A general calculation of the 3-D disk of least confusion using skew ray tracing

A general and analytical method is proposed to determine the 3-D contour of the disk of least confusion (DLC) produced by an optical system for a point light source located at any arbitrary position in the object space. By using the skew ray tracing method, the sensitivity method, and the Jacobian matrix, we can analytically obtain the caustic and the marginal rays. Consequently, the DLC can be determined by the intersection of the obtained caustic and marginal rays. In addition, this proposed method covers common cases with special light sources, e.g. mutually parallel incident rays parallel to the optical axis, or a point light source located on the optical axis. This proposed methodology will be useful in the analysis of rays and in the design of optical systems with a general point light source. A general case is used as illustrative example to validate its applications.     

CMYK防伪印刷微镜阵列

以印刷微镜的反射亮度、反射稳定性和CMYK颜色模式为基础,建立了一种新型的CMYK印刷微镜结构模型。利用微镜表面函数的雅可比行列式和梯度函数,对模型的表面反射亮度和稳定性进行了分析评价。结果表明:该结构模型表面函数的雅可比行列式近似为0,梯度函数随坐标变化而变化。因此,此结构模型表面的反射光具有足够大的亮度和稳定性,适用于创建基于位置和角度变化来改变光变图案反射密度的光学防伪效果。设计了一幅由不同CMYK印刷微镜组成的防伪光变图案,模拟了该防伪图案的印刷微镜阵列结构。     

光学CT中的图像重建算法

从理论上研究了利用正向模型求解逆问题的迭代算法，特别是其中Ｊａｃｏｂｉ矩阵的有限元解法，引入了图像恢复了领域广泛采用的规则化方法用于处理逆问题中的奇异性问题；作为总结，最后给出了ＦＥＭ法求解光学ＣＴ问题的完整步骤。     

A general mapping approach and new travelling wave solutions to the general variable coefficient KdV equation

A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein－Gordon equation.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: II

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again by using a new transformation, which and our extended Jacobian elliptic function expansion method form a new method still called the extended Jacobian elliptic function expansion method. The new method can be more powerful to be applied to other nonlinear differential equations.     

Pöschl-Teller势阱中的光整流效应

本文用量子力学中的密度矩阵算符理论导出了Pöschl-Teller势阱中的光整流系数的解析表达式.考虑到在Pöschl-Teller势阱中存在两个可调参量k和λ,并且势阱的形状随着k和λ取值的不同而明显不同,从而其光整流系数也发生相应的变化.因此我们可以通过调节k和λ的取值而获得Pöschl-Teller势阱中的光整流系数的变化规律,并找到其最大值,从而为实验提供必要的研究方向与理论依据.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅲ

More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations.     

New Jacobian Elliptic Function Solutions to Modified KdV Equation: Ⅰ

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu‘s allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.     

融合结构先验信息的稳态扩散光学断层成像重建算法研究

扩散光学断层成像作为一种无辐射损伤、低成本的光学在体成像技术,有着良好的应用前景,但具有空间分辨率低、难以定量的缺陷.为了提高扩散光学断层成像的分辨率,实现光学参数分布的精确重建,基于有限元方法,提出了融合结构先验信息的稳态扩散光学断层成像重建算法.该算法以扩散近似作为成像模型,通过软先验的Laplace 正则化方法引入由MicroCT提供的空间结构信息.采用伴随法计算Jacobian矩阵,Levenberg-Marquardt方法用来进行迭代优化.仿真结果表明该算法不仅能获得精确的光学参数值分布,而且显著地提高了迭代收敛的速度.     

New Jacobian Elliptic Function Solutions to Modified KdV Equation: I

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdV equation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to other nonlinear differential equations.     

基于双光路原理的海水IOPs高光谱测量仪方案

设计了基于双光路原理的海水固有光学参数测量仪。该仪器可同步测量水体光谱吸收系数a、光束衰减系数c和体散射系数b。其中吸收系数a采用反射式吸收管测量,光束衰减系数c采用全吸收式样品池测量,体散射系数b根据c=a+b计算。光信号由光纤收集、光谱仪分光后用CCD探测器测量。光谱分辨率为4nm,灵敏度为0 001m-1。该仪器直接在水下工作,由水泵抽取被测海水,水下最大工作深度为200m。测量数据可以自动记录,同时也可以通过水下电缆实时传输到调查船实验室。     

General method for determining the first order gradients of skew rays of optical systems with non-coplanar optical axes

Current commercial software for the analysis and design of optical systems uses finite difference (FD) approximation methodology to estimate the gradient matrix of a ray with respect to system variables. However, FD estimates are intrinsically inaccurate and are subject to gross error when the denominator is excessively small relative to the numerator. This paper avoids these problems and determines the gradient matrix of the exit ray traveling along an optical system with a non-coplanar axis. To achieve this, the gradient matrix of the rays reflected/refracted by flat or spherical boundary surfaces are first determined by directly differentiating the skew-ray tracing equations. By introducing a Jacobian matrix, which represents the partial derivatives specifying the rates of changes between boundary variables and element variables, one can obtain the gradient matrix of the exit ray of an element with respect to its independent variables. This methodology will be useful in the analysis of rays and in design of optical systems with non-coplanar axis. A right-angle prism is used as illustrative example to validate its applications.     

高阶非线性薛定谔方程的精确周期解和孤波解

本文利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶非线性薛定谔方程,得到了它的包络型Jacobian椭圆函数双周期解和孤波解.分析结果表明亮孤子的存在依赖于负三阶色散效应,暗孤子的存在依赖于正三阶色散效应.     

基于光学相干层析术的组织光学性质测量

通过在光学相干层析成像(Optical Coherence Tomography,OCT)模型中考虑多重散射的影响,提出了一种提取出不同深度处的组织光学性质,包括散射系数和各向异性因子的算法.当把吸收系数作为算法中的第三个拟合参量时,能减少算法拟合过程中由于吸收作用的影响而带来的误差.基于包含吸收因子的OCT扩展模型,改进的算法也能够提取出吸收系数.这些算法的有效性通过对聚苯乙烯微球溶液样品的测量实验得到验证.     

亚强非局域介质中的超高斯空间光孤子族研究

研究了亚强非局域介质中超高斯光束的传播特性.运用变分法,对任意实对称响应函数泰勒级数展开取至四阶,得到了1+1维亚强非局域非线性介质中光束传输的超高斯光束的近似分析解.分析结果表明：束宽解是椭圆雅可比双周期函数,相移、空间啁啾以及临界输入功率都正比于超高斯光束的阶数.提出了超高斯空间光孤子族模型和准方波形空间光孤子的实现可能性.     

Optical soliton with group delay in microring coupled-resonator optical waveguides

This paper derives the dispersion relation of microring coupled-resonator optical waveguides (CROWs) without any approximation by using the transfer matrix method. Based on the established dispersion relation of CROWs it obtains the slow group velocity and dispersion coefficient. It finds that the effect of dispersion on optical pulses can be adjusted to balance the effect of nonlinearity by changing coupling coefficient or loss, so optical soliton with group delay can be obtained in microring CROWs. The optical soliton with group delay is of great significance for applications of microring CROWs in delay lines and optical buffers of future all-optical communication systems.     

Controlling the optical bistability and transmission coefficient in a four-level atomic medium

A novel four level atomic configuration is proposed for controlling the optical bistability and transmission coefficient with application on all-optical switching. Two circularly polarized components from a weak linearly-polarized probe beam are interacted separately by two transitions of this medium. A coherent coupling field has derived another atomic transition. It is demonstrated that the transmission coefficient of two orthogonally polarized beams at different frequencies can be achieved by adjusting the magnitude of the external magnetic field. It is found that the threshold of the optical bistability can be controlled by magnitude of the external magnetic field. Also, it is shown that optical bistability can be converted to optical multistability by switching the two orthogonally polarized beams.     

The double of a Jacobian quasi-bialgebra

We show that the construction of the double of a Lie bialgebra can be extended to the case where a vector space is only equipped with the structure of a Jacobian quasi-bialgebra (also called a Lie quasi-bialgebra). In this case, the double is itself a Jacobian quasi-bialgebra and it is quasi-triangular. The more general case of the double of a proto-Lie bialgebra is also discussed. In the first section, the notions of exact, strictly exact, quasi-triangular and triangular Jacobian quasi-bialgebras are defined and their equivalence classes under twisting are studied.     

强非局域介质中高斯型损耗空间光孤子

 利用变分法研究了1+1维傍轴高斯光束在含有小损耗的强非局域非线性介质中的传输特性，得到了光束各参量的演化方程、束宽的演化规律和一个临界功率。在介质损耗足够小的前提下，当光束初始功率等于临界功率时，得到了一个束宽随传输距离缓慢展宽的准空间光孤子——损耗空间光孤子；当光束初始功率小于临界功率时，光束束宽则按雅可比椭圆正弦函数和椭圆余弦函数作准周期展宽变化；当光束初始功率大于临界功率时，光束束宽将从按雅可比椭圆正弦函数和椭圆余弦函数作准周期压缩变化过渡到按雅可比椭圆正弦函数和椭圆余弦函数准周期展宽变化。