平面波经小圆环衍射轴上光强特性分析

从标量衍射理论出发,采用瑞利-索末菲衍射边界条件,通过求解第一类瑞利-索末菲衍射积分得到平面波经圆环衍射后轴上的波函数,进而分析轴上的光强特性以及光强极值数量、位置和大小与衍射圆环内外孔径的关系.比较用传统的光强定义和精确定义得到的光强公式的偏差,以及偏差与内外半径的关系.并将圆环衍射向内半径为零和外半径为无穷大两个方向进行推广,即对圆孔和圆形障碍物两种情况下的衍射情况进行讨论.     

红外系统后向反射光的光强研究

 根据衍射光学理论分析了红外系统后向反射光强的分布,反射区域可以分成近场传输区域、菲涅耳衍射区域和夫琅和费衍射区域。在菲涅耳衍射区域内,反射光斑中心光强是呈明暗变化的,反射光斑中心光强在0～1km内剧烈振荡,1～3km之间达到峰值,然后随传输距离的继续增加,反射光斑中心光强逐渐减小。在夫琅和费衍射区域内,光斑图像中央是亮光斑,周围环绕着明暗交替的圆环。     

傅里叶变换光学基本原理讲座 第五讲 夫琅和费衍射实现了屏函数的傅里叶变换

一、接收夫琅和费衍射场的实验装置 通常按光源、衍射屏、接收场三者之间的距离是有限远还是无限远,将衍射装置分为菲涅耳和夫琅和费两大类.其实,由平面波照明衍射屏,并在无限远接收的装置,只能算作夫琅和费衍射的定义装置。还有其它几种装置,它们在一定条件下接收到的同样是夫琅和费衍射场. 在图5.1中,装置(a)是定义装置,它在概念上倒是朴素的,能直观地将夫琅和费衍射与菲涅耳衍射区别开来,但在实验上却是抽象的.其意义是强调衍射场的角分布,把复杂的衍射场分解成一系列平面衍射波,它给出夫琅和费衍射积分的标准形式.装置(b)由平面波照明衍…     

应用计算机数值求解实现激光衍射法精确测缝宽

在激光夫琅和费衍射法测缝宽实验中,可以发现测算值偏小,缝越宽,偏小程度越大。其原因就在于把平面波单缝衍射的简单缝宽计算公式应用于激光高斯束衍射问题,缝越宽,这种理论模型与实际差别就越大。能否获得激光束衍射条件下缝宽的精确解呢?显然,激光高斯束的复杂性使我们无法像平面波单缝衍射那样推出一个简单、精确的缝宽计算公式。本文尝试利用计机数值求解方法编制出了激光单缝衍射情形下精确的计算机缝宽解算程序,解算结果令人满意。下图是激光衍射测缝宽实验示意图。缝宽为b,缝与观察屏的间距为D,激光器仅     

双圆孔夫琅和费衍射的远场条件

夫琅和费衍射是菲涅耳衍射的特例。按定义,当照明点光源和接收屏幕距离衍射样品均为无穷远时的衍射为夫琅和费衍射。实现夫琅和费衍射的具体装置多种多样,同一衍射样品在不同装置上都能获得相同的衍射图样,它们之间只有放大倍数的差异。     

夫琅和费衍射模拟显示研究

本文利用计算机辅助设计手段,设计单缝夫琅和费衍射装置和参数变化时的衍射强度分布,解决了夫琅和费衍射实现难的问题。     

关于光学仪器分辨本领的几个问题──备课扎记

光学仪器的分辨本领,通常是由夫琅和费衍射求得最小分辨角 但是,我们经常会遇到一些形式略异的公式,特别是式中的系数有的是0.77或0.5.此外,(1)式中的a究竟应该用光学仪器的哪一个通光孔的半径?在讨论显微镜的成象时,为什么也可以用夫琅和费衍射计算分辨极限呢?这些问题都曾经是使笔者在备课中感到困惑的问题. 1.光学仪器的成象与夫琅和费衍射 由于衍射现象,即使光学仪器不存在象差,物面上的一个点在象面上也会形成一个光斑.如何计算这个光斑的大小和强度分布呢? 在圆孔的夫琅和费衍射中,可以算得光斑的强度分布为利用贝塞耳函数的性质,不难…     

应用振幅矢量法讨论夫琅和费单缝衍射光强分布

本文提供了夫琅和费单缝衍射（简称衍射，下同）光强计算公式，与一般文献中的理论公式相比，不但完全等效，而且计算简便精确，对衍射光强分布的实际应用及实验测量￣［３］具有一事实上的参考价值。     

标量衍射理论的非傍轴近似及其有效性

当光束束腰（或衍射孔孔径）可与波长相比拟或光束具有较大的发散角时,傍轴近似不再成立.在标量瑞利.索末菲衍射积分的基础上,进一步研究了衍射场的非傍轴近似解,并详细分析了解的有效性.以平面波圆孔衍射为例,对衍射场的精确解、非傍轴近似解以及菲涅耳近似解进行了详细的数值计算和比较研究.结果表明,非傍轴近似对微小孔衍射非常精确、有效.     

圆孔限制下有相位变化的高斯光束远场发散度的理论分析

依据夫琅和费衍射理论,通过引入高斯变换,即把夫琅和费衍射积分中的贝赛尔函数用一高斯函数来近似,详细分析并推导出圆孔限制下具有相位变化的高斯光束远场发散度的近似计算公式.与传统数值积分求光束发散度相比,它避免了繁琐数值积分,其误差不超过3％.     

非傍轴矢量高斯光束的圆屏衍射

利用矢量瑞利衍射积分公式，推导出非傍轴矢量高斯光束圆屏衍射的解析表示式.非傍轴矢量高斯光束圆屏衍射的轴上场分布、远场表示式、自由空间中的传输公式，以及傍轴近似下高斯光束圆屏衍射的菲涅耳和夫琅禾费衍射公式可以作为一般公式的特例统一处理.数 值计算和比较实例说明了非傍轴矢量高斯光束的光强分布和远场特性.分析表明，在圆屏衍 射中，f参数和截断参数决定光束的非傍轴行为. 关键词： 传输光学 非傍轴矢量高斯光束 圆屏衍射 矢量瑞利衍射积分公式     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems

Based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the approximate analytical expression for the output field distribution of a rectangular flattened Gaussian beam passing through a circular apertured and misaligned paraxial ABCD system is derived. The result brings more convenient for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of a rectangular flattened Gaussian beam through a circular apertured and misaligned optical system.     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

Focusing and diffraction by an optical lens and a small circular aperture

Based on the vectorial Rayleigh–Sommerfeld diffraction integrals, analytical expressions for the transversal and axial field distribution of plane waves propagating through a thin lens followed by a small circular aperture are derived and used to study the focusing and diffraction properties of plane waves. Some special cases of our general result are discussed, and illustrative numerical calculation results are given. It is found that the vectorial nonparaxial approach should be applied if the aperture dimension is comparable with the wavelength or the focusing is strong.     

Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture

As known, it is important for the propagation of Gaussian beams in optics. In this paper, based on the expanding a hard-edge circular aperture function as a finite sum of complex Gaussian functions and the scalar Rayleigh-Sommerfeld diffraction formula, an approximation analytical solution for Gaussian beams propagating through the anamorphic fractional Fourier transform system with an eccentric circular aperture is performed. Then, the detailed numerical calculation for the two-dimensional Gaussian beams in the above-mentioned optical system is presented. The simulation also shows that different location and size of aperture result in the change of diffracted field, including location, intensity and width. All these characteristics help us understand Gaussian beams propagation better.     

Propagation of vectorial Gaussian beams behind a circular aperture

Based on the vectorial Rayleigh diffraction integral and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian functions, an approximate analytical expression for the propagation equation of vectorial Gaussian beams diffracted at a circular aperture is derived and some special cases are discussed. By using the approximate analytical formula and diffraction integral formula, some numerical simulation comparisons are done, and some special cases are discussed. We find that a circular aperture can produce the focusing effect but the beam becomes the shape of ellipse in the Fresnel region. When the Fresnel number is equal to unity, the beam is circular and the focused spot reaches a minimum.     

Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures

The propagation properties of Bessel beam is a meaningful research. In this paper, based on the expanding the hard-edged circular aperture as a finite sum of complex Gaussian functions and the scalar diffraction theory, an approximate analytical solution for Bessel beam propagating through a fractional Fourier transform system is derived in the cylindrical coordinates. Then, the detailed numerical calculation for Bessel beam is presented. The simulation also shows that the beam parameter and the order of fractional Fourier transform result in the change of field distribution, including location, intensity and width.     

Vibration analysis of a wheel composed of a ring and a wheel-plate modelled as a three-parameter elastic foundation

The free in-plane vibrations of circular rings with wheel-plates as generalised elastic foundations are studied using analytical methods and numerical simulations. The three-parameter Winkler elastic layer is proposed as a mathematical model of the foundation. The effects of rotary inertia and shear deformation are included in the analytical model of the system. The motion equations of systems are derived on the basis of the thin ring theory and Timoshenko?s theory. The separation of variables method is used to find general solutions to the free vibrations. Elaborated analytical models are used to determine the natural frequencies and the natural mode shapes of vibrations of an arbitrarily chosen set of simplified models of aviation gears and railway wheels. The eigenvalue problem is formulated and solved by using a finite element representation for each simplified model. The results for these models are discussed and compared. The proposed solutions are verified by experimental investigation. It is important to note that the solutions proposed here could be useful to engineers dealing with the dynamics of aviation gears, railway wheels and other circular ring systems.     

Analytical formula for a circular flattened Gaussian beam propagating through a misaligned paraxial ABCD optical system

Based on the generalized diffraction integral formula for treating the propagation of a laser beam through a misaligned paraxial ABCD optical system in the cylindrical coordinate system, analytical formula for a circular flattened Gaussian beam propagating through such optical system is derived. Furthermore, an approximate analytical formula is derived for a circular flattened Gaussian beam propagating through an apertured misaligned ABCD optical system by expanding the hard aperture function as a finite sum of complex Gaussian functions. Numerical examples are given.