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。     

正支共焦非稳腔的离焦像差特性

 正支共焦非稳腔在出光过程中易受环境扰动而造成腔长失调，易受热积累影响而使腔镜变形，从而使输出光束产生离焦像差和部分其它像差。为了实现对离焦像差的校正，针对不同的产生原因，提出了2种离焦像差特性分析方法：一为腔镜相对位置失调引起的离焦像差特性理论分析方法，它是另一种分析方法的基础；二为腔镜变形引起的等效腔长变化导致的离焦像差特性分析方法，它是实际激光器中的主要分析方法。得到了离焦像差与腔长的特性关系和离焦像差与腔镜变形量之间的特性关系。研究表明：腔长改变和腔镜变形对离焦像差的影响本质是一样的，都是改变了谐振腔的共焦点位置；腔长改变或腔镜矢高变化与离焦像差都成近似的线性关系。实验验证了离焦像差特性分析方法的有效性，最后指出离焦像差特性可作为激光器中离焦像差动态补偿的有效依据。     

Aberrations of plane-symmetric multi-element optical systems

Based on a recently developed aberration theory of plane-symmetric grating systems, its aberration coefficients are firstly extended to be applicable to the plane-symmetric refractive optical surface. To justify the linear approximation of aperture ray in a multi-element system, the ray aberrations of double-element systems with the third-order accuracy of aperture ray are derived and expressed as the form of wave aberrations. The numerical comparisons are then made between the ray tracing, the aberration expressions with the linear and with third-order accuracy of the aperture ray. Moreover, the modifications of the wave and ray aberrations are discussed in the paper when the position of the principal ray changes.     

大口径平面镜的计算机辅助瑞奇-康芒检验

 在瑞奇-康芒检测中,被检平面本身所固有的像散和大曲率在被检系统波像差数据中都表现为像散。由于被检平面处于发散光路中,这就使得平面面形与系统波像差之间的关系(即影响函数)变得十分复杂,推导起来十分困难,只能进行定性或半定量检测。文中介绍了如何通过计算机光线追迹模拟瑞奇-康芒检验,在两个瑞奇角下得到两组影响函数,以此建立过定方程组,由干涉仪检测得到的两个不同瑞奇角下的系统波像差,通过最小二乘法解过定方程组,拟合得到被检平面镜的面形误差;实现了大口径平面镜的定量检测,并以平面镜直接检验的面形误差作为对比,检验结果的一致验证了该方法的准确性与可行性。     

阴极透镜象差的变分理论

本文运用变分原理研究了电磁复合聚焦阴极透镜的象差理论,导出了在任意象平面中象差系数的普遍公式。它们可以用Glaser导出的象差系数的线性组合来表示。这就表明了宽束与细束电子光学系统的象差都可以用统一的变分方法处理,并建立了两者之间的联系,本文采用矢量形式描写阴极透镜的近轴轨迹,并采用矩阵形式描写象差。本文所得的象差系数较之文献上已有结果形式更为简洁且适用于计算机计算。本文考虑了阴极面上磁场和横向电场不为零的情况,因而所得结果较为普遍。 关键词：     

荷电粒子光柱成象系统中空间电荷象差之解析计算

本文首先讨论粒子光学柱成象系统中空间电荷象差的概念,然后提出用梯形束元作为同时计算空间电荷象差、几何象差、色差和衍射象差的统一模型;最后,在此模型基础上推导并提出了所有计算成象系统中空间电荷象差的解析表达式.     

高斯光束的象差平衡

本文从有象差时的衍射积分出发,导出高斯光束中心点亮度与波象差方差的关系,依据斯特列尔判据,采用解线性方程组的方法讨论了高斯光束球差及轴外象差的最佳校正形式,并以表格方式给出了最佳校正形式.     

高级象差理论

本文的主要目的在以近似方法讨论高级象差特性。首先由对称性讨论了二级象差的独立象差数,近似讨论了象差的几何意义,再由坐标变换的观点导出了光栏移动时象差变化的规律。由Fermat原理和同一光线可看作是各不同点发出的观点导出了物体移动时象差变化的规律。由于运用Fermat原理,所得的结果实际上是略去初级象差影响后的近似结果,因此表示式相当简单。然后我们把象差产生的原因分为二类。其一称作是本徵的,是入射光束无象差时必然产生的象差,用象差看作球差的观点导出了它们的表示式,结果表明,高级球差和本徵轴外球差是象差产生的原因,并导出了各种象差同时产生的状况。象差的另一类称作是衍生的,它们是由入射光线原有象差引起的初级象差差异,由初级象差理论即可得出它们的表示式。这一些高级象差的规律和近似表示可作为评断象差产生原因的半定量依据。最后,用Fermat原理讨论了高级色差问题,并说明Fermat原理之所以可在高级象差理论中应用的理由及不致误差过大的应用范围。     

Aberration correction and its automatic control in scanning electron microscopes

An automatic aberration correction method has been implemented in scanning electron microscopes (SEM). Necessity of the automatic aberration correction is discussed. The procedure of the automatic aberration correction is explained in detail, where deconvolution techniques are used in order to extract probe information from SEM images. Due to the precise digitization and the usage of proper combinations of correction fields, linearity has been found between the amplitude of each aberration and the corresponding field strength. Experimental results are shown which demonstrate that the aberrations are corrected automatically by a linear feedback control method. After the automatic aberration correction, the image quality has been improved drastically.     

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。     

The study of the effects of higher-order aberrations on human contrast sensitivity with white-light retinal aerial image modulation (AIM)

The impact of higher-order aberrations on contrast sensitivity function (CSF) is calculated using individual white-light retinal aerial image modulation (AIM). Wavefront aberrations of 26 eyes are measured with Hartmann-Shack sensor, and the CSFs in natural light are acquired through a range of 2-48 c/deg. The white-light AIM is computed as the ratio of modulation transfer function (MTF) in white-light to CSF. Through manipulating the higher-order aberrations, the affected CSF is predicted by employing the white-light AIM. We find that coma aberration mainly influences CSF at higher spatial frequency and spherical aberration affects CSF in the whole spatial frequency range non-selectively. Additionally, it is spherical aberration rather than coma that impacts the CSF more substantially. Furthermore, the maximum value of area under CSF (AUCSF) is obtained without full correction of higher-order aberration, which indicates that there is compensatory mechanism among aberrations.     

Exact analytical theory of aberrations of centered optical systems

In the paper we present a new theory designed to overcome the deficiencies of the existing aberration theories. The main advantage is the theory’s capacity to perform analytical, direct, and accurate radius, and thickness calculations of aberration corrections for optical components and systems. Methodologically, we derive exact formulas for bilinear transformations from an object to an image space. Next, we introduce relative parameters in the matrix coefficients and by combining bilinear and matrix transformations we develop exact corrections on-axis aberrations and field aberrations such as distortion, astigmatism, and curvatures (including sagittal and tangential). The theory with an accuracy of 10^?8 mm (except for tangential and sagittal coma) allows precise radius and thickness calculation of components and systems for aberration corrections, sets exact coordinates of free-form surfaces, and enables the study of the surface and component capacities for aberration correction. The theory has supported the design of more than 10 different patented optical systems.     

On the chromatic aberration of magnetic lenses with a field distribution in the form of an inverse power low (B(z) ∝ z)

The chromatic aberration of magnetic lenses with the field distribution in the forms of inverse law have been studied by analytical and digital methods. These aberrations can be expressed in terms of Bessel function of fraction order. Analytical expressions for chromatic aberration coefficients of the spherical field model, which is useful for the study of single-pole magnetic lenses, are given.     

一种线性相位反演波前测量方法的原理和性能初步分析

对一种基于线性相位反演的新型波前测量方法的基本原理和性能进行了研究。事先对成像光学系统的自身像差进行定标并记录下定标图像。传感器工作时只需测量出有像差时的一幅远场图像与定标图像的差,就可以用线性矩阵相乘方法得到待测像差对应的泽尼克多项式系数。讨论了这种线性相位反演波前测量方法中确定泽尼克模式复原矩阵的方法。以大气湍流畸变波前像差的测量为例,对这种线性相位反演波前测量方法进行了数值仿真研究。结果表明,这种线性相位反演算法具有空间分辨力高、对小像差测量精度高的特点,但测量动态范围有限。这种线性相位反演波前传感器将适用于自适应光学闭环系统。     

Computational aberration correction for an arbitrary linear imaging system

We show that aberration corrections can be made in any arbitrary linear imaging system provided the aberrations are well characterized and at least one of these aberrations can be independently varied in a well-controlled manner. We derive a generalization of the Schr?dinger equation for wave propagation in aberration space assuming forward scattering. Transport equations in aberration space are derived. A general iterative algorithm which can retrieve the phase, and is robust in the presence of noise, is also derived. This is demonstrated using simulated data pertinent to electron microscopy, from a series of images with differing spherical aberration.     

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.     

The study of wavelength-dependent wavefront aberrations based on individual eye model

Theoretical calculations of the wavelength dependence of the ocular wavefront aberrations are performed with individual eye model. Individual eye model, based on the traditional Gullstrand-Le Grand eye model, has been established with measured individual cornea data, eyeball depth and wavefront aberrations. We analyze the wavelength-dependent wavefront aberrations at 12 different visible wavelengths (between 400 and 750 nm) for eight eyes. The change of defocus with wavelength (longitudinal chromatic aberration, LCA) is noticeable, and in good agreement with the results from references. In most cases, the primary spherical aberration changes significantly with wavelength. In comparison with the primary spherical aberration, the other higher-order wavefront aberrations have a smaller change with wavelength. These results have potential applications in those situations where defocus or higher-order wavefront aberrations information in arbitrary wavelength is required.     

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.     

界面反射偏振象差分析

在光学没计中,一般认为在同一光波面上,光束具有相同的振幅和偏振状态。事实上,光束经过许多光学元件后,偏振状态会发生变化,特别是入射角和光程的不同,会导致出射光波面上偏振分布不再均匀,形成偏振象差。本文主要就轴上物点发出的光束经过界面反射后的偏振象差方面进行了分析。     

Theory of paraxial lateral aberrations of electrostatic imaging electrostatic electron optics based on asymptotic solutions and its verification

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, and the general form of paraxial lateral aberration has not been studied theoretically.In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically on the basis of asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Through a bi-electrode electrostatic spherical concentric system model, two special solutions expressed by asymptotic solutions and accurate solutions in a bi-electrode electrostatic spherical concentric system have been deduced, and the paraxial lateral aberrations have been verified and tested, in which the aberration coefficients are solved by asymptotic solutions of paraxial equation. Result completely proves that the approach based on asymptotic solutions to solve the paraxial lateral aberrations are practicable and accurate enough. The paraxial chromatic aberration of magnification of third order and the paraxial chromatic aberration of third order have been firstly derived, and the Recknagel-Artimovich formula of paraxial chromatic aberration of second order which possess an greatest part in the whole paraxial lateral aberrations has been deduced and confirmed. A simple and clear form for expressing paraxial lateral aberrations of imaging electron optics is suggested for practical use. Results of the present paper will have theoretical value for aberration theory of imaging electron optics and practical significance for the design of image tubes.