aberrations associated with the reference optical configuration. When the incident rays are changed, each thin lens will induce new chromatic aberrations according to the thin-lens formulae. The new system aberrations are obtained by adding those individual thin-lens aberrations together. The module can be directly applied to finite and infinite conjugates, focal and afocal lenses, as well as telecentric and non-telecentric lenses. Evaluations of the chromatic aberration variations of three different types of lenses are demonstrated.     

自适应光学系统中变形镜和波前传感器共轭位置要求的分析

通过对几何光学和物理光学模型的数值计算,分析了自适应光学系统中小像差畸变波前在空间自由传播时自身的变化情况,进而给出了系统中对变形镜和波前探测器与被校正瞳面之间共轭位置关系的要求和允许范围.结果表明,波前自由传播时的变化程度决定于像差自身的类型和大小、光束的口径以及传播的距离,大口径小像差波前近距离传播时波前变化误差很小.一般来说,变形镜和波前传感器偏离被校正瞳面共轭位置距离满足菲涅尔数大于1000时,对系统校正效果的影响可以忽略.实际应用中,应该根据校正对象的特征来具体计算波前误差随传播距离的变化,从而设计波前传感器和变形镜的位置,以及选择使用4F光学系统.本文的分析可以为自适应光学系统的整体光路设计提供一定理论参考.     

Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils

The classical aberrations of an anamorphic optical imaging system, representing the terms of a power-series expansion of its aberration function, are separable in the Cartesian coordinates of a point on its pupil. We discuss the balancing of a classical aberration of a certain order with one or more such aberrations of lower order to minimize its variance across a rectangular pupil of such a system. We show that the balanced aberrations are the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point. The compound Legendre polynomials are orthogonal across a rectangular pupil and, like the classical aberrations, are inherently separable in the Cartesian coordinates of the pupil point. They are different from the balanced aberrations and the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil.     

光盘用光学头物镜性能的综合评估

论述了采用波象差均方根、点扩展函数、光学传递函数对高次旋转对称非球面光学头物镜性能进行综合评估的方法。作者在正则坐标理论基础〔１〕上编制了光学头物镜性能综合评估软件。给出了评估实例。     

Aberrations of anamorphic optical systems III: the primary aberration theory for toroidal anamorphic systems

We apply a new method for optical aberration derivation to anamorphic systems made from toroidal surfaces and obtain a complete set of primary aberration coefficients. This set is written in a form similar to the well-known Seidel aberrations for rotationally symmetrical optical systems and includes first-order quantities only, thus it can be easily applied to anamorphic lens design practice. By tracing four nonskew paraxial marginal and chief rays, the 16 anamorphic primary aberration coefficients can be easily calculated.     

Optimization method for ultra-wide-angle and panoramic optical systems

To an ultra-wide-angle and panoramic optical system, the aberrations of point object at any field angle are separated into two types: the aperture-ray aberrations of off-axis point object and the chief-ray aberrations. A simple form of the triangular formulae of tracing an oblique-incidence ray is derived to calculate the chief-ray parameters and their aberrations; moreover, the aperture-ray aberrations of an off-axis point object are analyzed with the plane-symmetric aberration theory. Based on the two types of aberrations, we present a merit function for ultra-wide-angle and panoramic optical systems; the optimization program with the differential-evolution algorithm is then developed. To validate the optimization method we finally optimize a fish-eye lens and a catadioptric omnidirectional imaging system.