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     

非对称轻小型头盔显示器光学系统设计

针对非对称光学系统视场范围和出瞳直径较窄、光学结构复杂、制造成本昂贵、装配调整麻烦等问题,本文采用在系统中加入自由曲面反射镜的设计方法。首先,论述了双反射镜非对称光学系统的设计要求和工作原理。然后,分析了三反射镜非对称光学系统的离轴结构控制方法。最后,采用XY多项式自由曲面反射镜折叠光路、消除遮拦、扩大视场、校正离轴像差,设计出一款适用于头盔显示器的非对称光学系统。设计的双反射镜非对称光学系统的视场为60°×30°,出瞳直径为8 mm。在截止频率52 lp/mm处,全视场的调制传递函数值大于0.25,系统畸变小于5%,单目系统重量约为190 g。设计结果表明,该非对称光学系统的视场大小和成像质量均有所提升,实现了小型轻量化,可应用于头盔显示器。     

红外扫描成像系统中冷像的分析和控制

提出了一种基于准近轴光线追迹的冷像噪声的快速分析方法，给出了适用于这类非对称光学系统的准近轴光线追迹公式，介绍了在光学系统自动设计阶段控制或消除冷像噪声影响的方法。这些分析和控制已全部在北京理工大学研制的ＧＯＳＡ软件中实现。     

失调分数傅里叶变换及其光学作用

利用失调光学系统的衍射积分公式,分析了失调的Lohmann分数傅里叶变换光学系统和准非对称非均匀介质的衍射特性,得到了两者具有相同的失调衍射积分表达式,表明两者具有等效性,从中提出了失调分数傅里叶变换新概念. 关键词： 分数傅里叶变换 失调光学系统 衍射积分 梯度折射率介质     

自由曲面校正光学系统像差的研究EI北大核心CSCD

利用条纹泽尼克多项式来表征自由曲面的光学元件,并将多项式中表示初级球差、彗差、像散项转换为矢量形式.利用矢量波像差理论,研究了自由曲面光学元件校正光学系统初级像差的特性.通过分析可知,自由曲面在光学系统中不同位置时所校正的像差特性不同.当自由曲面位于光学系统的孔径光阑(入瞳或出瞳)上可以校正光学系统全视场内为常数的初级像差;当自由曲面远离孔径光阑时,由于轴外视场成像光束口径的缩放与偏移,自由曲面可以校正非对称初级像差,且不同初级像差与视场依据关系不同.     

自由曲面校正光学系统像差的研究

利用条纹泽尼克多项式来表征自由曲面的光学元件,并将多项式中表示初级球差、彗差、像散项转换为矢量形式.利用矢量波像差理论,研究了自由曲面光学元件校正光学系统初级像差的特性.通过分析可知,自由曲面在光学系统中不同位置时所校正的像差特性不同.当自由曲面位于光学系统的孔径光阑(入瞳或出瞳)上可以校正光学系统全视场内为常数的初级像差;当自由曲面远离孔径光阑时,由于轴外视场成像光束口径的缩放与偏移,自由曲面可以校正非对称初级像差,且不同初级像差与视场依据关系不同.     

自适应光学系统的控制残余方差分析

分析自适应光学系统的控制残余方差与控制带宽的关系.对于存在时间延迟的自适应光学系统,推导了计算大气湍流控制残余方差的近似方式,并给出了有探测噪声情况下确定系统最优控制带宽的公式.以61单元自适应光学系统为例,讨论了实验自适应光学系统中控制带宽的优化选择问题.     

非对称光学系统的矩阵分解与等效变换

 使用矩阵光学方法研究了非对称光学系统的矩阵分解和等效变换。将Arsenault提出的分解方法推广应用于分块矩阵行列式为零的4×4矩阵的分解，并以用于光束对称化的光学系统为例说明该方法的应用。     

适用于非对称系统的Wassermann-Wolf方程组

根据Wassermann-Wolf方程的思路推导了适用于非对称光学系统中的非球面设计计算公式,通过编制CODE V宏语言程序,实现了通用非球面设计的自动化。     

无光焦度校正板在主镜后的牛顿光学系统的设计

描述了无光焦度校正板放在主反射镜后的无光焦度校正板-牛顿光学系统的设计.光栏放在主镜上,改变相对孔径A,选择校正板光焦度φ21、φ22和遮拦比α,进行光学系统的光线追迹,求解出光学系统的最佳选择,并给出各种设计曲线和设计结果,对光学系统进行合理的评价.     

Transformation of pulsed Gaussian beams in a four dimension domain

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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.     

测定核间距的不对称2D NOESY方法——1.从不对称2D NOESY峰强度求取完整的混合系数矩阵

本文提出不对称2D NOESY实验方法来测定完整的2D NOESY混合系数矩阵。理论研究表明,不对称2D NOESY实验信澡比要比传统2D NOESY的高,不对称2D NOESY峰强度矩阵是非对称的,因此可以只用不对称2D NOESY的非对角峰强度来求得完整的2D NOESY混合系数矩阵,避免测量大分子等复杂自旋系统的严重重叠的对角峰强度所引起的困难,而这是传统2D NOESY实验方法所无法作到的。本文最后应用数值模拟方法对理论研究结果进行了计算验证。     

测定核间距的不对称2D NOESY方法——1.从不对称2D NOESY峰强度求取完整的混合系数矩阵

本文提出不对称2D NOESY实验方法来测定完整的2D NOESY混合系数矩阵。理论研究表明,不对称2D NOESY实验信澡比要比传统2D NOESY的高,不对称2D NOESY峰强度矩阵是非对称的,因此可以只用不对称2D NOESY的非对角峰强度来求得完整的2D NOESY混合系数矩阵,避免测量大分子等复杂自旋系统的严重重叠的对角峰强度所引起的困难,而这是传统2D NOESY实验方法所无法作到的。本文最后应用数值模拟方法对理论研究结果进行了计算验证。     

测定核间距的不对称2DNOESY方法Ⅲ．从不对称2DNOESY重叠峰强度求取完整混合系数矩阵

建立了包括重叠峰在内的不对称２ＤＮＯＥＳＹ峰强度来求取完整混合系数矩阵的方法。并应用数值模拟方法验证了其正确性。该方法充分利用了不对称２ＤＮＯＥＳＹ重叠峰强度来求解完整混合系数矩阵，这对大分子体系中核间距的准确计算是有价值的。     

测定核间距的不对称2D NOESY方法Ⅲ.从不对称2D NOESY重叠峰强度求取完整混合系数矩阵

建立了包括重叠峰在内的不对称2D NOESY峰强度来求取完整混合系数矩阵的方法。并应用数值模拟方法验证了其正确性。该方法充分利用了不对称2D NOESY重叠峰强度来求解完整混合系数矩阵,这对大分子体系中核间距的准确计算是有价值的。     

Existence of the transfer matrix formalism for a class of classical continuous gases

For classical gases of particles interacting through nonnegative, many-body interactions of short range it is verified that the corresponding grand canonical Gibbs measures have the global Markov property for sufficiently low values of the chemical activity. This yields the existence of a (nonsymmetric in general) transfer matrix formalism for such systems.     

Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers

In this paper we describe efficient methods to obtain the stationary states of linear and nonlinear photonic systems, which have gained particular interest in the field of integrated and nonlinear optics. While the methods presented are directly applicable to optical physics, they are also general and should be of interest in a broad range of phenomena presently under study in other areas of physics and engineering. The strategy consists in combining the use of classical methods, such as inverse iteration or the Newton method, together with modern, nonstationary linear solvers, such as SYMMLQ or GMRES, in order to obtain efficient numerical computations to problems involving large matrices. We have selected several example problems in order to discuss the practical implementation details, not normally described in the present literature. Moreover, the problems we have selected provide a backdrop to contrast and motivate the use of different methods for systems which are symmetric and non-symmetric, single and multi-component, and also real and complex. Information relative to numerical performance of the different algorithms, including a survey for a nonsymmetric problem, which requires the adjustment of a restarting parameter for the GMRES algorithm, is also presented.     

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation on manifolds enabled with nonholonomic distributions is considered. We prove that, for certain types of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic noncommutative gravity theories models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in nonsymmetric gravity theories. It is concluded that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of some models and/or unconstrained solutions.     

Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a superoperator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is represented by a matrix continued fraction whose coefficients can be obtained from the nonsymmetric block-Lanczos method. The resulting algorithm, which is particularly convenient when large basis sets are used, allows for the calculation of the full spectrum of a system with a computational workload only a few times larger than needed for static polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.