Partially coherent Fresnel diffraction by a slit aperture. III. Fresnel diffraction patterns

The intensity distribution in the Fresnel diffraction pattern of a slit aperture illuminated with partially coherent light is obtained, as a function of the coherence condition across the aperture, by evaluating the formula developed in a previous paper. It is shown that the Fresnel diffraction pattern is affected by the coherence condition of illumination across the aperture and its form.     

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.     

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.     

Partially coherent diffraction by a defocused slit aperture in the presence of image motion and transverse vibrations

This paper presents an analysis of the far-field diffraction pattern of partially spatially coherent light by an optical system with a defocused slit aperture in the presence of linear image motion and sinusoidal transverse vibrations. For partially coherent light sinc and gaussian forms of correlations in the two points over the diffracting aperture are employed. The results for the irradiance distribution have been presented graphically for typical values of the coherence, defocusing and vibrational parameters.     

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.     

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.     

Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination

Analytical expressions for the spatial distribution of the spectral density and intensity of projection images are derived for a broad class of object transmission functions in the case of partially coherent Schell-model-type incident illumination. The expressions are linear with respect to the phase distribution in the transmitted wave. Associated methods for phase retrieval are discussed with the emphasis on a technique that allows simultaneous “automatic” phase retrieval and deconvolution of projection images of homogeneous objects by means of mutual cancellation at a specified defocus distance of the Fresnel diffraction effects and the image blurring due to the point-spread function of the imaging system.     

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.     

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.     

Effect of partially space coherent illumination on the performance of a defocused optical system with a slit aperture

The focusing properties of an aberration free defocused optical system with a slit aperture have been investigated in the case of quasimonochromatic partially space coherent light. The point spread function has been plotted for sinc and gaussian forms of the mutual coherence function. In certain cases, partially coherent illumination results in an improved performance of the system.     

Shaping the beam profile of a partially coherent beam by a phase aperture

By use of a tensor method, an analytical formula for a partially coherent Gaussian Schell-model (GSM) beam truncated by a circular phase aperture propagating through a paraxial ABCD optical system is derived. The propagation properties of a GSM beam truncated by a circular phase aperture in free space are studied numerically. It is found that the circular phase aperture can be used to shape the beam profile of a GSM beam and generate partially coherent dark hollow or flat-topped beam, which is useful in many applications, e.g., optical trapping, free-space optical communication, and material thermal processing. The propagation factor of a GSM beam truncated by a circular phase aperture is also analyzed.     

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.     

在Jaynes-Cumming模型中相干态的相位对量子相干性的影响

基于J-C模型,研究了相干迭加光场与二能级原子相互作用时的量子动力学行为,讨论了迭加态的相位对原子的量子崩塌-回复特性的影响.     

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.     

Point source diffraction by a slit in a moving fluid

The diffraction of a spherical acoustic wave generated by a point source from impedance slit in a moving fluid is investigated. The diffracted wave is calculated in the far field regime as a sum of fields produced by the edges of the slit and an incident field. The Myers’ impedance conditions are assumed along the edges of the slit. Such conditions are well adopted for the boundaries of the impedance barriers and yield reliable predictions of the diffraction patterns. A Wiener–Hopf technique is invoked to resolve the problem in combination with Fourier transform techniques and asymptotic analysis. The appositeness of the results and the effect of pertinent physical parameters on the separated field are presented and analyzed graphically.     

Diffraction loss analysis of a plane-parallel optical cavity with a phase step and a slit aperture

A model for calculating the round trip diffraction loss in a plane-mirror cavity with an intracavity phase step and an infinite slit aperture is developed. The round trip remaining intensity fraction for the low order transverse cavity modes can be calculated for any given location of the slit aperture and the phase step along the cavity and for any given phase delay on the phase step. The diffraction loss on the slit aperture is found to be a periodic function of the phase delay on the phase step. Transformation of the lasing spectrum emitted from a broadband pulsed dye laser on moving the phase step along the oscillator cavity is reproduced theoretically. The lasing spectrum affected by the phase step is interpreted as the wavelength dependence of the remaining intensity fraction for the principal transverse mode.     

Flexible coherent diffraction lithography by tunable phase arrays in lithium niobate crystals

Flexible coherent diffraction lithography is proposed and preliminarily tested by means of an optical phase mask. The phase mask consisted of a two-dimensional hexagonal lattice of reversed ferroelectric domains engineered in a z-cut lithium niobate substrate and was electro-optically tunable. Appropriate phase shift values across adjacent reversed domains were induced by the application of an external electric field along the z-axis of the crystal via transparent electrodes. Photolithographic exposures of the self-imaging near-field diffraction intensity patterns, at various planes corresponding to the Talbot distances, were performed by using different values of the driving electric field signal.     

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     

Noniterative phase retrieval from a single diffraction intensity pattern by use of an aperture array

A noniterative method for retrieving the phase of a wave field from a diffraction intensity measurement in a coherent wave field is proposed. In this method, the phase can be calculated from analytic equations based on the properties of entire functions by use of Fourier transforms. This method requires only a single measurement of the intensity of a diffracted wave through an array filter of rectangular apertures and then does not need to use any lens systems and coherent reference waves. Therefore, it provides a potentially useful means for coherent imaging in a wide class of wave fields such as optical, x ray, electron, and atomic waves.     

部分相干光照明下光栅的塔尔博特效应

首先利用部分相干光理论详细地分析了在部分相干光照明下光栅的菲涅耳衍射,给出了观察面上衍射光强分布的一般公式,并就光源的发光面积对光栅塔尔博特效应的影响进行了讨论,得到了光栅衍射光强的分布随着照明光源的发光尺寸的增加而逐渐变得平滑这一结论．并且,当光源发光尺寸增加到毫米量级时,光栅的塔尔博特效应将完全消失。在实验上埘不同发光尺寸的扩展作相干光源照明光栅时的菲涅耳衍射光强进行了测量,实验结果与理论分析得出的结论相符合。