窗口傅里叶变换轮廓术中窗口尺度选取的改进

多尺度窗口傅里叶变换法根据条纹信号的瞬时频率梯度来确定信号的局域平稳长度,再由局域平稳长度来控制窗口的尺度,即窗口的尺度和局域平稳长度成正比。使用多尺度窗口傅里叶变换法来使条纹信号的频谱局域化,可以在条纹信号的频率分辨率和空间分辨率之间达到一种较佳的调和。针对多尺度窗口傅里叶变换三维形貌测量技术中局域平稳长度提取算法的不足进行了改进,使窗口尺度的选取更具合理性,对变形光栅基频提取更精确,进一步减小了位相测量的误差。给出了理论分析、计算机模拟以及实验结果。     

High-speed fringe analysis by using stair-shaped virtual grating demodulation

This article describes a novel fringe analysis technique using stair-shaped virtual grating demodulation algorithm for extracting the phase information from a single fringe pattern. In contrast to the Fourier transform technique and quadrature multiplicative moire method, the new method processes a fringe pattern in the integer signal domain instead of the frequency domain and real-signal domain. The spatial carrier of fringe image is not limited to any particular frequency as long as it fulfills the sampling theorem. The errors analysis of this technique is conducted by computer simulation and experiments.     

Fourier transform profilometry based on a fringe pattern with two frequency components

A modified Fourier transform profilometry (FTP) based on a fringe pattern with two frequency components is proposed, which provides a larger measuring range than that of the traditional FTP. We analyze the maximum measuring range and give an expression to describe the measurable slope of the height variation limitation of this method. The modified FTP provides us another approach to eliminate frequency overlapping. When the spectra distribution of a measured object is not spherical symmetry, we can avoid the frequency aliasing through projecting a fringe pattern with two frequency components, instead of increasing the density of the projected fringe and the resolution of a CCD camera. The theoretical analysis and primary experiments verified the method.     

光载波条纹图的计算机辅助分析——阶梯形虚拟光栅解调法

本文提出一种两维光测条纹图的相位测量技术--阶梯形虚光栅解调算法。此法只需要获取一幅光载波条纹图,由计算机产生两个由N(整数)个象素构成、透射函数呈阶梯形分布、彼此间有一定相位差的两个虚光栅(参考信号),通过在整数域的运算实现对条纹图和虚光栅的相乘型叠加,低通滤波后得到两个相位差已知的叠栅函数,然后从两个相差为已知值的正弦信号中提取相位信息。理论分析和计算机模拟表明,具有相当高的测量精度,计算简便快捷。文中还给出了阶梯虚光栅解调法在投影光栅法三维形貌测量中的应用实例。     

Neural network applied to reconstruction of complex objects based on fringe projection

The neural network has been introduced into the reconstruction of the complex object based on fringe projection. In this method, the neural network with powerful property of approximation is used to get the continuous approximate function of a discrete fringe pattern captured by an image frame grabber. The depth-related phase of the measured object modulated into the fringe pattern can be demodulated by dealing with the approximate function. Compared with the Fourier transform profilometry (FTP), in the network method, one deformed fringe pattern is needed to reconstruct the tested object, and a high spatial resolution is maintained for no filtering process. Therefore, this method performs better than FTP in the measurement of the complex object. Moreover, the network method is capable of demodulating more depth-related phase even in the case that the local shadow exists in the fringe pattern. Computer simulations and experiments validate the feasibility of this method.     

Analysis on fringe pattern demodulation by use of 2-D CWT

We discuss the wavelet transform profilometry based on the continuous wavelet transform technique as viewed from frequency analysis. We deduce the expression of one-dimensional (1-D) and two-dimensional (2-D) wavelet transform in frequency domain and analyze their characteristics in the application of demodulating the fringe patterns. We also compare 1-D CWT and 2-D CWT in demodulating the oblique fringe patterns with dual carrier frequency components. When oblique fringe patterns are processed, the direction normal to the grating line and x axis or y axis is not identical. By 1-D CWT, in which wavelet transform is carried out row by row, we cannot obtain the most similarity between local signal and the wavelet functions with different dilation values. While a fan 2-D continuous wavelet transformation can deal with the fringe pattern as a 2-D unit as well as has multi-directions, its advantage is that it can be used to exact the information in the spatial direction. However, its spatial localization ability is not very good, which leads that it is not suitable for demodulating the fringe patterns with high phase variation. Computer simulations and experiments have verified our analysis.     

A comparison of phase shifting and fourier methods in the analysis of discontinuous fringe patterns

Phase Shifting Interferometry is a highly accurate data acquisition technique that efficiently utilizes several frames of information for each measurement. In this work, the advantages of phase shifting have been applied to a conventional moiré interferometer, yielding a system capable of recording phase shifted fringe patterns for both in-plane displacement components. Using this method, the phase of a wavefront of interest can be determined at each detector location, so that the resolution of the phase measurements is limited primarily by the detector discrimination and geometry. Unlike traditional Fourier fringe analysis, the noise rejection of phase shift processing algorithms does not degrade image fidelity in the presence of edges and discontinuities. A general discussion of both the phase shifting technique and the Fourier fringe analysis method is included to provide insight into the problems of processing discontinuous fringe patterns.     

Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.     

The use of carrier frequency shifting for the elimination of phase discontinuities in Fourier transform profilometry

This paper presents a novel application of frequency shifting in the Fourier transform fringe analysis technique applied to surface shape measurement. In recent years little use has been made of frequency shifting, although it was a feature of the method as originally proposed. The paper shows that if the angle between fringe projection and viewing is small, it is possible to employ a frequency shift to effectively eliminate the occurrence of any wraps in the resulting phase distribution. This is obviously of value in cases where the object to be measured contains several discontinuities which would lead to a highly complex, maybe unprocessable, wrapped phase distribution. The technique is presented and analysed, and its effects on measurement resolution discussed. It is illustrated with a measurement made on a populated surface mount technology printed circuit board.     

Using coloured structured light in 3-D surface measurement

The widest used algorithms for 3-D surface measurement using structured fringe patterns are phase stepping and Fourier fringe analysis. The techniques currently employed use mostly monochrome fringe patterns as a tool for phase information measurement and further surface reconstruction. However, the information contained in colour images is much more than that of monochrome, in this case, a new colour technique can be employed to analyse a measured scene with colour fringe patterns.This paper presents a new method for improving the measurement of 3-D shapes by using colour information of the measured scene as an additional parameter. The new method is based on primary colours (red, green and blue) to increase the number of the illuminated fringe patterns, which will remove or significantly reduce the common drawbacks of existing methods. The proposed technique produces a number of coloured structured lighting patterns, which are projected from different angles onto the scene. These patterns are analysed using masking algorithms, a specially adapted multi-colour version of the standard Fourier fringe analysis method and calibration routines. In this way a number of the standard difficulties are overcome.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

大剪切电子散斑干涉的载频调制与位移场测量

将电子散斑干涉场的载波调制引入到大剪切电子散斑干涉中,通过对参考物的微小偏转引入载波条纹;利用傅里叶变换法,解调出了变形场的相位,从而实现了物体变形场的精确测量。讨论了大剪切载频的调制机理,理论分析表明,调制条纹的空间频率与参考面偏转的角度成正比;因此,控制参考面的偏转角度可实现不同位移量系统的调制。利用中心加载周边固定圆盘进行了典型实验,实验结果证明在大剪切电子散斑干涉技术中可以通过参考面的旋转高质量地实现电子散斑干涉条纹的调制,求解位移场。该系统具有系统简单,不需要专门引入参考光,条纹质量好等优点。该技术可扩展电子散斑干涉的应用范围,有一定的实际应用价值。     

Analysis of moiré fringes for measuring the focal length of lenses

We describe a technique based on fast Fourier transform and least-squares fit for automated analysis of moiré fringe patterns for accurately measuring the focal length of lenses. An interference fringe pattern is produced by a reflective diffraction grating interferometer and illuminates the test lens. Moiré fringes are generated by digitally superimposing the magnified fringe pattern imaged by the lens on the interference fringe pattern without the test lens. We analyze two common ways to generate the digital moiré effect: multiplication and subtraction with successive rectification of the two digitally stored intensity distributions, and we show that in the latter case by means of the described technique it is possible to determine the moiré spatial frequency by a simple and fully automated procedure.     

Phase demodulation in the space domain without a fringe carrier

It is demonstrated that interference phase can be obtained from a fringe pattern using the spatial domain method known as spatial synchronous detection (direct interferometry) but without the usual fringe carrier (e.g. tilt) introduced into the interferometer. This is particularly useful in the study of transient events, where it is not always straightforward to introduce these carrier fringes. Spatial domain analysis is considerably faster than frequency domain (Fourier) methods, and could enable phase to be calculated in real time on relatively cheap personal computers. The main disadvantage of the new technique is that the sign of the recovered phase is lost, and must be inferred from object constraints.     

Automatic refractive index profiling of fibers by phase analysis method using Fourier transform

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. It is used to analyze the fringe pattern obtained by different optical techniques, such as multiple-beam Fizeau fringes. To perform accurate and fast automatic measurement of fiber refractive index profile, phase analysis method has been used with the Fourier transform technique. In this paper, the refractive index profiles of polyethylene fibers with different draw ratios are presented by two methods, fringe shift method and phase analysis method. A comparison between the results obtained is presented.     

基于双色条纹投影的快速傅里叶变换轮廓术

在实际傅里叶变换轮廓术测量中，获取的条纹图扩展的零频分量对傅里叶变换轮廓术的测量精度和测量范围有很大影响，甚至妨碍正确三维面形的恢复。π相移技术常被用来消除零频分量对测量的影响，但需要在测量系统中安装精密相移装置，并需要采集两帧具有π相位差的条纹图。传统傅里叶变换轮廓术中，完成精密相移需要较长的时间，影响了傅里叶变换轮廓术测量方法的实时性。提出了采用双色正弦光栅投影来实现从一帧条纹图中消除零频对傅里叶变换轮廓术测量的影响。该方法同传统的π相移方法相比，不需要相移装置，测量系统简单，并且能真正实现高速测量。     

基于图像二维小波多尺度分解傅里叶变换轮廓术

应用傅里叶变换轮廓术测量物体三维面形时,当被测物体形状复杂或是被噪声严重污染时,导致频谱分布展宽,发生频谱混叠现象,基频提取困难,无法准确恢复物体的三维面型.提出了基于小波分解的傅里叶变换轮廓术,采用小波变换的方法对变形条纹图进行二维多尺度分解,重构被测物的背景图像,滤出图像的零频成分,得到相对变形条纹.运用小波变换与傅里叶变换轮廓术相结合的方法,只需拍摄一幅变形条纹图,将被测物体与背景分离,不受背景成分的影响,且易于基频信息的提取,降低了对滤波器的要求.实验证明该方法较好地防止了频谱的混叠问题,提高了测量范围与解相精度.     

用电子学全息方法测量两平行光束微小夹角

提出一种根据电子学全息原理测量两平行光束微小夹角的方法，其基本思路是，用ＣＣＤ作为记录介质经图像采集卡将双光束干涉条纹图像采集于计算机中，并通过离散傅里叶变换实现干涉条纹图像从空域到频域的变换，根据所得到的频谱分布图，获取条纹数并算出条纹间距，进而推算出两平行光束的夹角。详细地阐述了该方法的原理，通过实验验证了其测量微小光束夹角的可行性，对其测量精度、范围和角度分辨率作了定量地分析。     

A flexible fast 3D profilometry based on modulation measurement

This paper proposes a flexible fast profilometry based on modulation measurement. Two orthogonal gratings through a beam splitter are vertically projected on an object surface, and the measured object is placed between the imaging planes of the two gratings. Then the image of the object surface modulated by the orthogonal gratings can be obtained by a CCD camera in the same direction as the grating projection. This image is processed by the operations consisting of performing the Fourier transform, spatial frequency filtering and inverse Fourier transform. Using the modulation distributions of two grating patterns, we can reconstruct the 3D shape of the object. In the measurement process, we only need to capture one fringe pattern, so it is faster than the MMP and remains the advantages of it. In the article, the principle of this method, the setup of the measurement system, some simulations and primary experiment results are given. The simulative and experimental result proves it can restore the 3D shape of the complex object fast and comparatively accurate. Because only one fringe pattern is needed in the testing, our method has a promising extensive application prospect in real-time acquiring and dynamic measurement of 3D data of complex objects.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.