夫琅禾费衍射公式的一般形式

从不同的途径导出了大角度情形下亦成立的夫琅禾费衍射积分的一般形式，指出此一般形式公式是求解夫琅禾费衍射的基本公式．并通过对夫琅禾费衍射公式的级数形式的推导，揭示了傅里叶光学中“夫琅禾费衍射公式”与一般形式公式存在的差别，以及消除这种差别的措施．此外，还较详细地讨论了倾斜因子对衍射花样的影响．这对于衍射测量及深入理解夫琅禾费衍射的本质有一定的指导意义．     

夫琅和费衍射与大角度衍射

众所周知,夫琅和费衍射的解析强度分布和暗纹位置是在一系列近似情况下导出的。其中最重要的条件是观测点必须限制在傍轴附近,衍射角不能太大,否则得不到简单的解析公式,也就不能称之为夫琅和费衍射。最近发现有人发明错误的理论将夫琅和费衍射概念及其测量扩展到90°角,其结论与常识截然相反,因此,有必要把混淆的概念予以澄清。     

夫朗和费近似与夫朗和费衍射测量的准确度

较详细地讨论了夫朗和费衍射的本质、夫朗和费近似的准确含义以及倾斜因子对衍射花样的影响。从不同的角度导出了单缝夫朗和费衍射的光强公式和测量公式 ,指出了这些公式之间的区别与联系以及傅里叶光学中作近似分析时存在的问题。认为文献 [1]、[3 ]得出错误结论的深层次原因是错误地理解了夫朗和费近似的概念。当用夫朗和费衍射测量微小物体的尺寸时 ,只要正确地应用测量公式 ,便能得到准确的测量结果。测量的准确度原则上与衍射角的大小及被测物的尺寸无关 ,最小可测尺寸仅由标量理论的成立范围决定     

夫琅禾费衍射自动演示仪

介绍了夫琅禾费衍射自动演示仪的功能和实现方法.该仪器由光源、PASCO公司制作的狭缝盘、探测器、液晶显示器、计算机、单片机及步进电机等硬件组成.通过对单片机和计算机上的软件设计实现演示夫琅禾费衍射现象.该仪器还既可实现由计算机控制操作,也可以脱机独立操作.     

夫朗和费衍射测量的正确度

夫朗和费衍射常用来测量微小尺寸，实验表明，衍射角较大时，存在较大的系统误差，测量结果不能正确反映被测量大小。本文以狭缝为例，采取一种新的近似处理方法，导出了较为准确的测量公式，分析了测量的正确度问题，指出夫朗和费近似只是必要条件，而要获得正确的测量结果，最大衍射角必须在一定范围内。同时，这种方法也不能测量任意微小尺寸，最小可测尺寸与所要求的正确度有关，要求的正确度越高，最小可测尺寸越大。上述结论同样适用于刻划光栅、金属丝网、徐层厚度及其它狭缝类或圆孔类物体的衍射测量。     

Fibre sizing using Fraunhofer diffraction

The light scattering pattern from absorbing cylinders is shown to be adequately described by Fraunhofer diffraction for cylinders with diameter greater than 8 μm for light of wavelength 632.8 nm. This permits the use of a simple inversion procedure based on a Fourier transform of the scattering pattern to obtain the size distribution of fibre widths. For fibres of diameter less than 8 μm the same inversion procedure may be used when an electron micrograph of the fibres becomes the scattering object. The maximum resolution of this inversion procedure is shown to be proportional to the largest angle scanned and its performance with experimental data is illustrated.     

夫琅禾费衍射的计算机仿真

提出了利用MATLAB软件并通过计算机仿真夫琅禾费衍射实验的两种方法：直接计算法和傅里叶变换法,前者适用于形状简单、能精确得到相应衍射强度公式的孔径的仿真;后者适用于获取复杂形状衍射屏的夫琅禾费衍射图样的仿真文中给出各种孔缝的衍射屏的仿真衍射实验结果事实表明,采用这种仿真方法可以得到任意形状衍射屏的夫琅禾费衍射图样和强度分布曲线。     

用半波带法讨论单缝夫琅和费衍射的课件演示与制作

根据半波带法的思路，介绍了利用计算机课件演示对单缝夫琅和费衍射的条纹光强与衍射角之间的关系，以便有效地化解教学难点，帮助学生对该知识点形成清晰的认识和深化理解，同时对课件制作要点作了简要说明。     

像面衍射场系夫琅禾费衍射

提出了一个标准积分形式其被积函数由屏函数与一线性相因子的乘积构成,作为夫琅禾费衍射场的普遍定义.据此证明了有4种实验装置能接收到夫琅禾费衍射场,特别强调了像面接收装置及其优点.最后介绍了夫琅禾费衍射与傅里叶变换的关系,以及3种可供选择的相干光学信息处理系统.     

Fraunhofer diffraction pattern of apodized semicircular apertures

The far-field diffraction pattern of apodized semicircular apertures is described. The exact amplitude is given using incomplete cylinder functions. The paper also presents a simple approximation for the intensity that is suitable for further computations when the aperture is part of an optical system.     

Spectral anomalies in a Fraunhofer diffraction pattern

We show that spectacular spectral changes take place in the vicinity of the dark rings of the Airy pattern formed with spatially coherent, polychromatic light diffracted at a circular aperture.     

方孔夫琅禾费衍射的数值模拟

根据惠更斯-菲涅耳原理,利用数值计算的方法对方孔夫琅禾费衍射实验进行了模拟,在验证衍射理论的同时,还得到了非傍轴区域和微方孔的衍射图,拓展了衍射的概念,为深入理解光的衍射提供了参考.     

X‐ray dynamical diffraction Fraunhofer holography

An X‐ray dynamical diffraction Fraunhofer holographic scheme is proposed. Theoretically it is shown that the reconstruction of the object image by visible light is possible. The spatial and temporal coherence requirements of the incident X‐ray beam are considered. As an example, the hologram recording as well as the reconstruction by visible light of an absolutely absorbing wire are discussed.     

Hybrid pattern recognition using the Fraunhofer diffraction pattern

A hybrid pattern-recognition method is proposed. The Fraunhofer diffraction pattern of an object was obtained in a coherent optical system and then it was processed by a digital image-processing system. The shift- and rotation-invariant characteristic values of the diffraction pattern was calculated and the classification of the object was carried out by using those values. The proposed method was tested in a simple experimental system by using some components of an electromagnetic relay as the sample objects to be recognized.     

推导圆孔夫琅禾费衍射光强分布的一种简便方法

由一维单缝衍射的振幅分布公式简便推导求得了圆孔夫琅禾费衍射的振幅及光强分布,并利用Mathematica通用数学软件对光强分布进行亮度模拟,从而得到相应的计算机衍射模拟图像.     

Computer simulation of Fraunhofer diffraction based on MATLAB

In this paper, we describe a novel computer simulation technique of generating Fraunhofer diffraction images from different patterns. The simulation can be performed in almost any PC using the software MATLAB. The patterns of five types of elements, including one slit, one rectangular aperture, two rectangular apertures, the grating and one circular aperture are discussed and simulated. Diffractions images can be generated for any wavelength of light and for any program are presented. Finally, the Fraunhofer diffraction optical intensity distribution is analyzed. Simulation results can improve the physics experimental teaching of Fraunhofer diffraction. The programs based on MATLAB have been used as the platform to real-time calculation and simulation and solve the optical problem.     

Cantor型分形光栅的夫琅禾费衍射特性研究

研究了Cantor型分形光栅的夫琅禾费衍射特性，使我们对分形结构上的衍射问题和特性有一定的了解。     

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.     

二维小孔的对称变换与夫琅禾费衍射光强分布

采用光波的复振幅叠加方法讨论了二维小孔夫琅禾费衍射的对称变换特性.通过小孔的对称变换,可以简便求得各种典型小孔的夫琅禾费衍射光强分布公式,进而利用Mathematica软件,对光强分布进行亮度模拟,得到了相应小孔的计算机衍射模拟图像.     

夫琅禾费衍射光强的反常分布和 Matlab模拟

讨论了夫琅禾费衍射实际实验中的反常现象,在一定条件下给出了计算机模拟的结果。实验表明,衍射图样的实验数据点分布结果与数值计算的模拟结果一致。由此可知,夫琅禾费衍射光强的反常分布是远场条件失效所致。