Vortex characteristics of Fraunhofer diffractions of a plane wave by a spiral phase plate limited by pseudoring polygonal apertures

We introduce a multilevel spiral phase plate (SPP) limited by a pseudoring polygonal aperture (PRPA). Such an SPP has the advantages of easier fabrication and greater suppression of the sidelobes of the diffraction field over that generated with a polygonal aperture (PA). The Fraunhofer diffraction fields generated by an SPP with a PRPA or with a PA have the same topological charge features and a similar diffraction pattern. Numerical evaluations show that the maximum bright annular-intensity difference between the diffraction patterns for the SPP with a PRPA and that of a PA does not exceed 3% under optimal design parameters.     

Diffraction of a plane, finite-radius wave by a spiral phase plate

We derive analytical expressions containing a hypergeometric function to describe the Fresnel and Fraunhofer diffraction of a plane wave of circular and ringlike cross section by a spiral phase plate (SPP) of an arbitrary integer order. Experimental diffraction patterns generated by an SPP fabricated in resist through direct e-beam writing are in good agreement with the theoretical intensity distribution.     

激光直写制作高阶螺旋相位板及其性能

将拓扑荷为4的螺旋相位光束与平面光干涉的计算全息图输入到空间光调制器中,得到含有多个衍射级次的高阶涡旋光束。为提高衍射效率,利用激光直写技术制作拓扑荷为4的高阶螺旋相位板,经测定,相位板深度理论数值为1.073 m,测量数值为1.082 m,相位板制作误差在0.83%以内。平行光束通过此相位板时,在夫琅和费衍射场获得一个高质量的高阶光学涡旋,光强分布与理论数值基本吻合,衍射效率达到86%。     

Diffraction equations for weak scattering reflective surface

In order to investigate the surface roughness dependence of speckle patterns, the complex-amplitude distribution of the speckle field should be obtained first. In previous studies, most investigators have treated this problem using the Fresnel or Fraunhofer diffraction equation. But for a weakly scattering reflective surface, when the observation plane is not parallel to the object plane, the Fresnel and Fraunhofer diffraction equations become inapplicable. Therefore, a reflective surface diffraction model (RSDM) is formed. When the difference between the RSDM and the transmission aperture diffraction model (TADM) is considered, then a general diffraction equation is presented. Considering the variations of the near-field approximation caused by coordinate system rotation, the near-field diffraction equation is derived. By introducing the far-field approximation, the far-field diffraction equation is obtained. The physical meanings of factors in the new equations are interpreted. Comparisons between the Fresnel and Fraunhofer diffraction equations and the newly derived ones show that the former are just the special cases of the latter. Finally, an application of these new diffraction equations is proposed.     

A theoretical method based on Fourier spectrum analysis for the focusing performances of the X-ray compound refractive lenses

It is important to predict the intensity distribution in focusing plane for designing the X-ray compound refractive lenses. On the basis of analyzing the structure of X-ray compound lenses and comparing it with Fraunhofer diffraction system, it is concluded that the X-ray focusing system can be regarded as a kind of Fraunhofer diffraction system. Therefore, a method based on Fourier spectrum analysis is presented to predict the intensity distribution in the focusing plane for the X-ray lenses. A brief analysis on the relationship between the parameters of X-ray lenses and their focusing performance is also given in this paper.     

Modeling Fraunhofer diffractive characteristics for modulation transfer function analysis of tilted ring metallic mesh

In order to analyze the Fraunhofer diffractive characteristics and modulation transfer function (MTF) of a tilted ring metallic mesh, an optical intensity distribution model of Fraunhofer diffraction is built using Huygens–Fresnel diffraction theory and the diffraction integral is carried out directly in the tilted mesh plane. The diffraction characteristics of the tilted ring metallic mesh are in good agreement with experimental results, which proves the correctness of the model established. MTF of an optical system with metallic mesh is calculated based on the model established and Fourier transform. Analysis shows that the degradation of MTF caused by diffraction of a ring mesh is much less than that of a square mesh whether they are vertical or tilted to the optical axis. Therefore, ring mesh can provide higher imaging quality than square mesh when they are used as high-pass filters in optical windows. A tilted array diffraction modulating factor is abstracted and believed useful in the analysis of diffractive characteristics of tilted square mesh and ring mesh, and it can be extended to Fraunhofer diffractive characteristics analysis of other tilted diffraction arrays.     

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．     

Numerical computation of in-plane displacements and their detection in the near field by double-exposure objective speckle photography

A model of a rough surface to the scale of the optical wavelength is proposed, with randomly distributed zero-mean Gaussian heights. It is assumed that the aforesaid surface is illuminated by a coherent light beam of homogeneous intensity. An in-plane pure translation of this surface is simulated on a PC by means of the Matlab program. In the near-field optical regions the Fraunhofer approximation and the subsequent FFT are not suitable for application in the generation of a speckle pattern. Hence, with the aim of calculating the translation of the rough surface by means of double-exposure objective speckle photography using the point-wise filtering technique (PWFT), the Fresnel-Kirchhoff integral is first employed to obtain the speckle intensity near the surface on a photographic plate, and then the intensity pattern produced by the diffraction of the plate is determined in the far field (Fraunhofer), which suffices to calculate the modulus of displacement through the Young’s fringes. The results are analyzed according to surface roughness and the sample distance to the recording plane.     

Distinguishing between Fraunhofer and Fresnel diffraction by the Young's experiment

Theoretical considerations, simulations and experiments have been carried out to distinguish between Fresnel and the Fraunhofer diffraction regarding the formation of interference patterns by a conventional Young's double-pinhole arrangement with variable separation, which is illuminated by a coherent plane wave. We show that the optical path difference introduced by this setup fits the Fresnel's phase difference between the pinholes. Consequently, it is possible to determine the number of Fresnel zones subtended by a circle centered on one of the pinholes and with radius equals to the pinhole separation. Then, we propose a criterion for distinguishing between Fresnel and Fraunhofer diffraction based on this number of Fresnel zones, which is applicable for diffracting apertures with any shape.     

计算机模拟任意形状衍射屏的衍射

把菲涅耳衍射积分化为含快速傅里叶变换的积分,对任意形状衍射屏的衍射进行模拟,其特点是直接用含快速傅里叶变换的积分求解出不同传播距离观察屏上的光场分布,得出菲涅耳衍射和夫琅禾费衍射的衍射花样.通过计算机对常见的缝孔的衍射的模拟,有助于理解衍射光在传播方向上近场衍射和远场衍射的不同和衍射花样的分布特征.     

Three-dimensional analysis of scattering by pressure-release plane surfaces and the validity of the image solution

Because of the complexity of the scattering integrals in three dimensions, numerous approximations are used to obtain closed-form solutions. By considering the scattering by an infinite, pressure-release plane surface, the effects of various phase approximations and source directivity approximations can be examined independently of the surface roughness. Calculations are carried out using the Fraunhofer and Fresnel phase approximations, and two directivity approximations. It has been shown experimentally that the image solution is valid for the reflection of an acoustic beam by an infinite, pressure-release plane surface if the plane is in the farfield of the source. Consequently, the image solution is used to compare analytical solutions obtained using various phase and directivity approximations, and it is found that both the Fresnel phase approximation and a realistic directivity approximation are required to achieve a good fit. The solution produced by the Fraunhofer phase approximation is obtained as an asymptotic limit of the modified Fresnel solution. Criteria for the validity of the Fraunhofer and Fresnel phase approximations are developed. The Fresnel phase approximation is valid under fairly broad conditions, but the Fraunhofer phase approximation is never valid for an infinite plane surface that must be in the farfield of the source.     

Fraunhofer diffraction of a plane wave by an elliptical annular aperture with offset or tilt

Fraunhofer diffraction field through an elliptical annular aperture is obtained for plane wave incidence when there is offset or tilt of the inner ellipse. The effects are observed through the field distribution.     

Experimental evidence of the phase reversal in diffraction patterns

In a diffracted wavefield occurs in patterns phase variations. The most familiar example is the Fraunhofer diffraction pattern through a single slit: the theory predicts that the side bands of the diffraction pattern alternate in phase. This paper deals with phase reversal phenomenon in diffraction patterns. Two interesting systems are recognized: the diffraction through a half plane and the diffraction through a single slit.     

菲涅耳衍射区和夫琅和费衍射区的动态部分相干光散斑场特性

研究了菲涅耳衍射区和夫琅和费衍射区动态部分相干光散斑的特性.利用部分相干光互强度传播的理论，得出了在部分相干光照明时，由运动散射体产生的动态散斑光强时空交叉的自相关函数的一般形式，并由此得出了散斑沸腾和平移的一般规律.通过适当选择光源和调整光路参数，在实验上得到了菲涅耳和夫琅和费衍射区的部分相干光散斑，对夫琅和费面上的动态部分相干光散斑的平移和沸腾现象进行了定性研究；采用光子计数及数据自动采集的方法，对部分相干光散斑随时间的演化及动态部分相干光散斑的沸腾进行了定量测量.这些实验结果与理论结果相符合. 关键词： 部分相干光动态散斑 时空交叉相关函数 沸腾     

Geometrical-numerical approach to diffraction phenomena

The calculation of diffracted fields is considered by means of a geometrical analysis of the incoming wave into semiperiodic zones in the aperture plane, followed by a numerical process for addition of the contributions corresponding to the semiperiodic zones. This general approach constitutes a novel interpretation of diffraction phenomena that permits exact evaluation of the mathematical expressions of diffraction theory and overcomes the limitations of any approximation. The method is illustrated by analysis of two important configuration in optics: the pinhole camera, for which we deduce the optimum radius for imaging, and the diffraction of a spherical converging wave through a circular aperture, from which we determine the limit of the validity of the Fraunhofer approximation (i.e., of the Airy pattern) and the influence of the obliquity factor.     

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     

Lensless imaging of an arbitrary object

A new class of imaging systems that do not require the use of lenses or similar optical devices is introduced and theoretically investigated. In particular, it is demonstrated that, if an arbitrary plane object is illuminated by an appropriate spherical wave front (generated from a monochromatic point source), then a magnified image of the object intensity distribution can be observed in any transversal plane along the light-propagation direction within the far-field (Fraunhofer) diffraction region. The phenomenon is based on the fact that, under certain conditions, the spherical wave front can modify the energy's angular spectrum of the field distribution in the object plane such that this spectrum replicates the spatial intensity distribution of the object.     

Plane-wave analysis of the near field of light diffracted by ultrasound.

Although the phenomenon of light diffraction by ultrasound has been studied very extensively during the last 40 years, almost all investigations were concentrated on the individual far field (Fraunhofer) diffraction orders. In the present paper, the basic theory is developed for studying the near field (Fresnel region) of light diffracted by an arbitrary plane ultrasonic wave and the fundamental periodicity properties are stated. The general plane-wave theory of Raman-Nath has been taken as a starting point. From the analysis, the near field of the diffracted light is seen to be highly sensitive to variations of the ultrasonic amplitude and this feature provides a useful technique for observing weak ultrasonic waves. In particular, for the specific case of Raman-Nath-type diffraction, a procedure is presented allowing the reconstruction of the time waveform of the ultrasonic wave from the diffracted light intensity signal.     

夫琅禾费衍射的光谱特性

基于MATLAB语言,以夫琅禾费衍射为研究对象,数值模拟了夫琅禾费圆孔衍射和单缝衍射光谱特性,通过改变狭缝宽度和入射波的波长,数值模拟得到夫琅禾费单缝衍射的光强变化图和光谱特性图。结果表明,圆孔衍射的光强比单缝衍射的光强曲线在次级明纹的强度更加低,夫琅禾费衍射的结论与实际理论和试验吻合的较好。研究结果为夫琅禾费衍射的研究提供参考。     

夫琅禾费圆孔衍射斑动态叠加过程的计算机模拟

本文介绍了利用面向对象的程序设计方法实现计算机模拟夫琅禾费圆孔衍射的具体过程，给出了用计算机模拟两个夫琅禾费圆孔衍射斑动态叠加过程的具体方法。