A Method for Optimizing Fourier Holograms

A computational method has been devised for optimizing holograms of high dynamic range. As an example the Fourier hologram of a slit is given and application to holographic correlation is shown.     

基于FFT的舍入不确定度评估

舍入不确定度是快速傅里叶算法不确定度评估中的一个重要来源。将表示成向量矩阵的FFT算法分解为稀疏矩阵,以此确定信号传递流图,从而得出舍入不确定度在每一级的传递形式。再利用GUM中的B类方法对其进行评定,评定时假设舍入测量不确定度为均匀分布,通过对FFT算法中基-2算法的舍入不确定度进行评定,最终经过算法传递后得到其舍入不确定度的结果,在此基础上建立了FFT舍入测量不确定度的通用评估方法。     

Coding of Many Phase Objects Using Computer-generated Binary Holograms

A method for coding many phase objects by means of a binary synthetic hologram is presented. The paper gives a vectorial analysis of the spectrum of multi-exposure synthetic holograms and the analysis of the storage capacity of the method. On the basis of theoretical considerations and experimental results, the errors caused by the overlapping of the first diffraction order reconstructed wavefront with beat frequencies are discussed.     

递归二元搜索型计算全息图的研究

在分析递归二元搜索算法合成计算全息图原理的基础上，计算机编程设计了递归二元搜索型计算全息图，并在实验上研究了计算全息图的恢复象。实验结果表明，递归二元搜索算法可合成任意波前分布的傅里叶变换计算全息图，并具有恢复象质量好，衍射效率高的特点。     

A Discrete Fourier Transform Framework for Localization Relations

Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green's function integrals are resolved, and the method is validated against finite element analysis.     

基于傅里叶变换的正弦信号源波形失真评价方法

介绍了一种直接利用经典傅里叶变换技术评价正弦信号源波形总失真度的过程和方法。借助于周期的精确测量技术,实现基波参数的精确测量。用时域能量方式计算失真,其内涵全面,包括了谐波、杂波、噪声等全部影响,并对测量系统本身的影响进行了补偿。同时,对不同条件下的失真度测量误差进行了分析,用一组仿真数据的实验结果,验证了正确性及可行性。所述方法可用于正弦信号波形失真度的精确测量和计量校准,尤其适用于大失真度的测量。     

基于傅里叶变换的点衍射干涉术

在相移算法的点衍射干涉术的基础上,提出了基于傅里叶变换的点衍射干涉测量术.基于傅里叶变换的点衍射干涉测量术是一种建立在点光源衍射干涉理论基础上的测量方法,它采用傅里叶条纹分析方法来求解干涉条纹的相位分布,运用基于BFGS的拟牛顿算法进行三坐标的迭代计算,确定点光源的三维空间坐标.通过计算机模拟实验,验证了该方法在有噪声干扰的情况下,可以有效降低干扰噪声对测量的影响.     

Spectral analysis using Fourier Transform techniques

The present study is intended as a guide for those who wish to undertake spectral analyses using Discrete Fast Fourier Transforms. Points of particular difficulty in using Fourier Transforms are derived in some detail. Experimental results are offered to illustrate the mathematical derivations. Finally the case of a signal with discontinuities along the time-axis is discussed.     

FFT谱连续细化分析的富里叶变换法

本文提出了利用富里叶变换对ＦＦＴ谱的局部进行细化分析的方法。在细化频谱分析时，可以得到某个主要频率成份频率、幅值、相位的精确值，极大地提高频率分辨力，对瞬态及恒定采样长度信号的频率细化分析十分有效。     

机器人视觉用双远距型傅立叶变换透镜

将光电信息技术运用于机器人视觉系统,使视觉信息处理速度达到光速。在光学信息系统 中,傅立叶变换透镜是关键的运算部件。根据傅立叶光学原理和视觉系统的要求,研制一组远距型的傅立叶变换透镜。透镜前、后焦点间的距离缩短到傅立叶透镜焦距的0.7倍,在整个视场范围内波像差小于1/10波长,其它性能指标均符合设计要求。     

Two-dimensional Fourier transform of scaled Dirac delta curves

We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of the nonscaled curve. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With the scaling relation we determine the spectrum of an elliptic curve by a circular geometry instead of an elliptical one. The generalization to N-dimensional Dirac delta curves is also included.     

用于沙体三维形态检测的二维傅立叶变换轮廓术

提出一种二维傅立叶变换轮廓术，对于在变换条纹图象中存在不连续条纹和类散斑结构噪声时，这种方法比传统的傅立叶变换轮廓术方法优越，能够正确地恢复物体三维面形，本文中给出这种方法的理论推导和沙体三维形态检测的实验结果。     

提高Fourier变换轮廓术测量精度的新方法

在傅里叶变换轮廓术测量方法中,对离散的条想方设法进行DFT（离散傅里叶变换）运算,存在“栅栏效应”,离散频谱不能完全无误地代表原连续频谱分布,相当于在频域内发生了谱信息损失。为了减小由“栅栏效应”引入的位相误差,采用了对条纹进行空域数值加权和外插补零方法,从而提高FTP的测量精度。计算机模拟证实了所提方法的有效性。     

利用灰度图提高Fourier变换轮廓术的测量精度

在ＦＴＰ测量中,常利用π相移方法来消除零频,以避免谱频混叠,提高ＦＴＰ的测量精度。此时,测量系统中包含相移装置,增加了系统的复杂性。然而,人们常常忽略了灰度图中包含的信息在ＦＴＰ测量中的作用。本文提出了在ＦＴＰ测量中利用一帧灰度图来提高测量精度的方法,该方法测量装置简单,又可以达到π相移的效果,在实际的ＦＴＰ测量中的意义。     

Discrete Fourier Transform for Short Samples in the Presence of Noise

We consider the dependences of the error of a discrete Fourier transform on the length of the realization of the considered signal. The introduction of a procedure of making a preliminary determination of the period makes it possible to consider signals in short samples and this significantly reduces the computing and apparatus costs.     

Linear Bijections and the Fast Fourier Transform

 Fast Fourier transform algorithms rely upon the choice of certain bijective mappings between the indices of the data arrays. The two basic mappings used in the literature lead to Cooley–Tukey algorithms or to prime factor algorithms. But many other bijections also lead to FFT algorithms, and a complete classification of these mappings is provided. One particular choice leads to a new FFT algorithm that generalizes the prime factor algorithm. It has the advantage of reducing the floating point operation count by reducing the number of trigonometric function evaluations. A certain equivalence relation is defined on the set of bijections that lead to FFT algorithms, and its connection with isomorphism classes of group extensions is studied. Under this equivalence relation every equivalence class contains bijections leading to an FFT algorithm of the new type. Received October 27, 1994; revised version January 25, 1996