菲涅耳轴上衍射场的计算

给出了一种计算菲涅耳衍射的方法,它既能比较精确地计算轴上的衍射场,也能用来近似地估算轴外的衍射场。     

菲涅耳-基尔霍夫积分与半波带法分析衍射光谱

惠更斯菲 涅耳原理指出光的衍射本质是无穷多次波的相干叠加.在研究衍射光谱的强度时可使用菲涅耳-基尔霍夫衍射积分进行计算,但该积分的计算较为复杂.为了简化计算而引入菲涅耳半波带的概念,把积分运算简化为振幅矢量的叠加,从而在研究衍射时由菲涅耳-基尔霍夫衍射积分过渡到菲涅耳半波带法.在菲涅耳半波带法中波前上相邻两个半波带到达叠加点的光程差为半个波长,从而导致相位差π.因此相邻两个半波带引起的振动在叠加点发生相消,最终叠加点的光强由发出次波的半波带数目的奇偶性决定.奇数个半波带在叠加点的光强得到加强,偶数个半波带在叠加点的光强发生相消.     

菲涅耳圆孔衍射的解析处理

推导了傍轴条件下菲涅耳圆孔衍射场的级数解,进而讨论了一些具有重要理论和实验意义的问题。     

基于菲涅耳衍射的无透镜相干衍射成像

相干衍射成像是一种新型的无透镜成像技术,在光学测量、显微成像和自适应光学等领域有重要应用．本文提出一种基于单幅菲涅耳衍射强度图样的无透镜相干衍射成像方法;该方法采用特殊设计的卷积可解阵列抽样屏,通过对抽样物波的菲涅耳衍射强度图样进行非迭代的逆菲涅耳变换和滤波等数字处理实现被测物波复振幅信息的恢复,最后通过数字衍射得到物体的数字再现像．文中对抽样孔径、衍射距离、图像传感器尺寸等参数对再现像的影响进行了理论分析和模拟实验研究．发现在针孔大小和记录孔径大小一定的条件下,存在一个最佳的衍射距离;衍射距离过大会给重建图样带来噪声,衍射距离过小则会使再现象的分辨率降低．文中还对抽样针孔大小对系统成像分辨率的影响进行了分析,为进一步开展相关实验研究和应用提供了理论依据．     

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     

菲涅耳圆孔衍射的解析处理

推导了傍轴条件下菲涅耳圆孔衍射场的级数解,进而讨论了一些具有重要理论和实验意义的问题．     

基于半波带分析法的菲涅耳波带片衍射特性的讨论

基于半波带的分析方法简单明了地分析了平行光经菲涅耳波带片衍射后的多焦点特性以及各焦点的光强变化规律．     

菲涅耳公式的几何图示与应用

电磁波通过两种透明介质的分界面时,反射波、折射波和入射波的电矢量分量的大小和方向之间的关系可由菲涅耳公式说明,作通过分析和推导,给出了菲涅耳公式的几何图示,这使得在分析光学问题时,谱得简单和直观。     

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.     

验证菲涅耳圆孔衍射中的一个重要结论

验证菲涅耳圆孔衍射中的一个重要结论温淑珍（黑龙江绥化师专）在菲涅耳圆孔衍射中，如图１，圆孔ＣＣ’露出的波阵面，在与点光源Ｐ０处同一轴上的Ｐ点引起的光振动的振幅”’为其中山和山分别为波阵面上相对于ＰＯ和Ｐ所作的第一个和最后一个菲涅耳半波带单独对该点引起...     

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.     

Propagations of Fresnel diffraction accelerating beam in Schrödinger equation with nonlocal nonlinearity

Accelerating beams have been the subject of extensive research in the last few decades because of their self-acceleration and diffraction-free propagation over several Rayleigh lengths. Here, we investigate the propagation dynamics of a Fresnel diffraction beam using the nonlocal nonlinear Schrödinger equation (NNLSE). When a nonlocal nonlinearity is introduced into the linear Schrödinger equation without invoking an external potential, the evolution behaviors of incident Fresnel diffraction beams are modulated regularly, and certain novel phenomena are observed. We show through numerical calculations, under varying degrees of nonlocality, that nonlocality significantly affects the evolution of Fresnel diffraction beams. Further, we briefly discuss the two-dimensional case as the equivalent of the product of two one-dimensional cases. At a critical point, the Airy-like intensity profile oscillates between the first and third quadrants, and the process repeats during propagation to yield an unusual oscillation. Our results are expected to contribute to the understanding of NNLSE and nonlinear optics.     

相因子判断法分析菲涅耳波带片的衍射场

基于波前相因子判断法,并考虑到波带片孔径的影响,揭示了波带片的衍射场所含基元成分及各成分在衍射场的积分表达式,并导出了沿轴的衍射场振幅分布公式及沿轴的振幅分布曲线,得到多个实焦斑的横向半值线宽和轴向半值线宽公式.本研究为波带片作为一种光学元件提供了一理论基础.     

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.     

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．     

Geometrical theory of diffraction

Geometrical theory of diffraction (GTD) is an alternative model of diffraction propounded first by Thomas Young in 1802. GTD has a long history of nearly 150 years over which many eminent people enriched this model which has now become an accepted tool in the calculation of diffraction patterns. In the conventional Helmholtz-Kirchhoff theory the diffracted field is obtained by computing the net effect of the waves emitted by all points within the area of the aperture. But GTD reduces this problem to one of computing the net effect of waves from a few points on the boundary of the aperture or obstacle, thus simplifying considerably the labour involved in computations. Also the theory can easily be modified to include polarization effects. This has been done specifically by Keller (1962) who exploited the Sommerfeld solution of diffraction of electromagnetic waves at a half plane, making the theory more versatile than the Kirchhoff scalar wave theory. Interestingly the geometry of difffracted rays is predictable from a generalized Fermat principle. According to this the total path chosen by light from the source to the point of observation via the diffracting boundary is an extremum. Historically it should be stated that many of the salient features of GTD were established by a school led by Raman which was active from 1919–1945. Later when Keller (1962) revived GTD independently, he and others who followed him rediscovered many of the results of the Raman school. We have stressed wherever necessary the contributions of the Indian School. We have also discussed certain geometries where GTD can be effectively used. We get some new and interesting results, which can be easily understood on GTD, but are difficult to interpret on the conventional theory of diffraction.     

光栅衍射和布拉格公式

在斜入射光栅衍射中,第k级明纹的衍射角θk随入射角α变化,衍射光偏离入射光的角度φ=f（α）,此函数有极小直点,并且此时以和光栅常数的关系与布拉格公式形式相同．     

一种校正相位测量轮廓术量化误差的算法

为了减小相位测量轮廓术中因数字化设备内部结构的量化处理过程引起的相位量化误差,提高相位测量精度。针对相位测量精度要求较高且表面凹凸变化不大的被扫描物体提出了一种能够有效校正相位测量轮廓术量化误差的算法,测量相位中的每一个像素点利用其相邻像素点进行校正。实验结果显示,校正之后,相位量化误差标准差减小了41.38%,相位测量的精度得到了提高。