Puiseux parametric equations of analytic sets

We prove the existence of local Puiseux-type parameterizations of complex analytic sets via Laurent series convergent on wedges. We describe the wedges in terms of the Newton polyhedron of a function vanishing on the discriminant locus of a projection. The existence of a local parameterization of quasi-ordinary singularities of complex analytic sets of any codimension will come as a consequence of our main result.

     

多孔径扫描波面恢复技术的精度评定及影响因素

多孔径扫描波面恢复技术是一项新的高精度大孔径面形检测手段.本文从建立波面恢复精度的评价标准出发,结合实测结果进行讨论,并对影响精度的两个重要因素即拼接模式及拼接区大小进行分析.     

瑞奇-康芒两角度检测法的一种波像差解读方法

瑞奇-康芒法是大口径平面元件面形检测的有效方法.通过分析检测光瞳到被检平面的位置转换关系以及波像差到面形误差的幅值转换关系,分别对检测得到的波像差以及干涉仪离焦产生的Power进行转换处理,利用最小二乘法计算出瑞奇-康芒两角度检测时的干涉仪离焦量,从而获得被检平面的面形误差分布.实验部分给出了第4项到第37项泽尼克多项...     

Expected thermal deformation and wavefront preservation of a cryogenic Si monochromator for Cornell ERL beamlines

Cornell energy‐recovery linac (ERL) beamlines will have higher power density and higher fractional coherence than those available at third‐generation sources; therefore the capability of a monochromator for ERL beamlines has to be studied. A cryogenic Si monochromator is considered in this paper because the perfect atomic structure of Si crystal is needed to deliver highly coherent radiation. Since neither the total heat load nor the power density alone can determine the severity of crystal deformation, a metric called modified linear power density is used to gauge the thermal deformation. For all ERL undulator beamlines, crystal thermal deformation profiles are simulated using the finite‐element analysis tool ANSYS, and wavefront propagations are simulated using Synchrotron Radiation Workshop. It is concluded that cryogenic Si monochromators will be suitable for ERL beamlines in general.     

Time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise

<正>This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise.The dimension of the Fokker-Planck equation is reduced by the linear transformation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon’s information entropy.The relationships between the properties of dissipative parameters,system singularity strength parameter,quasimonochromatic noise,and their effects on information entropy are discussed.     

板条增益介质波前畸变诊断方法

对波前重构算法中的区域法进行了改进,使其能够应用于板条增益介质的波前畸变诊断。利用该方法对47块Nd: YAG板条增益介质沿厚度方向波前畸变进行测量,指出镀膜和加工等环节对增益介质的波前畸变可能造成的影响。按照波前畸变峰谷（PV）值对测量结果进行了统计,结果表明:增益介质造成的静态波前畸变参差不齐,测量样本中静态畸变PV值最多可达5 m以上,且仅有4.1%的增益介质静态畸变PV值小于1 m。通过选取某些增益介质使之级联,测量其组合波前畸变,发现在系统中使用两块波面互补的增益介质有助于减小系统的静态波前畸变。     

太阳米粒结构相关哈特曼-夏克波前传感模拟研究

基于互相关因子和绝对差分算法以及相关哈特曼－夏克波前传感器的基本原理，根据室内模拟太阳米料结构研究了低对比度扩展目标情况下应用相关哈特曼－夏克波前传感器探测波前误差的可行性，结果表明，相关哈特曼－夏克波前传感器能够有效探测光学波前误差。     

数字全息图取样模型的简化研究

数字全息研究领域目前存在两种不同的数字全息图取样模型.按照这两种模型进行研究时, 不但涉及较复杂的数学运算, 在许多情况下还会导致不同的研究结果, 不便于理论分析及实际应用.基于对数字全息图记录的物理过程分析及电荷藕合器件(charge coupled device, CCD)几何结构的研究, 本文将这两种取样模型简化为相同的数学表达式. 利用数字全息图的余弦级数展开及取样定理对简化模型的研究表明, 简化模型不但具有清晰的物理意义, 而且可以方便地为应用研究服务. 基于简化模型对物光波通过光学系统到达CCD的数字全息记录系统进行了研究, 导出得到实验证实的波前重建表达式. 关键词： 数字全息 波前重建 相干光成像     

Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Geometry and Physics Today

“Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “physical theories of a geometrical character.” Thence, “physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “differential” equations, are also being discussed.