Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation

Using the intermediate coordinate--momentum representation |x>_s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F(r,s) and the Fourier transform operator F by decomposing U. We also find that the matrix element _s,r< x| U|f> just corresponds to an optical scaled Fresnel--Fourier transform.     

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.     

New theorem relating two-mode entangled tomography to two-mode Fresnel operator

Based on the Fan-Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F₂⁺ρF₂, where F₂ is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.     

基于同心圆光栅的远心三维测量系统

针对条纹投影术对简化系统模型、降低运算量并有效抑制误差扩散等要求,提出并构造了一种基于同心圆光栅的广义远心三维测量系统。该系统利用菲涅尔透镜与投影仪产生平行光线建立线性投影模型,降低运算复杂度,利用傅里叶变换得到经物体高度调制的初始相位信息,同时结合同心圆光栅标定技术的并行运算,通过逐点计算获取真实相位。全过程只需对一个系统参数进行标定,并且摆脱解相过程,有效抑制了误差扩散。对最大高度20 mm的物体进行形貌测量,最大误差0.23 mm,相对误差仅为1.15%。     

THE LAW OF THE ITERATED LOGARITHM OF THE KAPLAN-MEIER INTEGRAL AND ITS APPLICATION

For right censored data, the law of the iterated logarithm of the Kaplan-Meier integral is established. As an application, the authors prove the law of the iterated logarithm for weighted least square estimates of randomly censored linear regression model.     

由菲涅尔反射测量平行平面介质的折射率

一激光束投射在一平行平面介质的表面上，在此表面有一反射光束和从介质内折射出来的另一光束，只要测出这两光束的Ｐ光和Ｓ光的强度，就可计算该介质的折射率。本文介绍测量原理及方法。     

解析日本互联互通新规则

日本2001年《电信事业法》主要通过规范互联协议来解决互联问题，主要包括7方面：第一类电信经营者拥有的电信设施的互联；与一类指定电信设施的互联；与二类指定电信设施的互联，电信设备互联协议的通知与公开；关于电信设备互联谈判及争议解决的命令；关于改变或增加特定电信设备功能的计划，电信设施共享协议及共享命令等，日本2001年修改的《电信事业法》中关于互联互通的规则有诸多可借览之处， 如在对第一类电信运营商的互联义务规定中，重点针对了安装有一类指定电信设施和二类指定电信设施的第一类电信经营者等。     

The use of antiphased zones in an acoustic Fresnel lens for a scanning sonar transmitter

A simple acoustic Fresnel lens is described, which, when used with a plane array of sonar transducer elements, produces a wide beam in azimuth. Test results are compared to computed beam plots and good agreement between theory and measurement was found when all the array elements were in phase. When alternate zones are 180° out of phase, the lens can be reduced in thickness as the step height is halved; however, more careful placing of the transducer elements is required. Such a reduction in lens thickness could be desirable at low operating frequencies, or if a very wide sound beam is desired.     

在超短脉冲照射下光栅的瞬时Talbot效应的研究

本文给出了光栅在超短脉冲照射下其瞬时Fresnel衍射光场的解析解.对该解析解的数值计算表明:当脉冲光波的半极大值全宽Δτ在几十个fs内,光栅的瞬时Talbot自成象现象消失,且Δτ越小或距离越远,瞬时光强波形与初始波形差异较大.而当Δτ达到ps的数值级时,瞬时Talbot自成象现象是存在的.     

A tail empirical process approach to some nonstandard laws of the iterated logarithm

We show that a number of nonstandard laws of the iterated logarithm have limiting constants which may be expressed as the extreme values of functionals off, wheref varies over suitable compact sets of functions. By solving the corresponding extremal problems, we show how these constants are generated. In addition, several new laws are presented.