A new pixel matching method using the entire modulation of the measured object in online PMP

A method using entire modulation information of the measured object itself for pixel matching is proposed in online phase measuring profilometry (PMP). Only one fixed sinusoidal grating is projected onto the moving measured object and then five deformed patterns are captured by the imaging system (CCD). Because the contrast of the sinusoidal grating is a constant, the modulation distribution of each deformed pattern reflecting the gray of the measured region can be extracted. The entire modulation of the object cut from one of them is regarded as a template, and then the distance of the measured object's movement between each two adjacent deformed pattern can be calculated by the correlation operation so that we can cut the corresponding parts containing the measured object's information from five deformed patterns. Then the discrete phase can be calculated with Stoilov algorithm. By the phase unwrapping and the mapping algorithm, the object can be reconstructed exactly. A series of simulations and experiments confirm its feasibility and validity.     

Surface profile inspection of a moving object by using dual-frequency Fourier transform profilometry

The 2π phase ambiguity caused by surface isolations and large height step can be solved by dual-frequency projection grating profilometry. However, in the Fourier transform profilometry (FTP) of a moving object, only one single deformed fringe pattern can be obtained. In order to introduce the dual-frequency technique into the FTP of moving object, a novel experimental system is designed to capture two fringe patterns with different frequency at the same time. A grating structure comprising two regions with different frequencies is projected upon the surface of the detected object. Two line-scan CCD cameras are used to capture the surface images encoded by the two kinds of patterns, respectively. By getting the corresponding image intensity at the same point of the object surface in the two acquired images, the dual-frequency technique is applied to extract the real phase without phase ambiguity. The surface profile of a specimen with a large height step is measured to prove the feasibility of the proposed method. The experimental results show that the proposed method can solve the 2π phase ambiguity problem successfully in the surface profile inspection of a moving object.     

光学投影式三维轮廓测量技术综述

主要用于散射物体的宏观轮廓测量的光学投影式轮廓测量技术可以分为两大类：直接三角法和相位测量法。直接三角法包括激光逐点扫描法、光切法和新近出现的二元编码图样投影法。相位测量法以测量投影到物体上的变形栅像的相位为基础，包括莫尔法、移相法、傅氏变换法等等。本文以基于相位测量和光栅投影法为重点综述了光学投影式轮廓测量技术的几种典型方法，讨论了它们的优缺点，并分析了研究热点和发展方向。     

一种用于在线三维测量的五步非等步相移算法

提出了一种五步非等步相移算法,并成功应用于在线三维测量中。仅投影一固定正弦光栅条纹到物体上,通过物体在线运动产生等效相移,在一个条纹周期范围内任意采集五帧变形条纹图,通过像素匹配使各帧条纹图中的物点一一对应并计算出相应的等效相移量。采用所提出的五步非等步相移算法,即可重构物体。计算机模拟与实验验证了该方法的可行性和有效...     

一种无需标记的在线三维测量方法

提出了一种无需标记的物体在线三维面形测量方法。将一固定的正弦条纹投影到待测运动物体上,借助物体运动产生等效的相移变形条纹。基于傅里叶变换轮廓术的调制度对各帧变形条纹计算,提取其具有某一特定分布的特征区域,采用相关度最大法,检测各帧变形条纹对应的调制度特征区域的位移量来检测出物体的移动,从而实现像素匹配,得到一组像素坐标完全一一对应的等效相移变形条纹图。利用Stoilov相移算法得到物体的截断相位,利用位相展开算法展开位相,通过位相和高度映射即可实现在线移动物体的面形测量。通过计算机仿真验证了该方法的可行性。     

On-line phase measuring profilometry based on phase matching

On-line phase measuring profilometry based on phase matching is proposed. While just one fixed sinusoidal fringe is projected on a measured object moving with the pipeline, deformed patterns modulated by the object moving at the same distance moment are captured synchronously by the CCD camera. The phase information of the object in those captured deformed patterns can be predicted using FTP method to assist the pixel matching so as to realize the point-to-point correspondence of the object in the captured deformed patterns. Meanwhile, the equivalent phase-shifting deformed patterns can be extracted. So the three dimensional shape of the object can be reconstructed successfully with an equal phase-shifting algorithm. Numerical simulation and experiments show feasibility and validity of the proposed method.     

基准光栅重构傅里叶变换轮廓术

应用傅里叶轮廓变换术进行三维形貌测量中,为了获得待测物体的高度相位信息,通常需要采集两幅图像.因此当光学系统发牛变动时,必须重新采集基准光栅图像,不利于快速测量.提出一种从变形光栅图像中获取基准光栅图像信息的测量方法.首先在变形光栅图像中记录基准光栅信息,然后通过傅里叶分析提取基准光栅频率信息,通过图像分析获得基准光栅相位信息,最后重构出一幅完整的基准光栅图像,实现三维物体形貌测量.实验结果验证了该方法的可行的.     

台阶状面形的投影栅线法测量技术

采用光栅投影式三维轮廓术测量物体三维形貌时，当物体是台阶状物体时，物体表面的光栅条纹有阴影，导致后面的叠相还原过程无法进行。为了解决这一问题，将被测物体放在精密的旋转平台上。通过2次成像后，对2幅图像进行图像拼接，得到清晰的被光栅调制的物体图像。在图像拼接时，引入区域黑白对比度概念，区域的黑白对比度最大位置就是黑白区域的分界线。从而精确确定中间块2个边界的位置,然后进行图像拼接。最后采用双频光栅的傅里叶变换轮廓术来实现物体的三维形貌重建。结果表明：本方法简单、精度高，可以成功解决投影时具有阴影物体的三维形貌重建问题。     

Fourier transform profilometry: : a review

Fourier transform profilometry is one of the popular non-contact 3-D measurement methods, where a Ronchi grating or sinusoidal grating is projected onto a diffuse three-dimensional surface, and the resulting deformed grating image is detected by a CCD camera and processed by a computer. This method requires only one frame (or two frames) of the deformed fringe pattern in some algorithms to retrieve the surface of measured object, so it has obvious advantage for real time data acquisition and 3-D measurement of dynamic process. In this paper, we review some algorithms in FTP, discuss some important problems, including frequency spectra overlapping, phase unwrapping, sampling, and 3-D measurement of dynamic process. With the development of computer hardware and software and availability of high-resolution image grabber, FTP method will be a promising one for acquiring 3-D data of object, and more and more researchers pay attention to it.     

Shifted-phase calibration for a 3-D shape measurement system based on orthogonal composite grating projection

This paper proposes a novel method for reducing measurement error caused by spectrum overlapping in orthogonal-composite-grating-based 3-D measurement method. For 3-D measurement systems based on orthogonal composite grating projection, spectrum overlapping causes phase of each deformed phase-shifting fringe changed differently, which violates the principle that the shifted phases between adjacent deformed fringes must be equivalent to 2π/3, and therefore results in phase measurement error. The proposed shifted-phase calibration method is based on that phase variation of each deformed fringe is independent of height and reflectivity of the measured object. Three composite gratings are projected on the reference plane, and each carrier channel includes three phase-shifting gratings needed in phase measuring profilometry (PMP). Because the adjacent phase-shifting fringes demodulated from the same carrier channel have the phase difference of 2π/3, we can respectively calculate the reference plane's phases of three carrier channels by the phase algorithm of PMP method, and the shifted phases between them are obtained. When an object is measured, the shifted phases between deformed phase-shifting fringes can be calibrated. A new 3-D measurement mathematical model is set to reconstruct object. Our experiments prove that the proposed method can effectively restrain the effect of spectrum overlapping and improve measurement accuracy almost one times.     

BP neural network applied to 3D object measurement based on fringe pattern projection

In the fringe projection profilometry, the traditional triangle method, such as Fourier-transform profilometry (FTP), is difficult to recover the stepped shape object from the deformed fringe pattern. In order to solve this problem, the neural network is introduced to deal with this kind of fringe patterns and gain the three-dimensional (3D) information of the measured object. By training the network, the relationship between the deformed fringe pattern and the height of the object can be obtained, and thereby the height of the object can be obtained. Furthermore, the object can be reconstructed perfectly without knowing the optical parameters of the experiment system. An obvious merit of this network method is that it can recover the 3D object in a short time and only need one deformed fringe pattern. Computer simulations and experiment validate the feasibility of the method.     

Application of wavelet transform to 3D shape measurement

A new method for analyzing the phase distributions of deformed grating images on the surface of three-dimensional (3D) object to obtain its shape information has been presented. In the conventional technique, Fourier transform profilometry (FTP), there is an intrinsic problem of extracting the fundamental frequency component if the deformation of the grating pattern is either considerable or complicated, which will definitely bring bad influence to the analysis' accuracy. That means FTP is not appropriate to deal with the complex surfaces of 3D objects. The approach that we here introduce to solve this problem is to utilize Gabor wavelet transform (GWT), a tool excelling for its multiresolution in time-frequency domain, to analyze the phase distributions.     

Discuss the measuring range of dual-frequency wavelet transform profilometry

We discuss the structure condition and sampling condition of wavelet transform profilometry (WTP) based on dual-frequency fringe pattern in this work. In the mentioned method a grating fringe with dual-frequency components is projected onto an object. And two wavelet ridge lines can be extracted by means of wavelet analysis, from which we can calculate two groups of wrapped phase information. Afterwards the retrieved phase with higher precision can be obtained through phase unwrapping process. However, it should be noted that the spectral aliasing of the deformed fringe pattern must be avoided in order to restore the correct phase information. And the two fringe carrier frequencies have to obey some rules as well. In this paper, the structure condition and sampling condition of the proposed method is deduced from the point of view of frequency analysis. It is proven that there would be no frequency overlapping in the deformed fringe pattern only when both of the two conditions mentioned previously are fulfilled. The results of computer simulations and experiments verify the validity of our theory.     

A novel color fringe projection based Fourier transform 3D shape measurement method

A novel Fourier transform 3D shape measurement method based on color fringe projection is proposed in order to solve the spectrum overlapping and phase unwrapping problems existed in Fourier transform profilometry (FTP). The R and G components of the color fringe are set to two sinusoidal patterns with different frequencies and the B component is set to the average value of R or G component. Then this pattern is projected to the object and the deformed fringe image is captured. Three gray patterns are separated from the color fringe, the background and high frequency noise can be eliminated using our method and the accurate unwrapped phase can be got. Only one shot color pattern is projected to get the 3D information of the object. Experiment results show that the 3D information of an object can be obtained rapidly and accurately.     

Circular carrier-frequency photography for observing phase objects

A circular grating is photographed through a phase object which deforms the image of the grating lines. By super-imposing these deformed lines with a master grating on photographic film, moiré patterns are observed. These patterns are interpreted as fringes of constant radial derivative.     

一种新的双频光栅轮廓术

物体含突变部分时,包裹相位很难准确恢复.若用双频光栅技术分两次测量,测量次数增加,不符合实时要求.提出用软件方法生成含两种不同频率的复合光栅,用液晶投影仪投影.针对不同物体突变情形,生成各种不同灵敏度的复合光栅.只一次采集,就达到过去双频多次采集的效果.两幅不同灵敏度的相位图可同时获取,相位去包裹时高精度光栅相位不确定性由粗光栅对应相位修正.最后,进行了实验测试.结果表明,新方法具有速度快、精度高、测试范围广等特点.     

Automatic Analysis of the Phase Object Using Projection Moire Deflectometry

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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.     

Phase-unwrapping algorithm in the presence of discontinuities using a system with crossed grating

A new phase-unwrapping algorithm for the phase map containing discontinuities by the use of a system with crossed grating is described in this paper. A crossed grating is projected onto the object in the usual way, the deformed grating image acquired is Fourier transformed and the frequency spectra for the individual gratings are separated. Using both phase distributions which have different sensitivities, the correct phase values in the presence of discontinuities, especially those caused by the object with height steps, can be obtained. This algorithm is fast and accurate. The results of the measurement of a three-dimensional object with height steps are presented.     

相位锁定循环投影技术及其应用

由一组规则栅线投影到物体表面的变形光栅,采用相位锁定循环解调算法解调出含有物体表面高度信息的相位.该技术的最大优势是不需传统的相位去包裹.利用该算法对二维栅线图扫描确定的相位.本文给出了一个典型试件的实验结果和分析.