高斯光束圆孔衍射光强分布的解析解

本文从菲涅尔-基尔霍夫衍射公式出发,结合贝塞耳函数等特殊函数的性质,计算了正入射高斯光束圆孔衍射的光强分布,并以洛默尔函数的形式表示了焦点附近的光强分布.之后选取了几何焦平面、光轴以及几何阴影区域边界这三个特殊区域,理论结合数值方法给出了光强分布的解析表达式以及数值结果,并发现高斯光束束腰半径越小,艾里斑半径越大,同时焦深也越大.最后计算了焦平面上的光强积分强度,结果表明束腰半径越小,光强就越向中心集中.同时高斯光束相较于平面波的衍射,不会改变光强分布的整体轮廓,但会使得光强向焦点处集中.     

阿达玛光谱仪的入射狭缝选择方法研究

为了确定光谱仪的入射多狭缝结构设计的可靠依据,研究了4种阿达玛S型狭缝阵列发生衍射后的光强分布.采用MEMS加工技术制作出最小狭缝单元为6 μm×6 μm的一体式微硅片阿达玛狭缝阵列,对3种S7型狭缝和一种S15型狭缝进行比较.首先利用阿达玛矩阵构造狭缝阵列的孔径函数,得到了衍射后的光强分布函数;然后运用Matlab软件对光强分布函数仿真,获得了符种狭缝衍射后的光强分布图及光通镀对比.搭建了试验装置进行验证,试验表明实际衍射光强分布及光通量间的比值都与仿真结果相符.最后分析了狭缝结构参数对光强分布的影响,总结了S型狭缝阵列衍射规律.所提出的衍射光强分布方法,为光谱仪中入射狭缝的选择与设计提供了理论依据,为实际应用提供了有价值的参考.     

用于光束整形的多功能衍射相位板的设计

提出一种设计多功能衍射相位板的随机搜索和模拟退火混合设计方法利用这种方法,通过采用多个评价函数,可设计出在不同观察面上同时产生所需光强分布的衍射相位板设计用于高斯光束整形的多功能衍射相位板可以在焦面上产生高能量利用率、小旁瓣的光强分布,同时在离焦面上获得具有良好顶部均匀性的光强分布该方法提高了衍射器件的设计灵活性,对于设计同一块器件在光路的不同位置产生所需的光强分布提供了新的思路,在激光武器、激光加工和激光手术等领域有广阔的应用潜力.     

边界衍射波理论公式的准确性数值分析

利用数值分析的方法分析了由边界波理论公式所得的圆形光阑衍射场的光强分布.通过对边界波理论公式所得的光强分布曲线,对几何照明区与阴影区的光强分布曲线与面衍射积分公式所得的光强分布曲线进行比较,分析了边界波理论公式对衍射场描述的准确性.     

MATLAB辅助的多缝夫琅禾费衍射分析

根据衍射的基本理论,利用Matlab软件的计算功能和绘图函数,研究了单缝衍射和多缝衍射的光强分布曲线及衍射图样,分析了各参数衍射结果的影响.     

用实函数直接计算光栅衍射的光强分布

给出了依据惠更斯-菲涅耳原理,用实函数积分直接导出光栅衍射在光屏上任一点的合振动的表达式以及光强分布函数的方法.     

夫琅和费衍射颗粒粒度测量中的改进Chin-Shifrin反演算法

在基于线阵CCD的夫琅和费衍射颗粒粒度测量中,采用Chin-Shifrin积分变换反演算法使得反演的粒度分布出现假峰现象.为解决此问题,提出在该Chin-Shifrin积分变换反演算法中引入矩形窗函数,并在分析颗粒粒径与衍射光强导数最小值之间关系的基础上,确定矩形窗函数中心点位置及左右边界,利用该矩形窗函数对粒度分布进行截断处理,消除虚假峰,提高反演颗粒粒度分布的准确性.分别对两种标准颗粒进行了测量,并对不同算法的反演结果进行了对比.实验结果表明:引入矩形窗函数的改进Chin-Shifrin算法,能够有效排除粒度分布中的多假峰;粒度分布测量相对误差小于3%,重复性小于4%.     

细丝Fresnel衍射光强分布函数的推导

本文给出了Ｆｒｅｓｎｅｌ积分的函数解，并推导出细丝Ｆｒｅｓｎｅｌ衍射的光强分布函数。     

圆屏(球)和圆环菲涅耳衍射的解析表达式

在标量衍射理论的基础上，给出了圆屏（球）和圆环菲涅耳衍射的振幅及光强解极表达式。计算了光强分布曲线，并将计算实例和有关资料中的实验与计算结果进行了比较。同时指出所谓无衍射光束实际上是一种菲涅耳衍射现象。     

双胶子交换模型中J/ψ的衍射产生

利用双胶子交换模型并结合重夸克偶素的色八重态产生机制,计算了π与p碰撞过程中J/ψ的衍射产生总截面.结果发现:随着质心系能量的增加,J/ψ衍射产生的总截面逐渐增大;并且,不同的π介子中的胶子分布函数给出的总截面偏离也逐渐加大.计算结果与未来的实验数据比较,可以检验π介子中的胶子分布函数及双胶子交换模型.     

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.     

Beam spreading of truncated Gaussian beams in Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the hard-edge aperture function expanded as the sum of finite-term complex Gaussian function, analytical expression for average intensity of truncated Gaussian beam in Kolmogorov turbulence is derived, and some limiting cases are discussed. The influences of many factors, such as Fresnel number, wavelength, truncation parameter and structure constant on beam spreading are studied with the help of the average intensity formula. We found that the peak value of average intensity decreases and the beam spot spreads with the decrease of Fresnel number. The change of peak intensity against Fresnel number is slower with large aperture than that with small aperture. When Fresnel number is not small enough the influence of turbulence on intensity profiles is so small that can be neglected if structure constant is small.     

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.     

Axial intensity distribution behind a Fresnel zone plate

An analytical expression based on an improved Rayleigh–Sommerfeld diffraction formula with evanescent term is derived for analyzing the axial light intensity distribution throughout the whole space behind a Fresnel zone plate. The effects of the number of Fresnel zones and the size of aperture on the axial intensity distribution are calculated for two kinds of Fresnel zone plate with larger and smaller aperture. The validity of the general formulae for calculating the focal lengths and the relative intensities of the foci of a Fresnel zone plate is analyzed.     

X光能点、放大倍率及针孔尺寸对空间分辨的影响

X光针孔成像是惯性约束聚变(ICF)研究中重要的诊断方法,对其点扩散函数的计算可用于图像重建和系统空间分辨的判断。对菲涅耳衍射公式进行了化简,分析了X光能点、针孔尺寸及放大倍率对针孔点扩散函数的影响。实验在保证成像能获得足够高信噪比的条件下,通过模拟获得在最佳空间分辨时所要的针孔大小、放大倍率和X光能点等参数。在流体力学不稳定性的静态样品定标实验中,通过模拟获得了针孔的调制传递函数(MTF),结合实验测量的结果反推获得分幅相机本身的MTF值。同时采用测刀边函数的方法获得了分幅相机本身的刀边函数,进而得到相机在各空间频率下的MTF值。两种方法得到的分幅相机MTF值一致,验证了通过菲涅耳衍射模拟X光针孔成像的可行性。     

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.     

菲涅耳衍射解析表达式的物理意义

文中讨论了圆孔菲涅耳衍射解析表达式的物理意义,指出了精确解(在菲湿耳近似下)与近似解的区别,并与用数值积分法计算的结果进行比较,证明了圆孔菲涅耳衍射解析表达式的正确性。     

平面波经小圆孔非傍轴衍射的轴上光强解析分析

用亥姆霍兹 基尔霍夫积分定理和基尔霍夫边界条件,推导出了平面波经小圆孔非傍轴衍射时轴上强度的简单解析表达式,研究了平面波经小圆孔后整个衍射空间非傍轴的轴上光强分布.给出了计算圆孔菲涅尔数的精确公式,重新检查了通常的菲涅尔数公式的有效性.数值计算显示,应用解析表达式所得的结果与应用衍射积分公式所得的结果完全一致.     

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.