Analysis of Off-Axial Optical Systems (1)

We have established a new method of aberration analysis for off-axial optical systems which are generalized concepts of co-axial optical systems, by introducing two kinds of newly defined 4-element vectors and expanding these vectors with the help of tensor algebra. In this method, since aberration properties are represented in tensor form, we can easily formulate the aberration relations between different azimuths. We can then evaluate the azimuth dependence of aberration properties in greater detail by separating them into inherent optical properties parts, which are independent of azimuths, and the paraxial ray-tracing part, which includes the expression of the evaluation azimuth.     

Analysis of Off-Axial Optical Systems (2)

The extended 4×4 Gaussian bracket matrix Gij represents the lowest order quantity of “aberration coefficient tensor quantities” which are defined to as the peculiarity of off-axial optical systems and are independent of azimuths. We newly confirmed this extended 4×4 Gaussian bracket matrix of deflection (refraction or reflection), transmission and “twisting.” The result determined by use of a new representative method of asymmetrical surfaces and a method of paraxial expansion along the folded reference axis shows that the 4×4 Gaussian bracket matrix is the extended form of the 2x2 Gaussian bracket matrix which is used in co-axial rotational symmetric optical systems. Furthermore, we analyze and formalize the crossterm effects, which are the most serious problem in optical systems having multiple off-axial surfaces, using the concept of a chain of “optical systems divided into former and latter” and the vector-tensor analysis method. The result of this analysis reveals the structure of the cross-term effects and proves the usefulness of the vector-tensor analysis method in general image analysis.     

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.     

Propagation of elliptical cosh-Gaussian beams and off-axial elliptical cosh-Gaussian beams in apertured optical systems

Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical propagation expression for an elliptical cosh-Gaussian beam (EChGB) truncated by an elliptical aperture and passing through an axially nonsymmetrical optical system is obtained by use of vector integration. Furthermore, the analytical propagation expression for a truncated off-axial EChGB is derived as an application example. Some numerical simulations are given to illustrate the propagation properties of EChGBs and off-axial EChGBs passing through a free space with an elliptical aperture. PACS 41.85.Ew; 42.60.Jf; 42.25.Bs     

Analytical propagation expression of elliptical Gaussian beams through nonsymmetric systems with an elliptical aperture

A tensor form for describing approximately the elliptical aperture function is defined that can be expanded into a finite sum of complex Gaussian functions. An analytical propagation formula of elliptical Gaussian beams through nonsymmetric and paraxial optical systems with an elliptical aperture is obtained by using tensor method. A simple numerical example is given to illustrate for its applications.     

Off-axial elliptical Hermite-cosh-Gaussian beams

A new kind of light beams named the off-axial elliptical Hermite-cosh-Gaussian beams (EHChGBs) is introduced in this paper by use of tensor method. An analytical propagation expression for an off-axial EHChGB passing through an axially nonsymmetrical optical ABCD system is derived by use of vector integration. The derived formula can be easily reduced to the propagation formulas of off-axial elliptical cosh-Gaussian beams and elliptical Hermite-cosh-Gaussian beams. Some numerical simulations are illustrated for the propagation properties of off-axial EHChGBs passing through a free space and a focusing optical system, and further extensions are suggested.     

Optical implement of Hartley transform on elliptical Gaussian beams

The optical Hartley transform (HT) is expressed in matrix form. The analytical formula of an off-axial elliptical Gaussian beam passing through the HT system is obtained. Numerical examples show that the information about the displacement magnitude and direction of the source can be represented in the form of fringes at the output plane of the HT system.     

静电聚焦同心球系统验证电子光学成像系统的时间像差理论

关于动态电子光学成像系统的时间像差理论,计算时间像差系数有两种方法——τ变分法和直接积分法.它们的差别在于：τ变分法计算二级几何时间像差系数必须求解微分方程,而直接积分法仅需进行积分运算.采用静电同心球系统的理想模型对这两种方法的正确 性进行了检验.结果表明：这两种方法求解电子光学成像系统的时间像差系数的结果完全一致,所求得的时间色差系数与理想模型的解析解完全相同,从而证明两种方法是等价并且正确的.通过验证表明,直接积分法的计算更为简便,适于实际系统的计算与设计. 关键词： 阴极透镜 电子光学成像系统 动态电子光学 时间像差理论     

Chromatic aberrations of thin refractive variable-focus lens

We present an approach to an analysis of the third order chromatic aberrations of thin refractive fluid lenses with a variable focal length. A detailed theoretical analysis is performed for a simple fluidic variable-focus lens and formulas are derived for an optical design of such lenses. Aberration coefficients of the third order of the variable-focus lens can be completely characterized by three parameters which depend only on refractive indices of fluids forming the variable-focus lens. Formulas were derived for the change of the third-order aberration coefficients with the wavelength. Calculations are provided for Varioptic lens Arctic-416.     

Propagation of off-axial cosine-Gaussian beams passing through an apertured and misaligned optical system

A closed-form expression for the one-dimensional off-axial cosine-Gaussian beams passing through an apertured and misaligned paraxially ABCD optical system is derived. As special cases, the corresponding closed-forms for the off-axial or non off-axial cosine-Gaussian beams passing through apertured or unapertured and misaligned or aligned optical systems are also given. The obtained results could be straightforward to the two-dimensional case or sine-Gaussian beams.     

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.     

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.     

基于二元光学的红外成像光谱仪离轴系统设计

对Lyons采用二元光学元件的红外成像光谱仪的设计理论进行了分析，为消除其二元光学元件作为透射式成像元件导致的焦距随波长的变化而变化的缺陷.提出将离轴三反射镜系统与具有二元光学透镜的变焦距系统相结合的新技术方案，并从军事目标的红外热探测的基本要求出发，给出了具体的设计实例.设计结果表明，系统具有设计精巧、结构简单、光能接收率高、消像差特性好、对材料的要求低以及满意的红外焦平面凝视阵列探测器的配准精度和探测精度.     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：     

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。     

基于近红外光谱的人眼像差校正系统中变形镜性能对比研究

对比分析了基于近红外光谱的人眼像差校正系统中两种微机械薄膜变形镜(OKO37单元和BMC140单元)的结构特征和空间特性,着重对变形镜的影响函数进行了主成分研究,建立了变形镜电压控制模型,并通过调整参数d确定变形镜最优控制模式。最后对Zernike单位模式波前像差和Thibos模式人眼波前像差进行拟合仿真实验,结果表明BMC140单元变形镜对Zernike各阶模式的拟合能力均为OKO37单元变形镜的2倍以上。对RMS均值为0.683λ(λ=0.785 μm)的Thibos模式人眼像差,BMC变形镜校正后残余像差RMS值为0.063λ,达到了光学系统的衍射极限(λ/14)。而OKO变形镜由于受相邻电极交连值大、电极分布密度小等因素的影响,其校正能力不及BMC变形镜,残余像差RMS值为0.168λ。本方法也可用于其他种类变形镜的性能评估。     

光学系统的低对比分辨本领和象差的公差

具有大象差的光学系统象差公差问题一直还未得到很好解决。本文中提出以低对比分辨本领作为光学系统的质量指标,并将光学系统的传递函数近似表示为正交多项式之和,象差任意大小的光学系统的最佳校正方案和公差之值就可以求出。在小象差情况下,所得的结果与Strehl判断的结果基本一致。 关键词：     

直接积分法研究电子光学成像系统的时间像差理论

提出了计算动态电子光学成像系统时间像差系数的新方法——直接积分法.以阴极面逸出的轴向电子初能为ε_z1（0≤ε_z1≤ε_0max）的近轴电子 轨迹为比较 基准,给出了时间像差的定义,详细叙述了直接积分法并给出求解动态电子光学成像系统时 间像差系数的积分表达式.τ变分法求得的二级几何时间像差系数必须求解微分方程, 而直接积分法求得的二级几何时间像差系数全部以积分形式表示,仅需进行积分运算,更适 用于成像系统的实际计算与设计. 关键词： 电子光学成像系统 阴极透镜 动态电子光学 时间像差理论     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

Conditions for identical position of optimal image plane for axial imaging with different values of f-number

By analysis of the dependence of longitudinal spherical aberration on the numerical aperture, it is possible to find such values of the numerical aperture, where spherical aberration is zero. Such values of the numerical aperture are called correction zones. The work theoretically analyses the described problem and equations are given for wave aberration coefficients using correction zones for spherical aberration of the third and the fifth order. Our work presents an analysis of optimal values of correction zones and an optimal position of the center of the reference sphere based on the variance of wave aberration for the image quality evaluation. Relations are described for calculation of correction zones of an optical system having an identical position of the optimal image plane for two values of the f-number. The analysis of optical systems using correction zones is performed on an example.