傅里叶变换的局限性及其改进方法

从对傅里叶变换的局限性分析入手 ,揭示了窗口傅里叶变换、小波变换和分数傅里叶变换的出现是傅里叶变换本身发展的必然 ,阐明了其改进方法产生的原因及其优缺点 ,分析了其改进方法与傅里叶变化的关系 ,这些有助于加深对傅里叶变换的认识。     

快速傅里叶变换的并行计算

本文是"快速傅里叶变换向量化程序包"研制工作的部分内容,主要介绍一维、二维复数据快速傅里叶变換的并行计算方法及其计算效率。在银河机(YH—1)上的计算实践表明,向量运算比相应的标量运算,平均可提高功效数十倍。     

傅里叶变换光谱仪中的主要技术环节

本文总结了在研制傅里叶交换光谱仪(FTS)或成象傅里叶变换光谱仪(IFTS)时应当考虑的主要技术环节,包括仪器函数、光谱分辨率、扩展光源、动镜运动误差、噪音等效功率、信噪比等,并给出相应计算公式.     

空间采样傅里叶变换光谱仪光谱反演研究

根据相似性准则,对采集到的干涉图像进行干涉图元的拆分,通过寻址定位,得到与离散光程差序列相匹配的采样干涉图序列。采用过零采样方式,对大单边干涉图序列与小双边干涉图序列利用不同的窗函数进行切趾。为了校正相位误差,结合所研究采样干涉图的特点,对频域光谱乘积校正和空域干涉图卷积校正进行了研究和改进,获得了比较理想的光谱线形,其中空域干涉图卷积校正后的光谱偏差仅为0.012088,具有最好的校正效果。     

傅里叶变换轮廓术中频谱泄漏的讨论

讨论了频谱泄漏对傅里叶变换轮廓术测量精度的影响。由于用傅里叶变换轮廓术进行三维面形测量时 ,测得的变形光场是空间有限函数 ,故离散傅里叶变换时先要进行周期拓展 ,如果拓展周期选择不当 ,拓展后的条纹将不连续 ,对之进行傅里叶变换会产生频谱泄漏。文章从理论上推导了拓展周期与变形结构光场频谱泄漏之间的关系 ,给出了由泄漏引起的视场边缘误差的计算模型和定量分析。提出采用条纹外插以减小泄漏误差的方法 ,计算机模拟及初步实验证实了该方法的有效性。     

傅里叶变换、拉普拉斯变换和伽博变换的关系

傅里叶变换、拉普拉斯变换和伽博变换,作为三种常见的积分变换,无论在数学物理的理论研究中还是在各种工程应用中,都有着极重要的价值.本文以傅里叶变换为中心,从逐级修正的角度,详细阐明了三者的理论渊源.     

傅里叶变换红外光谱和近红外傅里叶变换拉曼光谱法无损鉴定中国字画

利用傅里叶变换红外(FTIR)和近红外傅里叶变换拉曼(NIR FT-Raman)光谱法鉴定了中国字画,结果表明：与荧光光谱法相比,根据谱峰的强度和位置可更容易地将真伪字画区别开来。拉曼光谱和红外光谱相互印证,互相补充,在鉴定中具有快速、准确、操作简单、重复性好、不需对样品进行预处理的优点,适于珍贵字画的无损鉴定。     

倒格子不同角度的引入

介绍了从几个不同的方面引入倒格子的数学方法及有关步骤.     

教学用自组式傅里叶变换光谱仪

对原有的傅里叶变换光谱实验进行了全面的升级改造，研制了一种新型的教学用自组式傅里叶变换光谱仪，波长精度较原有实验提高了两个数量级，由该仪器构成的傅里叶变换光谱实验内涵丰富，不但可以使学生学习一种重要的光谱技术，更可以很好地培养学生综合运用所学知识解决实际问题的能力。     

倒易点阵与晶面指数的关系

倒易点阵的概念和性质可以在没有任何假定的情况下很自然地从晶面指数的定义导出.这和流行教科书中分开定义的办法相比,简单而不易引起混乱.     

Holographic interferometry and the fractional Fourier transformation

The fractional Fourier transform (FRT) is shown to be of potential use in analyzing the motion of a surface by use of holographic interferometry. The extra degree of freedom made available by the use of the FRT allows information regarding both translational and tilting motion to be obtained in an efficient manner.     

EPR entangled states and complex fractional Fourier transformation

Starting from the Einstein-Podolsky-Rosen entangled state representations of continuous variables we derive a new formulation of complex fractional Fourier transformation (CFFT). We find that two-variable Hermite polynomials are just the eigenmodes of the CFFT. In this way the CFFT is linked to the appropriate operator transformation between two kinds of entangled states in the context of quantum mechanics. In so doing, the CFFT of quantum mechanical wave functions can be derived more directly and concisely. Received 21 February 2002 / Received in final form 1st June 2002 Published online 24 September 2002 RID="*" ID="*"Work supported by National Natural Science Foundation of China under grant 10175057 and the President Foundation of Chinese Academy of Science. RID="a" ID="a"e-mail: fhym@ustc.edu.cn     

Empty spaces and perfect fluids with homothetic transformation

A class of Lorentzian metrics in one variable that admits homothetic transformation is introduced. Solutions of Einstein's empty space equations are presented. The case of perfect fluids is discussed.     

Talbot self-imaging in fractional Fourier planes of real and complex orders

A study of Talbot self-imaging associated with fractional Fourier transforms (FRFTs) of real and complex orders, as realised by bulk lenses, is presented. Self-images of a periodic object, corresponding to different orders, can be observed in different FRFT planes, herein called Talbot-FRFT planes. The spatial scaling factor of the self-images is shown to be a harmonic function of the FRFT order.     

Measurements of flame-front curvature based on Fourier transformation

An optimized image processing method for calculating the local curvature of two-dimensional digitized flame-front contours is proposed. This contour-smoothing method is based on Fourier transformation of the entire contour and is different from conventional methods in which a chosen number of neighbouring pixel points is locally fitted to an ad hoc smooth function along the contour on a point-by-point basis. The maximum curvature that can be measured with the proposed method is determined by the inner cut-off scale from a fractal length measure of the flame-front contour and is limited by image spatial resolution only. Curvature measurements are also made in highly stretched turbulent premixed methane–air jet flames. The measured probability density functions of local flame curvature are consistent with the generalized form of a symmetric Gaussian distribution suggested by Bradley et al. (Combustion and Flame, 135, 503–523 (2003)). Advantages and limitations of the proposed method are also discussed.     

A hierarchy of lattice soliton equations and its Darboux transformation

A new discrete spectral problem is introduced and the corresponding hierarchy of the lattice soliton equations are derived by means of the trace identity. We find a new Darboux transformation of the lattice soliton equation, through which the explicit solutions are shown.     

The reciprocal lattice construction from axial coordinates of diffraction spots on Weissenberg photographs

An alternative method for constructing of the reciprocal lattice planes from Weissenberg photograph is presented. The radial coordinates of the diffraction spots necessary for the reciprocal lattice plane construction in current method are not introduced into this procedure. The method takes advantage of the coupling of the rotational and translatory motion of the Weissenberg camera. Both the magnitudes and the mutual orientations of the reciprocal lattice vectors can be then determined solely from the measured axial coordinates of the diffraction spots on the Weissenberg photographs. The knowledge of the camera radius as well as the non-uniformity of the radial adhesion of the film to the camera are thus fairly eliminated. The method was successfully applied to the interpretation of Weissenberg photographs of small fragments of lunar olivines from the Sea of Fertility (Luna 16 sample).