信息光学视角下菲涅耳双棱镜干涉的研究

菲涅耳双棱镜干涉在相衬成像和全息显微术中有重要应用。为了促进其应用,本文从信息光学角度研究双棱镜干涉,首先利用光场与脉冲响应函数之间的关系,理论导出了菲涅耳双棱镜干涉条纹强度公式,分析并讨论了狭缝缝宽及狭缝到双棱镜距离对菲涅耳双棱镜干涉条纹的影响,狭缝宽度大于0. 1 mm时,干涉条纹分辨率变差。接着给出了改变狭缝宽度(变化量为0. 08 mm)和改变狭缝到双棱镜的距离(从8 cm变化到12 cm)的实验结果,理论分析和实验结果一致。该结果有助于促进菲涅耳双棱镜干涉在相衬成像等领域的应用。     

Calculation of the vectorial field distribution of an axicon illuminated by a linearly polarized Guassian beam

An analytical expression describing the vectorial field distribution of Gaussian light beams diffracted by an axicon is obtained. The theoretical analysis and simulation calculation show that for the linearly x-polarized light incident on an axicon, the y-component of the diffraction field is very small and the x-component dominates. The intensity of the z-component along the propagation direction is related with the open angle and index of axicon. The open angle plays the more important role in determining the polarization than does the index. For a small open angle, the z-polarized effect can be neglected and the scalar method is simple and valid to evaluating the diffraction field distribution of axicon. However, the vectorial method has to be used for great open angle.     

关于"双棱镜必须均匀照亮"的深入探讨

讨论了菲涅耳双棱镜实验中，双棱镜“必须均匀照亮”的意义，并强调指出，只要双棱镜的中心(棱脊的附近)被“均匀照亮”即可，从而对教材中的“均匀照亮”的含义作了明确的界定．     

长程轮廓仪菲涅耳双棱镜对分束结构

针对长程轮廓仪中的一个重要光学部件分束器,设计了一种菲涅耳双棱镜对分束结构。其功能是将一束正入射平行光分成两束间距可变、强度相等且光程差为零的平行光。对菲涅耳双棱镜对结构特点进行了详细的描述,并对基于菲涅耳双棱镜对分出的两束光在傅里叶透镜后焦面上的干涉条纹振幅分布和能量分布做了理论分析和数值仿真。分析和仿真结果表明,菲涅耳双棱镜对不仅具有已有的等振幅分束结构同样的功能,而且能使长程轮廓仪探测精度更高。对比菲涅耳双棱镜对与已有的4种等振幅分束结构的性能发现,菲涅耳双棱镜对兼备结构简单、满足等光程条件以及分出的两束光间距可变等优异分光效果,可作为已有等振幅分束结构的一种替代结构。     

Homogenization of on-axis intensity distribution produced by a Fresnel refractive axicon

The on-axis intensity distribution of a beam generated by a Fresnel axicon (fraxicon) is experimentally and numerically examined and compared to a classical axicon. Monochromatic illumination produces strong oscillations in this distribution due to diffraction from the fraxicon facets combined with shadowing effects. It is shown that by proper selection of the ratio of the illuminating light wavelength to the period of the fraxicon these oscillations can be minimized by exploiting interference. In addition, polychromatic illumination of the fraxicon also permits homogenization of the on-axis intensity with some remaining oscillations at the start of the depth of field which can be reduced by decreasing the period of the fraxicon.     

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.     

Angular criterion to distinguish between Fraunhofer and Fresnel diffraction

The distinction between Fresnel and Fraunhofer diffraction is an essential condition for the accurate analysis of diffracting structures. In this paper we propose a criterion based on the angle subtended by the first minimum of the diffraction pattern from the centre of the diffracting aperture. The determination of the minimum of the diffraction pattern is the crucial point to assure the accuracy of the criterion. Therefore, the applicability of adequate thresholds for detection is discussed. The criterion is also generalized by expressing it in terms of the number of Fresnel zones delimited by the aperture. Simulations are reported to illustrate the feasibility of the criterion.     

软X射线Bragg-Fresnel二维聚焦镜的设计理论和方法

Ｘ射线Ｂｒａｇｇ－Ｆｒｅｓｎｅｌ元件是近十年发展起来的一种用于Ｘ射线波段的新型光学元件。本文介绍一种具有二维聚焦效能的Ｂｒａｇｇ－Ｆｒｅｓｎｅｌ元件的设计理论和方法。设计中采用衍射理论并用Ｃ语言编制计算机程序系统对衍射图形进行设计。对于使用波长１３．８ｎｍ，入射角５°，使用焦距２００ｍｍ的使用条件，设计结果为３５Ｍｏ／Ｓｉ双层多层膜，周期厚度７．１４ｎｍ，理论反射率约为６０％；衍射图形共４００个环带，最内环半宽度５２．５μｍ，最外环宽度１．３μｍ。     

环形光栅的菲涅耳衍射

在圆孔的菲涅耳衍射的基础上 ,讨论环形光栅的菲涅耳衍射 ,并给出了计算机仿真结果     

二次电位分布静电双棱镜

本文提出了一种新的静电双棱镜——二次电位分布静电双棱镜,用此棱镜可增强干涉电子的强度,并扩大等间距干涉条纹的区域.     

An indirect algorithm of Fresnel diffraction

An indirect algorithm for Fresnel diffraction calculation at any distance is presented in this paper. Using this indirect algorithm, the Fresnel diffraction on a near plane can be realized in two steps, the first is to acquire the diffractive field on a far field and the second is to obtain the diffractive field on a near plane using an inverse Fresnel integral. Compared with conventional algorithms, this algorithm is valid at any range of distance. The sampling theorem, as the basis of this indirect algorithm, is discussed in detail. Theoretical calculations show good agreements with experimental results.     

Diffraction of terahertz waves after passing through a Fresnel lens

The spatiotemporal and spectral characteristics of ultrawide-band terahertz pulses after passing through a Fresnel lens are studied by using the scalar diffraction theory. The simulation shows that the transmitted terahertz waveforms compress with increasing propagation distance, and the multi-frequency focusing phenomenon at different focal points is observed. Additionally, the distribution of terahertz fields in a plane perpendicular to the axis is also discussed, and it is found that the diffraction not only induces focusing on-axis but also inhibits focusing at off-axis positions. Therefore, the Fresnel lens may be a useful alternative approach to being a terahertz filter. Moreover, the terahertz pulses travelling as a basic mode of a Gaussian beam are discussed in detail.     

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.     

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.     

平面透射光栅的菲涅耳衍射

从标量场的菲涅耳衍射理论出发,研究了球面波入射平面透射光栅的衍射场,导出菲涅耳衍射场的复振幅分布,并得到光栅菲涅耳衍射角的计算公式．结果表明,在理想情况下菲涅耳衍射的每一级衍射波都是一个球面波;在对菲涅耳衍射角进行新的定义后,衍射角的计算仍然可以采用夫琅禾费衍射的光栅方程．     

菲涅耳衍射的数值计算

利用Mathematica软件分别计算了单缝衍射及双缝衍射的光强分布,成功解决了菲涅耳衍射的计算这一较难问题,并得到了双缝衍射向杨氏双逢干涉过渡的具体条件,完成了实验室内难以完成的任务.     

Free-space Fresnel diffraction for the approximation of fractional Fourier transform

Fractional Fourier transformation of an object can be approximated by the object's free-space Fresnel diffraction pattern under some restricted conditions and plane wave illumination according to Hua's method. A better approximation is achieved under least-squared conditions developed in this paper. Simulation results verify that our theoretical development works for any fractional order a compared with the previous approach.     

菲涅耳衍射和分数傅里叶变换

介绍了衍射孔的菲涅耳衍射和分数傅里叶变换的对应关系，使得可以用分数傅里叶变换来描述光电原始光场经过菲涅耳衍射区一直到无穷远处夫琅禾费衍射区的自由空间标量衍射传播全过程。     

基于菲涅耳衍射的无透镜相干衍射成像

相干衍射成像是一种新型的无透镜成像技术,在光学测量、显微成像和自适应光学等领域有重要应用．本文提出一种基于单幅菲涅耳衍射强度图样的无透镜相干衍射成像方法;该方法采用特殊设计的卷积可解阵列抽样屏,通过对抽样物波的菲涅耳衍射强度图样进行非迭代的逆菲涅耳变换和滤波等数字处理实现被测物波复振幅信息的恢复,最后通过数字衍射得到物体的数字再现像．文中对抽样孔径、衍射距离、图像传感器尺寸等参数对再现像的影响进行了理论分析和模拟实验研究．发现在针孔大小和记录孔径大小一定的条件下,存在一个最佳的衍射距离;衍射距离过大会给重建图样带来噪声,衍射距离过小则会使再现象的分辨率降低．文中还对抽样针孔大小对系统成像分辨率的影响进行了分析,为进一步开展相关实验研究和应用提供了理论依据．     

圆孔的菲涅耳衍射

得到了圆孔菲涅耳衍射光强分布的表达式,此式由贝塞尔函数的数列(或Lommel函数)给出,因此很容易利用普及的数学软件算出结果.并且利用CCD照相机量度了衍射光强分布,与运算的结果作了比较,也与Burch在1985报导的结果作了比较.