A three dimensional on-line measurement method based on five unequal steps phase shifting

A three-dimensional on-line measurement method based on five unequal steps phase-shifting with phase measuring profilometry is presented. While only one sinusoidal grating pattern is projected onto the measured object moving with the pipe-line, five arbitrary deformed patterns are captured by CCD as the measured object moves within a duty cycle of the grating pattern. The modulation distribution based on Fourier transform profilometry is introduced to realize pixel matching so as to calculate the corresponding equivalent shifted phase on the deformed patterns. A five unequal steps phase shifting algorithm is developed, which is suitable for non-uniform motion of the pipeline. The experiments verify its feasibility and validity.     

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.     

相移阴影莫尔条纹正交化解调技术

提出一种基于克莱姆正则化分析法的三帧自标定相移阴影莫尔三维轮廓技术.该技术首先采用移动光栅的方法获得相移条纹图,然后通过不同帧相移条纹图相减去除条纹图背景,进而结合克莱姆正交化法和最小二乘法,发展了一种相位解调方法,提取了测量相位.以五步Harlharan算法为参考,用不同算法对同一物体表面进行测量.结果表明,相对于典型的三步相移法和主量分析方法,提出的方法测量得到的相位误差最小(0.5rad),且简化了测量过程.     

次条纹积分法解调位相的三维面形测量

提出一种新的条闰相分析技术用于三维面形自动测量。将光栅图案投影于物体表面上，投影像随物体三维面形变形，形变的投影像用次条纹积分算法分析，求出位相变化和相应的三维面形。     

双频光栅轮廓术的研究

在投影栅相位法轮廓检测中,当物体含突变部分时,包裹相位很难准确恢复,对此可用双频变精度技术来解决。如果用两种不同频率光栅分两次进行测量,无疑增加了测量负担,也无法满足实时检测的要求。提出用软件生成两种不同频率成分的复合正弦光栅,用液晶投影仪投影,针对不同物体具体突变部分的情况,可灵活生成各种不同灵敏度的复合光栅。只采一次图像就可以达到以往双频技术中多次采集的效果,该法具有快速和去包裹精度高的特点。最后,进行了实验测试,结果非常满意。     

A novel Fourier transform profilometry based on dual-frequency grating

The projecting grating method is used to measure the profile of the object. When the object has the steps shape or there are shadows in the grating stripes, the disconnected phase cannot be correctly unwrapped. In order to resolve these problems, the dual-frequency grating is programmed by the computer. And it is projected to the measurement object. The measurement object is placed on the exact rotary platform. After getting two images, the two images are mosaiced, the clear object image modulated by the grating is got. Then a novel Fourier transform profilometry is used to process the image, and the filter is designed to filter the high frequency and the low frequency. The phase difference of high frequency is worked out based on that of the low frequency. At last, the three dimension profile measurement is realized. Comparing with the traditional Fourier transform profile, the method cuts down three times frequency shifting reduces the calculation time and improves filter precision. The result indicates that the method is simple, with high precision. Three dimension profile measurement of the object that has the steps shape or there are shadows in its grating stripes can be successfully resolved.     

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.     

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.     

Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry

Phase unwrapping is a task common to many applications like interferometry imaging, medical magnetic resonance imaging, solid-state physics, etc. Fourier transform profilometry (FTP) values the height distribution of object, elaborating the interference between a plane reference grating and a deformed object grating. Since the height information is extracted from the phase of a complex function, the phase unwrapping is a critical step of the process. Several unwrapping algorithms are proposed in literature, but applied to measurement technologies different from FTP. The purpose of this paper is to define the performances of eight different unwrapping algorithms applied to FTP optical scan method and to define the best one. The algorithms chosen are: Goldstein's algorithm, quality guided path following method, Mask cut method, Flynn's method, multi-grid method, weighted multi-grid method, preconditioned conjugate gradient method and minimum L_p-norm method. The methods were tested on real images acquired by a FTP scanner developed and calibrated for these experiments. The objects used vary from simple geometries, like planes and cylinders, to complex shapes of common use objects. Algorithms were qualified considering the phase unwrapping errors, execution time and accuracy of the shape of objects obtained from the scan method in comparison with real ones. The results show that quality guided algorithm best fits in FTP application.     

Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps

A new approach to reconstructing the object wave front in phase-shifting interferometry with arbitrary unknown phase steps is proposed. With this method the actual phase steps are first determined from measured intensities with an algorithm based on the statistic property of the object phase distribution in the recording plane. Then the original object field is calculated digitally with a derived formula. This method is simple, accurate, and capable of retrieving the original object field, including its amplitude and phase distributions simultaneously, with arbitrary and unequal phase steps in a three- or four-frame method. The effectiveness and correctness of this approach are verified by a series of computer simulations for both smooth and diffusing surfaces.     

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.     

Measurement of a discontinuous object based on a dual-frequency grating

The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed: one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00~mm in height is simulated and a discontinuous object of ladder shape which is 32.00~mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.     

Shape measurement by multi-illumination method in digital holographic interferometry

In this paper, temporal phase unwrapping and short time Fourier transform (STFT) are proposed for shape measurement of an object with height steps by digital holographic interferometry (DHI). A series of digital holograms is recorded with a high-speed CCD camera using a multi-illumination method. Each pixel is processed along the time axis independently of other pixels. Two novel methods are proposed to process the wrapped phase maps: the first method is based on complex phasor (CP) and temporal phase unwrapping, and the second method is based on CP and STFT. In the STFT method, continuous phase maps are obtained by integration of the exacted instantaneous frequency. The continuous phase map can characterize the profile of the object with height steps. An experiment is conducted to verify the validity of the proposed methods.     

Two-exposure quasi-common-path point diffraction interferometric phase microscopy using a four-step algorithm

A two-exposure nearly common-path point diffraction interferometric phase microscopy (IPM) is presented using polarization modulation and one-step grating shifting to implement quantitative phase imaging. The IPM is constructed by an improved Michelson configuration with a reflective grating, and its frequency spectrum generated by a circularly polarized object beam makes double copies through a beam splitter. One copy is low-pass filtered and reflected by a reflective pinhole mirror to create a reference beam, and the other copy is converted by a polarizer and then reflected by a reflective grating to achieve a 45° linearly polarized object beam. By the combination of a polarizing cube beam splitter with 45° tilted angle and a translation of the reflective grating with a π phase shift, four interferograms with π/2 phase shift can be obtained in two exposures. The standard four-step algorithm can then be used to reconstruct the phase of the specimen. The utility of the proposed method was demonstrated with measurements on a phase plate, cells and an oil drop.     

点阵绝对相位彩色多频光栅傅里叶变换轮廓术

提出一种将三角法测距与多频光栅相结合的方法,充分利用数字投影的RGB通道,将多频光栅与点阵同时投影在物体表面,综合控制受高度调制的相位信息的提取,最终获取物体的三维形貌。仿真结果显示,在高度跳变使高频光栅位移达102量级个周期时,可以准确还原原始形貌。通过实验验证,本方法能够同时复原169mm的陡峭高度跳变以及3mm的微小细节,提高了传统双频光栅的性能,具有处理较大截断面和保证细节部分的测量能力,较好地改善了傅里叶变换轮廓术(FTP)的应用性能。     

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。     

基于结构光编码的相展开方法

探讨了一种新的基于结构光编码相展开技术。实现方法是先将计算机构造的用于解相的光栅由投影仪投射到物体上 ,再将计算机构造的一系列黑白相间的编码光栅也由投影仪投射到物体上 ,然后将畸变栅线图像由摄像机采集到计算机中 ,用解相光栅进行解相得到折叠在 [-π ,π]区间内的相主值 ,用所述结构光编码方法进行相展开得到相位的周期 ,二者相加得到真实相位值。与传统的相展开方法相比 ,该方法相展开过程变得相对简单 ,不依赖于路径 ,不存在误差的传播 ,对噪声的抗干扰能力强 ,能够得到准确的周期 ,并能够与解相过程有机结合起来。实验证明该方法获取光栅周期快速、准确     

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.     

Error evaluation for Zernike polynomials fitting based phase compensation of digital holographic microscopy

Combining the experimental research with the simulation calculation, the error evaluation for Zernike polynomials fitting (ZPF) based phase compensation of digital holographic microscopy (DHM) is performed. The obtained results show that the reconstructed phase with high precision can be obtained by ZPF phase compensation algorithm. Moreover, the phase error for ZPF based phase compensation algorithm increases with both the variation of object height and object transverse area, the larger variation of object height, the larger of phase error, and the larger of object transverse area, the faster increase of RMS phase error. To decrease the error of ZPF phase compensation algorithm, it is required to ensure one of the variations of object height and object transverse area to be a small value. Importantly, the proposed method supplies a useful tool for the error evaluation of phase compensation algorithm.