Design of Plane-Symmetric Low <Emphasis Type="Italic">F</Emphasis>-number Reflective System Based on Perturbation Aberration Model

All-reflective optical systems have theoretically no chromatic aberration and are suitable for wide spectral application, but co-axial reflective systems are difficult to design as low F-number optical systems. In this paper, the aberration of plane-symmetric optical systems with low F-number is analyzed based on the wavefront derived from optical path length. Up to third-order aberrations are classified into three categories by their characteristics. The reduction method of the dominant aberration, astigmatism-like aberration, is proposed. In the method, the Gauss image plane is modeled by means of a simplified mirror surface with third-order approximation. Because the system is plane-symmetric, symmetric cross section and asymmetric cross section are modelled differently. The design example of a three-mirror system with F/2 is shown.     

Aberration theory of plane‐symmetric grating systems

Aberration theory of plane‐symmetric optical systems of mirror and grating has been developed based on the wavefront aberration method. A toroidal reference wavefront surface is used to define the wavefront aberration. Based on the ray geometry, the coordinate mapping relationships of the ray between the optical element and the incident and aberrated wavefronts are derived using a polynomial‐fit method; this enables the resultant coefficients of the wavefront and the transverse aberration to be kept to the fourth‐order accuracy of the aperture‐ray coordinates. By setting up the transfer equations of the field and aperture rays, the contribution to wavefront aberrations from each mirror and grating can be added to make the aberration calculation of multi‐element systems feasible. The theory is validated by the analytic formulae of the spot diagram.     

面对称光学系统的初级波像差理论研究

非旋转轴对称光学系统波像差理论的建立有利于理解旋转 轴对称光学系统的装调误差和离轴三反射光学系统等非旋转轴对称光学系统的选型设计. 本文利用旋转轴对称球面光学系统的全口径初级波像差理论推导了子孔径面对称光学系统的初级波像差分布公式, 证明了面对称光学系统中的节点像差理论, 即除球差外的所有初级像差的零值节点偏离视场中心, 而不再是视场的旋转对称函数; 并首次阐述了多零值节点初级非对称像差产生的根源和变化特性. 该理论可以有效指导非对称光学系统初始结构的选择和优化设计过程. 关键词： 面对称 像差 几何光学     

Design of unobscured reflective zoom system with three mirrors

A method for the design of an unobscured reflective zoom system with three mirrors is described. This method applies the vector aberration theory, which helps designers analyze third-order aberrations for optical systems with decentered and tilted surfaces. As the vector aberration theory presents the variation of third-order aberrations in asymmetric systems through analytic expressions, real ray tracing is unnecessary. Hence, the design with vector aberration theory is faster, and the analytic expressions are more comprehensive and intuitive. To demonstrate the practicability of the method, a design example is given, which shows that the presented method can guide designers achieve a good unobscured reflective zoom system with three mirrors.     

Third-order aberration analysis of an off-axial optical system

The aberration theory applied to co-axial optical systems is extended to off-axial systems, for which third-order aberration coefficients are considered. The derived aberrations are analyzed using three-dimensional ray bundles, spot diagrams, and image charts, and classified in relation to the system symmetry. This theory is very useful for optical designers, allowing them to clarify the relationship between the structures of off-axial optical systems and the corresponding off-axial aberrations.     

Extension of aberration theory of grating systems from one- to two-dimension extended source

The aberration theory of grating systems is extended from one-dimension to two-dimension extended source. In deriving the aberration formulae, the concept that pupil in the meridional plane is separate from the one in the sagittal plane is applied and the principal ray is determined by a linear equation. Using the Seidel aberration for reference, the aberrations are classified into seven types according to the geometrical characteristics. The numerical simulation of imaging of one model optical systems is made with the aberration formulae and exact ray tracing to examine the accuracy of the aberration formulae.     

X射线同轴全息术中像差的数字模拟

给出了Ｘ射线同轴全息中像差的数值模拟，分别研究了其三级波差和光线像差，用一个较为简便的方法计算出光线像差，给出了类似于光线追迹中的点列图，并由此相应地估计出像差对分辨率的限制，所有的计算都是基于一个典型的Ｘ射线激光全息实验听参数进行的，根据分析还讨论了减小像差的条件。     

光学系统的偏振像差分析

偏振像差是影响光学系统性能的重要因素之一,尤其对偏振有严格要求的光学系统来说更是如此。论述了偏振像差的理论和偏振光线追迹的方法,并对旋转对称光学系统、倾斜偏轴光学系统的偏振像差进行了分析,指出了薄膜设计对偏振像差所产生的重要影响。介绍了提高光学系统偏振精度的几个方法,包括尽可能的减小入射角、薄膜设计的优化和像差之间的相互平衡。     

Non-approximate method for designing annular field of two-mirror concentric system

Annular field aberrations of a three-reflection concentric system,which are composed of two spherical mirrors,are analyzed.An annular field with a high level of aberration correction exists near the position where the principal ray is perpendicular to the object-image plane.Aberrations are determined by the object height and aperture angle.In this letter,the general expression of the system aberration is derived using the geometric method,and the non-approximate design method is proposed to calculate the radii of the annular fields that have minimum aberrations under different aperture angles.The closer to 0.5（the ratio of the radius of convex mirror to the radius of concave mirror）is,the smaller the system aberration is.The examples analyzed by LABVIEW indicate that the annular field designed by the proposed method has the smallest aberration in a given system.     

Third-order aberration analysis of tilted-pupil optical systems

The aberration field of an optical system with a tilted pupil is explored through expanding the vector expressions of the third-order wavefront aberrations. First, the vector forms of the wavefront aberrations are modified to obtain the aberration expressions with the pupil tilted; full field displays of coma and astigmatism in this situation are given. Then, the third-order aberration formulas with the pupil decentered and tilted simultaneously are derived and discussed. Finally, an example is taken to certify the validity of aberration distribution properties.     

Spherical aberration from trajectories in real and hard-edge solenoid fields

For analytical, real and hard-edge solenoidal axial magnetic fields, the low-energy electron trajectories are obtained using the third-order paraxial ray equation. Using the particle trajectories, it is shown that the spherical aberration in the hard-edge model is high and it increases monotonously with hard edginess, although the focal length converges, in agreement with a recent field and spherical aberration model. The model paved the way for a hard-edge approximation that gives correct focal length and spherical aberration, which is verified here by the trajectory method. In essence, we show that exact hard-edge fields give infinite spherical aberrations.     

双贴合无光焦度校正板在双球面镜次镜后的系统的像差特性研究

讨论了双贴合无光焦度校正板放在次镜后的双反射球面系统.根据像差理论分析了消像差的条件，研究了主镜的相对孔径变化、校正板在次镜后的位置变化以及无光焦度校正板的正负透镜的不同组合形式对系统高级残余像差的影响.结果表明：当主镜的相对孔径增加或校正板靠近次镜时，系统的残余像差增加；无论校正板的第一个透镜是正透镜还是负透镜，系统在某一光焦度处残余像差最小，并且靠近次镜的透镜最好采用负透镜.     

衍射现象对高精度偏转器设计的影响

基于波动光学理论,计算了由衍射、球差和色差三者共同作用的电子束斑电流分布,得到了电子束斑的精确信息和电子束曝光机的轴上分辨率。针对某一个具体系统的不同电子束孔径角,以偏转器的位置和相互转角为变量进行了偏转系统的优化设计;综合考虑了电子光学系统的衍射、轴上像差和偏转像差三者与光阑孔径角的不同关系。得到了光柱体的最佳总体性能,保证了电子束曝光机的高分辨率和均匀性。     

Ronchi线条法检验大非球面镜的理论计算

由光线追迹和三级像差理论计算大抛物面的Ｒｏｎｃｈｉ弯线条。分析这两种理论计算方法的结果和偏差，其偏差值随镜子的口径增大而增加，用所计算的结果制作的Ｒｏｎｃｈｉ弯线条检验可移动式平行光管的φ７００ｍｍ口径的抛物面主镜。给出检验结果。     

Aberrations in fractional-Talbot images of periodic binary gratings

We discuss the ray-optical aberrations which appear in the fractional-Talbot image of a periodic binary grating with coherent illumination. First we examine the complex amplitude of an aberration-free imaging field at a fractional-Talbot plane. We then trace the path of a diffracted ray of specific order which contributes to the fractional-Talbot imaging. Next we formulate the focus-shift and third-order aberrations which arise from a focusing error and a fourth-order approximation of the path length, respectively. We then evaluate the amplitude and phase of an aberrated imaging field that are represented in terms of aberration functions. When the grating period decreases to approach the optical wavelength, the aberrations of lower-order rays are shown to be more influential on the fractional-Talbot imaging field than those of higher-order rays. The theory of aberration discussed here could be very useful in evaluating the fractional-Talbot image of a periodic binary grating.     

偏心和倾斜光学系统的像差特性

运用一种新的分析偏心和倾斜光学系统初级像差特性的方法—矢量像差理论,分析了具有较大交叉倾斜角的平行平板光学系统和具有较大倾斜角的光楔光学系统的像差特性.通过ZEMAX光学设计软件像差分析功能中的垂轴像差曲线、场曲曲线和点列图加以比较,两者非常吻合,证明该理论可以对具有较大倾斜元件的非共轴光学系统设计起指导作用.     

Geometrical aberrations of self-imaged line gratings

We analyze the properties of a self-imaging system from the point of view of aberration theory. We examine analytically and numerically the geometrical aberrations that are observed in the self-image of a parallel-line grating. We first derive the raytracing equations for determining the optical path of a self-imaging ray with the order of diffraction l. We then obtain the third- and fifth-order contributions to ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of an actual ray. We show that the overall ray aberrations are entirely undercorrected. The ray aberrations approach zero as the ratio of the grating constant to the wavelength of light becomes large enough. In a case of unit magnification, no curvatures are observed in the self-imaged lines. If the magnification is bigger than unity, the light rays passing through the point in a positive or negative domain of the aperture variable contribute to the formation of the curved images. The image evaluation technique discussed here can be useful in the various applications related to the self-image formation of a parallel-line grating and it can also provide insight into the self-imaging of other periodic objects.     

投影光学系统中的偏振像差分析

当光束斜入射时,光学薄膜存在一定的偏振效应。在飞利浦棱镜系统中,当一定大小孔径角的照明光束斜入射到分色合色薄膜后,S偏振分量和P偏振分量存在一定的相位差,使得线偏振光变成椭圆偏振光。利用琼斯矩阵偏振光线追迹的方法,分析了投影光学系统中由于两偏振分量相位差引起的偏振像差,以及它与暗态泄漏光强和系统衬比度的关系。得出了系统出瞳面上的光波偏振特性,以及在不同大小孔径角的照明光束入射下偏振像差的变化。分析了膜厚监控误差对光学系统偏振像差的影响,发现膜厚监控误差对偏振像差和系统衬比度有很大的影响。所使用的分析方法可以应用于其他大口径光学系统。     

基于波像差函数建立大口径施密特校正板方程

施密特光学系统由施密特校正板和球面反射镜组成,校正板设置在球面反射镜的球心处,系统的焦点不一定和反射镜的焦点重合。为了得到精确的校正板面形初始结构参数,基于波像差函数建立了带有离焦量的大口径施密特校正板的数学模型,同时校正了系统的三级和五级球差。利用光学设计软件对校正板口径为1000mm、主镜的曲率半径为2000mm、F数为1的系统进行了设计和分析,来验证校正板面形数学模型的正确性。结果显示此校正板的数学模型与优化后结果吻合得较好,校正板面形初始结构参数的精度得到了极大的提高,这为大口径、大相对孔径的施密特光学系统的设计提供了理论基础。     

Φ0300激光扩束器光学系统设计

从三级像差理论出发，分析伽里略（Galilean）和开卜勒（Keplerian）两种类型扩束器的轴外像差没有得到很好校正的原因.通过合理的光路分析，设计出一种轴上和轴外像差都得到很好校正、大口径大相对孔径、视场可增大的、光学性能优于伽里略和开卜勒扩束器的新型扩束器.并给出了物镜通光口径为300 mm、物镜焦距为800 mm、视场为4 mrad、放大倍率为30倍、主工作波长为0.6328 μm的非球面扩束器光学系统结构参量，且进行了像质评价.调整此扩束器目镜组中各镜片的间隔以及物镜和目镜的间隔可以使该扩束器在三个波长使用.