一阶光学系统分数傅里叶变换的相空间分析

在维格纳相空间中,通过将一阶光学系统的传输矩阵分解为坐标旋转、比例缩放和啁啾矩阵的组合,得到了一阶光学系统在空域的分数傅里叶表示.结果表明:任意一阶光学系统均可表示为经过比例缩放和二次相位调制的分数傅里叶变换.通过将输入输出光场在相空间中作π/2角旋转,得到了一阶光学系统在频域的传输矩阵和衍射积分公式,进而得到了一阶光学系统在频域的分数傅里叶表示.比较空域和频域一阶光学系统的相空间变换矩阵,说明2个系统本质上属同一变换在不同基坐标下的表示,并推导出了光学系统在空域和频域具有相同分数傅里叶变换的条件.     

光学系统的等效变换

本文在普遍情况下使用矩阵方法详细讨论了光学系统的等效变换,证明光线变换矩阵为的光学系统当C≠0时可等效为一个薄透镜,当C=0时等效为一个薄透镜组。文中所得结果能用于分析光线或光束通过复杂光学系统的变换和多元件光腔的问题。     

光偏振态的群论描述:转动矩阵的生成元

应用偏振光描述中的变换矩阵与群论的对应关系[1]和相应的计算理论,讨论了与偏振光学系统中的Jones矩阵、Mueller矩阵相对应的SU(2)群、SO(3)群和Lorentz群的生成元问题,给出了用单位矩阵、Pauli自旋矩阵和稀疏矩阵分别作为无耗偏振光学系统中SU(2)群元(Jones矩阵)和SO(3)群元(Mueller矩阵)生成元以及部分损耗偏振光学系统中的幺模群(Jones矩阵)和Lorentz群(Mueller矩阵)生成元的具体形式;矩阵计算理论说明这些群元的生成元表示可以简化偏振光学系统的计算。     

自适应光学系统模式控制动态优化方法

像差校正模式项数是自适应光学系统模式控制算法中的一个重要参数,其大小对补偿效果影响明显。通过对系统响应函数矩阵的奇异值分解构建像差模式空间,以不同控制项数下残余像差的均方根估计为依据确定每次校正的模式项数,提出了一种模式项数动态优化的控制方法。以Hartmann-Shack波前传感器和薄膜变形镜为主要部件搭建自适应光学实验系统,通过拟合不同像差验证上述控制方法,实验结果表明,和固定项模式控制方法比较,动态优化方法校正的系统残余像差更低,可明显提高自适应光学系统的空间拟合性能。     

高斯光束经复合光学系统的聚焦特性

 讨论了高斯光束经由凹透镜，子系统和凸透镜构成的复合光学系统的聚焦特性，利用矩阵光学方法，推导出了高斯光束经复合光学系统聚焦后束腰宽度和像距的计算公式。计算例表明，选择适当参数的复合光学系统，既可以获得较小的束腰宽度，又可以获得较长的像距。     

变形镜高斯函数指数对迭代法自适应光学系统的影响

基于613单元自适应光学系统, 描述了迭代矩阵和斜率响应矩阵的特性. 在变形镜驱动器间距和交连值不变的情况下, 研究了变形镜高斯函数指数对迭代矩阵和斜率响应矩阵稀疏度的影响, 对自适应光学系统稳定性和校正能力的影响. 研究表明, 迭代矩阵和斜率响应矩阵的稀疏度随着变形镜高斯函数指数的增大而减小. 高斯函数指数过大或者过小都会影响自适应光学系统的稳定性和校正能力. 最后, 综合迭代矩阵和斜率响应矩阵的稀疏度、自适应光学系统的稳定性和校正能力, 给出了合理的变形镜高斯函数指数的取值范围.     

基于坐标变换的动态光学成象性质研究

本文利用齐次线性坐标变换,将光学系统的高斯物象共轭理论用齐次坐标变换的方法来描述,并与动态光学理论中的作用矩阵相比较,阐述了坐标变换方法与动态光学理论的关系;推导了一些重要的动态光学系统的成象性质,验证了动态光学的一系列结论.通过本文的研究,证明了坐标变换方法与动态光学理论的一致性,也明确了在动态光学系统内坐标变换方法的应用方法.     

发射光学系统分析

 采用矩阵光学方法导出了发射光学系统的传输变换矩阵和具有两级扩束系统的发射系统的调焦公式,研究了输入激光不是平行光时远场焦点位置的变化和一级扩束系统焦距变化对系统焦距的影响。     

外差探测的信噪比:矩阵系

在考虑本机振荡器场分布、接收光学系统和大气湍流的条件下,提出一种计算光接收机外差效率的矩阵方法。圆形对称接收机的外差效率由若干矩阵的乘积给出,每一矩阵代表该系统的一种光参数,例如散焦、光学系统的费涅尔数、中心模糊区域或大气相干半径等。     

自适应光学系统的非光滑H_∞控制研究

为了设计出结构简单、低阶次的自适应光学系统鲁棒控制器,提出了自适应光学系统的非光滑H∞控制.采用传统H∞控制方法结合基于Hankel奇异值的模型降阶法,设计了全阶H∞控制器和降阶H∞控制器,控制器的阶次分别为226阶和163阶.采用非光滑H∞控制方法,所设计出的控制器仅为一个常数矩阵与4阶单输入单输出传递函数的乘积.为了验证和比较控制效果,模拟了动态大气湍流波前相位及采用全阶H∞控制器和采用非光滑H∞控制器的自适应光学系统的校正后残余波前相位,仿真结果表明,两个自适应光学系统有着近似的控制效果,证明了自适应光学系统非光滑H∞控制的有效性.     

一维大气边界层光学折射率结构常数数值模式的实验检验

提出了一种大气光学折射率结构常数的数值模式。一次输入日期、时间、经纬度、温度、湿度、风速、粗糙度、土壤参数，云量等相关参数，可得到24h内的温度、湿度、风场、折射率结构常数等量。通过与实测对比表明，无论是月平均折射率结构常数还是某天的折射率结构常数，模式计算与实测数据都符合得很好。模式计算的向下总辐射通量与实测数据基本一致。     

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.     

Matrix methods in treating decentred optical systems

A set of matrix methods treating decentred optical systems in the paraxial approximation is reviewed. Misalignment phenomena of optical systems can generally be described by an augmented 4×4 matrix; propagation of optical rays in an asymmetric, inhomogeneous medium by a 3×3 matrix. In order to simplify the operations with these matrices, ray transfer flow graphs are introduced.A lot of optical problems can be solved in a clear and simple manner, including optical arrays. Some examples are given.     

Mueller matrix differential decomposition

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.     

Optical Operator Method in Two-Mode Case and Entangled Fresnel Operator＇s Decomposition

Based on the entangled Fresnel operator （EFO） proposed in [Commun. Theor. Phys. 46 （2006） 559], the optical operator method studied by the IWOP technique （Ma et al., Commun. Theor. Phys. 49 （2008） 1295） is extended to the two-mode case, which gives the decomposition of the entangled Fresnel operator, corresponding to the decomposition of ray transfer matrix [A, B, C, D]. The EFO can unify those optical operators in two-mode case. Various decompositions of EFO into the exponential canonical operators are obtained. The entangled state representation is useful in the research.     

An algorithm for solving the optical problem for stratified anisotropic media

An algorithm for solving the Maxwell equations for propagation of light through anisotropic stratified media is considered. The algorithm uses the Berreman matrices of order 4 × 4. In contrast to the numerical methods suggested by Berreman, the new method is exact. The Sylvester theorem for calculating functions of a matrix and the Laguerre method for determining eigenvalues provide the basis for an algorithm with an efficiency comparable to that of the algorithms based on analytic solutions, which exist only in the case of uniaxial media. The method suggested in this paper allows for the analysis of complex optical systems where the effects of biaxiality, magnetic anisotropy, and optical activity play an important role.     

Matrix-based paraxial skew ray-tracing in 3D systems with non-coplanar optical axis

Matrix-based Gaussian paraxial ray-tracing is commonly used for first estimates in early design stages of optical systems. However, the usual techniques are suitable only for rays in systems with a common straight-line optical axis, and cannot be used in systems containing mirrors and/or prisms. Attard extended these methods to matrix-based skew ray-tracing for systems containing cylindrical lenses with orthogonal cylinder axes and spherical lenses with combinations of cylindrical lenses, but had problems with non-straight and non-coplanar optical relations. This paper develops a novel general matrix method for paraxial skew ray-tracing in systems with non-coplanar optical axes containing spherical and flat boundary surfaces. First-order Taylor series expansion is used to approximate skew ray-tracing equations in simple repetitive linear matrix form. Sufficiently good accuracy is obtained if the proposed method is restricted to skew rays in the immediate neighborhood of the optical axis, as demonstrated by numerical examples. This study extends earlier Matrix-based paraxial ray-tracing design technique to include non-coplanar systems containing mirrors and/or reflecting prisms such as projectors, with special application potential for first estimates in early design stages of 3D optical systems.     

Accurate calculation of reflectance spectra for thick one-dimensional inhomogeneous optical structures and media: stable propagation matrix method

Numerical instability is usually observed when the propagation matrix method is used to calculate the reflectance and transmittance spectra for the thick one-dimensional inhomogeneous optical structures and media. To remove this numerical instability we applied two procedures, the normalization and the singular-value decomposition, for the propagation matrix and the matrix involved in calculating the matrix of reflection coefficients, respectively. Examples of a cholesteric liquid crystal and a helical structure of ferroelectric liquid crystals with a twist defect show that the modified propagation matrix method is able to accurately calculate the reflectance spectra for thick structures.     

BEPCII横向束流反馈系统前端电子学

选择了一台商业化的前端电子学RFTF（radio frequency front-end for transverse feedback system）用于BEPCII横向束流反馈系统, 这是跟进世界先进加速器技术的具体实施。在BEPC同步运行模式下对RFTF的性能进行了测试实验，结果表明使用RFTF可以得到理想的波形，能够满足BEPCII横向反馈系统的需要，但是，当储存环出现不稳性时，系统无法正常工作，这就要求BEPCII纵向不稳定很小或者用纵向反馈系统来抑制存在的纵向不稳定。     

Decomposition algorithm of an experimental Mueller matrix

This study deals with the interpretation of experimental Mueller matrices. The understanding of such a matrix is not straightforward in the case, in particular, of a strongly depolarizing medium, which is therefore disturbed and where relevant pieces of information are often distributed among its various elements. As a result, information data need to be extracted by a decomposition of any Mueller matrix into simple elements to uncouple the existing polarimetric effects. This led us to develop an algorithm in order to characterize any depolarizing, or not, polarimetric system. In addition to differentiating the experimental noise from the intrinsic depolarization of the optical system under study, this algorithm proved to: (i) separate depolarization from birefringence and dichroism and (ii) characterize the isotropic or anisotropic nature of the depolarization. At last, this algorithm was validated through the study of several optical systems with different polarimetric properties.