Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.     

Fresnel diffraction of solitons in the Synge model

The problem of Fresnel diffraction of complex scalar solitons by an infinite rectilinear slot in an absorbing screen is considered. The intensity of the scattered solitons is computed in a first approximation of perturbation theory, and the ratio between the characteristic dimension of the soliton and the slot width is taken as the smallness parameter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–38, January, 1982.     

Effects of mask-alignment error on point spread function for multi-level Fresnel diffractive lenses

The full aperture complex amplitude transmittance function of a multi-level diffraction lens with maskalignment errors was derived based on scalar diffraction theory. The point spread function(PSF) was calculated by the Kirchhoff diffraction integral. It is found that the radius of the Airy disk increases with the increase of the error in the direction of misalignment, and the image center shifts along the direction of misalignment. A fourlevel diffractive lens with a diameter of 80 mm was fabricated, and its PSF and diffraction efficiency of +1 st order were calculated and measured. The distribution of PSF is consistent with the calculated results, and the tested diffraction efficiency is slightly smaller than the calculated value; the relative error is 5.71%.     

Fresnel diffraction model for mode-mismatched thermal lens with top-hat beam excitation

A theoretical model, based on the Fresnel diffraction integral, is developed to describe the thermal lens (TL) signal in a mode-mismatched collinear configuration, which is optimized for a near field detection scheme and excitation by a cw modulated laser beam with a top-hat profile. The TL amplitudes obtained with both top-hat and Gaussian beam excitations are numerically computed and compared, and the dependence of the TL amplitude on the experimental parameters is discussed. Numerical results show that the top-hat beam TL instrument is more sensitive than the Gaussian beam TL instrument, with a potential doubling of the sensitivity. The use of the top-hat beam excitation with TL detection is a significant improvement because a top-hat beam can be easily obtained with a low-cost, wide-spectral emission white-light source. The use of incoherent light sources as the excitation sources would substantially expand the applicability of the TL technique to the general area of chemical analysis.This revised version was published online in March 2005. In the previous version, the published online date was missing     

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．     

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     

Fresnel diffraction on the edge of causality

Taking advantage of the slow optical response of low-temperature rare earth ion-doped crystal, we explore the similarity between causality and Fresnel diffraction by a straight edge. We relate these features to spectral resolution and selectivity. The concept is illustrated with experimental data.     

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.     

对激光单缝衍射光强分布测量实验的改进

分析了目前单缝衍射光强分布测量中存在的问题,给出了改进后的测量方法。     

On the Fresnel diffraction pattern of phase holographic gratings

The Fresnel diffraction pattern of phase diffraction gratings is studied on the example of idealized sinusoidal relief-phase plane holographic thermoplastic gratings. It is shown that, in the region of low spatial frequencies, which are more than two times lower than the inverse wavelength of the reading coherent radiation, the intensities of the main diffraction maxima, the diffraction efficiency, and the light-scattering power are independent of the spatial frequency of the phase gratings under investigation, which are characterized by a sinusoidal law of modulation of the reading-radiation phase. It is established that the range of spatial frequencies at which a plateau is observed in these dependences increases with decreasing amplitude of the phase modulation of the reading light. These dependences are also observed to have similar character for the thermoplastic holographic gratings under study. Calculations were performed to analyze the influence of real profiles of thermoplastic strain on the diffraction efficiency and light-scattering power of such gratings. On the basis of analysis of the results obtained, recommendations on using holographic and raster techniques of recording data on phase carriers are given that make it possible to improve the quality of the restored optical image.     

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.     

Self-consistent diffraction in the multiperipheral model (II)

We present a self-consistent solution to a multi-peripheral model in which the triple pomeron vertex vanishes. This solution possesses all of the good features of our previous model, having naturally diffractive and multiperipheral terms in the total cross section and in particle production. In addition, its region of validity has been increased to include the normal Regge region and a smooth transition from Regge-like behavior to the diffractive limit is obtained.     

Self-consistent diffraction in the multiperipheral model (IV)

Numerical fits to high-energy proton-proton scattering data are made using formulae obtained previously from a self-consistent solution to the multiperipheral model. Agreement with the total cross section and elastic differential cross section is satisfactory.     

Optical testing of ultrasonic phase gratings using a Fresnel diffraction method

A simple optical method is proposed for studying the Raman-Nath parameter of plane, sinusoidal, ultrasonic beams. The Fresnel diffraction field of a continuous ultrasonic grating illuminated by a collimated laser beam is measured by a photodetector placed mid-way between the self-image planes of the grating. Measurement of the amplitude of the fundamental of the output signal enables the absolute determination of the depth of phase modulation. A comparison of the proposed method with the techniques discussed in the literature is presented.     

对实屏的夫琅禾费衍射中心亮点(亮纹)的半定性半定量论证

光经圆盘、细丝等实屏衍射后,衍射光场中其几何阴影中心有不为零的光强分布.显然这是阐述光的波动性的最好例证,它比圆孔、单缝之类的光孔衍射更具说服力.然而对圆盘等的衍射中心亮点(如泊松点)的论证通常都是从菲涅耳衍射出发,但是在绝大多数非物理类专业的大学物理中,对光的衍射的具体分析都只涉及夫琅禾费衍射,因而给学生对于上述问题...     

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.     

Local transverse diffusion of light due to laguerre laser beam diffraction

When shading half of a Laguerre laser light beam with a semi-infinite metal screen with an imperfect edge the effect of fine structure formation in a transverse diffusion of “half-beam” light and its further evolution in the process of half-beam space propagation were experimentally revealed.     

Two-dimensional diffraction calculations for a fast-flow CO laser

Conclusion We have developed, a two-dimensional diffractive model of a free-flow CO:N₂ laser, using a detailed kinetic model of the active medium.We have shown that the constant-gain model and the diffractive model yield practically the same calculated energy characteristics of a free-flow CO laser. Calculation of the spectral characteristics has shown that the diffractive model yield the same numbers and intensities of the rotational-vibrational transitions on the cavity axis as the model with constant gain. We have determined the errors incurred in calculations by the constant-gain model.At an active-medium density 0.25 Amagat the angular divergence of the radiation is determined by the large-scale inhomogeneity of the subsonic gas flow while the radiation directivity in the far zone is manifested by a noticeable angular shift and is split.Translated from Preprint IAE-5724/11, Kurchatov Institute of Atomic Energy, Moscow, 1990.