Correlation and fractal properties of speckles in the extremely deep Fresnel diffraction region

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields,the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated.The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated.We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region,and the experimental results prove the conclusions drawn from our simulations.     

随机表面散射光场的格林函数法与基尔霍夫近似的比较

从简谐光波满足的亥姆霍兹方程出发，将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组，并对其进行数值求解，实现了光场的数值计算. 同时，由透射光场的格林函数积分得出了基尔霍夫近似下光场的表达式. 通过类比推导夫琅和费面上散斑场自相关函数的方法，提出了产生随机表面及其导数的傅里叶变换方法. 在此基础上，对采用基尔霍夫近似进行自仿射分形随机表面的散射光场数值计算的精确程度进行了研究. 发现在随机表面粗糙度比较小时，基尔霍夫近似的精度比较高；在粗糙度相同的情况下，表面的分形 关键词： 格林函数积分 基尔霍夫近似 自仿射分形随机表面     

菲涅耳深区散斑强度统计特性及演化

利用直透光波和高斯散斑场的叠加理论和基尔霍夫近似研究了菲涅耳深区散斑的构成,给出了菲涅耳深区散斑场及其强度概率密度和对比度的表达式.利用原子力显微镜测量的随机散射表面高度分布数据模拟菲涅耳深区不同散射距离处散斑,并计算绘出其强度概率密度和对比度曲线.理论与模拟相结合研究这两个统计函数的特征和直透光强所占比例的影响,以及它们随散射距离的演化规律.     

The accuracy of Kirchhoff's approximation in describing the far field speckles produced by random self-affine fractal surfaces

We describe an array of microscopic atom traps formed by a pattern of magnetisation on a piece of videotape. We describe the way in which cold atoms are loaded into one of these micro-traps and how the trapped atom cloud is used to explore the properties of the trap. Evaporative cooling in the micro-trap down to a temperature of K allows us to probe the smoothness of the trapping potential and reveals some inhomogeneity produced by the magnetic film. We discuss future prospects for atom chips based on microscopic permanent-magnet structures.     

菲涅耳区衍射光学束匀滑器件的设计

 采用精细化设计方法，进行了菲涅耳区衍射光学束匀滑器件的设计，利用爬山-模拟退火混合优化算法，获得了真实的束匀滑分布，不仅控制了算法采样点上的光强分布，还控制了其他非采样点上的光强分布。优化得到的束匀滑器件的位相深度小于π，易于后续加工。     

Computer simulation of Fresnel diffraction from rectangular apertures and obstacles using the Fresnel integrals approach

In this paper, we describe a new computer simulation technique of generating Fresnel diffraction images from rectangular apertures of arbitrary dimensions by using Fresnel integrals instead of the more common fast Fourier transform methods. The simulation can be performed in almost any PC using the software MATLAB. Diffraction images can be generated for any wavelength of light and for any aperture–screen and aperture-source distances. Images for rectangular obstacles can also be simulated. Details of the algorithm and program are presented, as well as the interesting insights than can be gained from using the program. Finally, it is shown that the simulated images reduce to the simple Fraunhofer diffraction patterns for certain limiting situations.     

菲涅耳衍射与夫琅禾费衍射公式对自由传播问题的自洽性

考察了菲涅耳衍射积分公式和夫琅禾费衍射积分公式在处理相继自由传播问题中的行为，证明了只要注意近似条件的正确运用，这些公式对自由传播问题可以给出自洽的结果；同时讨论了菲涅耳公式中当λz→0时的极限情况及其物理意义。这些分析对于加深对两个公式的物理意义、运用条件及有效性的理解是有益的。     

关于菲涅耳衍射图样相似性的分析与讨论

与夫琅禾费衍射不同,菲涅耳衍射图样对于给定波长,当衍射距离变化或输入图像几何缩放时一般都不具有相似性.但我们的分析表明,若波长、衍射距离和输入图像几何线度诸参数满足一定关系,或对于某些特殊类型孔径,菲涅耳衍射图样有可能彼此相似.本文导出了在上述诸参数发生变化时菲涅耳衍射图样保持相似性的普适条件,以及此时衍射图样大小与诸参数的定量关系,并对包括圆孔衍射和直边衍射等情况都得到了一系列有价值的推论.     

菲涅耳圆孔衍射计算机模拟演示的实现

为了克服菲涅耳衍射积分计算的复杂性和因光波频率高而导致的采样点数目巨大两大难题,利用Hankel变换算法,将二维计算变换为一维计算,并利用球面波因子处理,在普通PC上实现了菲涅耳圆孔衍射的计算机模拟演示．     

The two-mode quantum Fresnel operator and the multiplication rule of 2D Collins diffraction formula

By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional (2D) Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.     

Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.     

小孔衍射和近场散射数值计算的格林函数方法

从简谐光波满足的亥姆霍兹方程出发,将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组,并对其进行数值求解,实现了光场的数值计算。然后将这一方法应用于亚波长尺度的小孔衍射的光波以及自仿射分形表面产生的随机光场及其在近场区域范围内的传播的计算。在随机表面产生的光场计算中．提出了类比推导夫琅禾费面上散斑场自相关函数的方法产生随机表面,以及计算其导数的傅里叶变换方法。对光场的计算结果表明,在近场范围内,光场随离开表面的距离的增加而迅速变化,其传播特性完全不同于光场在远场范围内的传播特性。     

随机信号双参数脉冲模型的分形特征

为了研究随机信号的统计特性,以幅度、宽度两个相对独立的特征参数为基本概念,建立随机信号的双参数脉冲模型.采用PCI-9812高速数据采集卡,对空气中悬浮颗粒随机性光散射脉冲信号、光电传感器本底噪声随机信号进行计数分布的统计分析.实验结果表明,随机性脉冲信号幅度、宽度子集的计数分布以很高的精度与以自然数为自变量的对数正态分布符合;进一步的计算结果表明,在脉冲信号幅度、宽度定义域内,随机脉冲信号集合的两个特征参数之间存在非线性变换关系,即随机信号的双参数统计分布具有非整数维分形特征. 关键词： 分形 双参数 对数正态分布 随机脉冲信号     

菲涅耳衍射公式误差相位的讨论

根据波动光学的理论,对菲涅耳近场衍射公式误差相位的影响进行了分析。以单缝衍射为例,讨论了误差相位与计算精度的联系。结合菲涅耳线波带片焦面光强分布的计算,对比了菲涅耳衍射公式与基尔霍夫衍射公式的计算结果,说明在不满足误差相位近似条件下使用菲涅耳衍射公式带来的影响。最后对影响波带片焦面光强分布的几个因素进行了讨论。     

菲涅耳区衍射光学束匀滑器件的设计

采用精细化设计方法,进行了菲涅耳区衍射光学束匀滑器件的设计,利用爬山-模拟退火混合优化算法,获得了真实的束匀滑分布,不仅控制了算法采样点上的光强分布,还控制了其他非采样点上的光强分布。优化得到的束匀滑器件的位相深度小于π,易于后续加工。     

Characteristics pathlength Fresnel number equations and ideal lens wavefront Kirchhoff formulation: analysis of focused spherical wave diffraction fields

Derivation and applications of the characteristics optical pathlength Fresnel number equation for spherical waves focused by an ‘ideal’ circular lens illustrate the wealth of information which is quickly available from its use. A Kirchhoff wavefront diffraction formulation of this problem is developed and used to aid in this analysis. New characteristics about the diffraction field are revealed.     

Intensity and phase distribution in deep Fresnel diffraction region generated by multi-pinhole aperture

The Kirchhoff diffraction theory is applied to the multi-pinhole aperture diffraction screens, and the intensity, the zero-contour of the real and imaginary parts of complex amplitude and the phase distribution in deep Fresnel diffraction region are simulated. It is found that the number of bright spots, the zero-contours of the real and imaginary parts of complex amplitude and the phase singularities are all related to number of pinholes in diffraction screens. The brightness of bright spots in center of each pattern would become larger with increasing number of pinholes. In addition, there are many lines, on which the intensity value is close to 0.     

The dimensions of some self-affine limit sets in the plane and hyperbolic sets

In this article we compute the Hausdorff dimension and box dimension (or capacity) of a dynamically constructed model similarity process in the plane with two distinct contraction coefficients. These examples are natural generalizations to the plane of the simple Markov map constructions for Cantor sets on the line. Some related problems have been studied by different authors; however, those results are directed toward generic results in quite general situations. This paper concentrates on computing explicit formulas in as many specific cases as possible. The techniques of previous authors and ours are correspondingly very different. In our calculations, delicate number-theoretic properties of the contraction coefficients arise. Finally, we utilize the results for the model problem to compute the dimensions of some affine horseshoes in ⁿ , and we observe that the dimensions do not always coincide and their coincidence depends on delicate number-theoretic properties of the Lyapunov exponents.     

强散射体产生的像面散斑对比度与随机表面及成像系统关系的研究

在对4f光学成像系统中强散射体形成的像面散斑的统计特性的研究中, 首先通过散斑场光波复振幅的一般形式和双重指数函数近似求出散斑光强的系综平均, 然后利用散斑场光波复振幅的实部和虚部的旋转变换法求出散斑光强的方差, 最后得出了散斑对比度与随机表面统计参量和系统参量的直接表达式. 本结果与现有文献中包含随机表面相关面积或散射粒子数目的隐含表达式相比具有明显的改进, 并对标定随机表面的散斑对比度法具有重要意义. 关键词： 随机表面 像面散斑 对比度