Partially coherent Fresnel diffraction by a slit aperture. II. Axial intensity distributions

The general formula derived in a previous paper is applied to obtain the intensity distribution along the axis normal to a slit aperture in the Fresnel diffraction field when the spatial mutual coherence function of the illumination over the aperture takes three different forms of correlation. It is shown that the axial intensity distribution of Fresnel diffraction by the slit aperture is effectively influenced by the coherence condition across the diffracting aperture.     

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.     

Partially coherent Fresnel diffraction by a slit aperture. IV. Effect of the phase term in the coherence function

A formula was derived in paper 1 of the this series for investigating the Fresnel diffraction field of a slit aperture when the mutual coherence function of the illumination contains a quadratic phase term. That formula is applied to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source. The phase term has a big effect on the features of Fresnel diffraction.     

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.     

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.     

关于菲涅耳衍射图样相似性的分析与讨论

与夫琅禾费衍射不同,菲涅耳衍射图样对于给定波长,当衍射距离变化或输入图像几何缩放时一般都不具有相似性.但我们的分析表明,若波长、衍射距离和输入图像几何线度诸参数满足一定关系,或对于某些特殊类型孔径,菲涅耳衍射图样有可能彼此相似.本文导出了在上述诸参数发生变化时菲涅耳衍射图样保持相似性的普适条件,以及此时衍射图样大小与诸参数的定量关系,并对包括圆孔衍射和直边衍射等情况都得到了一系列有价值的推论.     

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。     

Acoustically modified optical Fresnel diffraction by a slit and a periodic object in relation to periodic partial coherence

Optical Fresnel diffraction by a slit and a periodic rectangular wave object, illuminated with accoustically phase-modulated laser light, is investigated in association with partial coherence. The periodic partial coherence, produced by acousto-optic interaction, much deformes the Fresnel diffraction patterns of the respective objects. A nearly flat-top diffraction pattern by the slit is obtained if the acoustic and slit parameters are adjusted. The self-image by the periodic rectangular wave object is reversed in contrast if the acoustic power exceeds a critical value.     

菲涅耳圆孔衍射计算机模拟演示的实现

为了克服菲涅耳衍射积分计算的复杂性和因光波频率高而导致的采样点数目巨大两大难题,利用Hankel变换算法,将二维计算变换为一维计算,并利用球面波因子处理,在普通PC上实现了菲涅耳圆孔衍射的计算机模拟演示．     

Non-modified propagation of optical mutual intensity in the Fresnel diffraction region

The propagation problem of mutual intensity from a source plane to an object plane is discussed. The propagated mutual intensity remains unmodified in any object plane in the paraxial approximation region of Fresnel diffraction if the mutual intensity in the source plane is space-invariant and propagated to a region of interest around the propagation axis in which the Fresnel diffraction effect by the edge of an aperture in the source plane is almost negligible.     

Partially coherent fresnel diffraction by a slit aperture. 1. Theoretical analysis

A formulation is developed for investigating the intensity distribution of Fresnel diffraction by a slit aperture illuminated with partially coherent light. The formulation is further extended to the case that the complex degree of coherence of the illumination contains a quadratic phase term.     

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．     

Intensity and phase distribution in deep Fresnel diffraction region generated by multi-pinhole aperture

The Kirchhoff diffraction theory is applied to the multi-pinhole aperture diffraction screens, and the intensity, the zero-contour of the real and imaginary parts of complex amplitude and the phase distribution in deep Fresnel diffraction region are simulated. It is found that the number of bright spots, the zero-contours of the real and imaginary parts of complex amplitude and the phase singularities are all related to number of pinholes in diffraction screens. The brightness of bright spots in center of each pattern would become larger with increasing number of pinholes. In addition, there are many lines, on which the intensity value is close to 0.     

A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.     

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.     

Enhanced harmonic generation efficiency using focussing devices based on Fresnel diffraction

We propose the use of focusing devices based on Fresnel diffraction (such as a Fresnel zoneplate) as a means to enhance the efficiency of nonlinear-optical processes starting from radiation in the ultraviolet region, where ordinary lenses cannot be used. We present experimental results of a proof-of-concept experiment involving the efficient generation of second-and third-harmonic laser radiation in the visible range. An enhancement of a factor 6 in the third-harmonic yield is obtained by simply limiting the laser beam with a circular aperture. Higher enhancement factors (up to 16) are obtained using a Fresnel zoneplate. The experimental findings are in good agreement with the results of a simple theoretical analysis.     

A fresh outlook for Fresnel diffraction

Fresnel theory, with certain level of assumptions, explains satisfactorily observed diffraction patterns. It is a scalar theory and basically it deals special way of superposition of fields originated from several points of Huygens wave front. In the present paper a total new approach is proposed according to which the interacting electric fields are not originated from the secondary emitters of the same wave front, instead, they are originated from the successive Huygens wave fronts. The proposed approach is explained with the help of the circular aperture. This new view supports Fresnels theory without a set of assumptions.     

The iterative Fresnel integrals method for Fresnel diffraction from tilted rectangular apertures: Theory and simulations

We applied the iterative Fresnel integrals method for the numerical computation of Fresnel diffraction patterns from rectangular apertures tilted at an arbitrary angle to the optical axis. Detailed theoretical formalism is developed and discussed, and then is applied for the numerical computation and simulation of the actual diffraction patterns for an arbitrary optical configuration. The generated intensity distributions (images) show distortion and stretching in the direction of the tilt, but not in the other orthogonal direction. Significant decrease of the intensity is also predicted and observed, the decrease being proportionate with the tilt angle. The simulated images qualitatively resemble those published in the literature. In addition to single-axis tilts, simultaneous rotations (tilts) of the aperture in two orthogonal coordinate axes were also briefly considered and simulated.     

大孔径会聚光束的圆孔和圆屏衍射及其反演变换

实验中发现,经常使用的大孔径会聚光束的圆孔和圆屏衍射图样不同于一般的菲涅耳圆孔和圆屏衍射图样.通过对这种光束进行的实验性研究发现,这是一种由球差引起的畸变了的会聚球面波光束.解释了衍射图样的形成,证明了这种光束的衍射图样中存在反演变换关系.利用这种光束可以对微小的衍射物体进行反演放大.     

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