A novel 3D measuring method for discontinuous object by non-integral twin-frequency grating

A new 3D shape measurement method based on non-integral twin-frequency grating projection is proposed. In this paper, the projected composite grating is composed of two sinusoidal gratings, and the quotient of whose frequencies is not an integer. By using appropriate phase-shifting algorithms, two wrapped phases can be obtained from sixteen frames of the distorted grating patterns. In aid of appropriate phase unwrapping method, the unwrapped phase of high frequency fringe is obtained only from the relation of the two wrapped phases by a pixel-to-pixel phase unwrapping technique. Therefore the unwrapped phase of high frequency fringe pattern is independent of the low frequency fringe pattern, different from traditional integral twin-frequency grating projection methods in which the phase unwrapping error of low frequency fringe pattern may be propagated onto the unwrapped phase of high frequency fringe pattern. The new theory proves that the proposed method is applicable to measure discontinuous object, and has considerable measurement accuracy.     

The separation of out-of-plane displacement from in-plane components by fringe carrier method based on large image-shearing ESPI

A fringe carrier method for separating out-of-plane displacement from in-plane components based on large image-shearing electronic speckle pattern interferometry (ESPI) is presented. If the test object is respectively illuminated by two expanded symmetric illuminations in large image-shearing ESPI, two interferometers are formed. Carrier fringe patterns can be introduced by tilting reference surface a small angle. The carrier fringe patterns are demodulated after deformation of the object. Two phase maps, which include out-of-plane and in-plane displacement, can be obtained by using Fourier transform. Then out-of-plane displacement can be easily separated from in-plane displacement by simple operation between two unwrapped phase distributions. The principle of spatial carrier frequency modulation in large image-shearing ESPI is discussed. A typical three-point-bending experiment is completed. Experimental results are offered. The results show that the method offers high visibility of carrier fringes. And the system presented does not need a special beam as a reference light and has simple optical setup.     

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。     

Fringe projection profilometry with nonparallel illumination: a least-squares approach

Under a nonparallel illumination condition, fringe patterns projected on an object have unequal fringe spacing that would introduce a nonlinear carrier phase component. This Letter describes a nonlinear carrier removal technique based on a least-squares approach. In contrast with conventional methods, the proposed algorithm would not magnify phase measurement uncertainty, nor does it require direct estimation of system geometrical parameters. The theoretical expression of the carrier phase function on the reference is derived and expanded in a power series. The unknown coefficients in the series are determined by a least-squares method. By subtracting the calculated carrier phase function from the unwrapped phase map, the phase distribution of the object profile is obtained.     

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.     

Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry

Although temporal phase unwrapping method can be applied to solve some problems to measure an object with steep shapes, isolated parts or fringe undersampling in three-dimensional (3D) shape measurement, it needs to acquire and process a sequence of fringe pattern images which would take much time. Servin et al. proposed a 2-step temporal phase unwrapping algorithm, which only needs the 2 extreme phase-maps to achieve exactly the same results as standard temporal unwrapping method. But this method is only validated by computer simulation, shortage of experimental demonstration, its sensitivity coefficient G is limited, and it cannot be used when the G value is larger. We proposed an iterative two-step temporal phase-unwrapping algorithm which is an extension of Servin׳s method. First, add a fringe pattern with an intermediate sensitivity, project the fringe patterns of different sensitivity onto the tested object’s surface, and collect deformed fringe patterns with a CCD camera. Then we obtain the unwrapped phase with larger sensitivity coefficient G by cascading the sensitivity coefficients. And we derive the initial phase conditions of the 2-step temporal phase unwrapping algorithm. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The results are analyzed and compared with Servin׳s method. The experimental results show that the proposed method can achieve higher sensitivity and more accurate measurement, and it can overcome the main disadvantages encountered by Servin׳s method.     

Simultaneous quantitative evaluation of in-plane and out-of-plane deformation by use of a carrier method of large image-shearing shearography

A carrier method for separating out-of-plane displacement from in-plane components based on large imageshearing shearography is presented. A reference surface is fixed on the side of a test object. They are illuminated by two expanded symmetric illuminations respectively. The carrier is introduced by rotating the reference surface to modulate the displacement of an object. By using Fourier transform to demodulate the modulated fringe pattern, two phase maps, which include out-of-plane and in-plane displacements, can be obtained. Then the out-of-plane displacement can be easily separated from in-plane displacement by subtraction and addition of the two unwrapped phase distributions. The principle of the method is presented and proved by a typical three-point-bending experiment. Experimental results show that the method enjoys high visibility of carrier fringes. The system does not need a special beam as a reference light and has simple optical setup.     

Fourier fringe processing using a regressive Fourier-transform technique

Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has led to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However, the basic processing technique, in case of the 2D-Fourier transform, is subject to a major drawback. Because this technique supposes periodicity in a fringe image, the so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive Fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier-transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.     

非单调条纹图的相位恢复新方法

在连续小波变换和展开相位拐点识别的基础上,提出一种非单调条纹图的相位恢复新方法.包裹相位通过连续小波变换的方法提取,提出小波变换尺度步长的选择准则及对粗糙尺度作迭代均值滤波的技术.基于展开相位拐点与符号歧义点的单应性,可通过检测并修正展开相化拐点的方法恢复非单调条纹图的真实相位.给出了详细的理论推导、数值模拟及实验验证过程.数值模拟包括一维及二维的含噪声信号,实验为基于显微干涉法的微桥的静动态形貌和变形测试.模拟及实验结果表明,该法只需一幅条纹图即可准确解调非单调条纹的相位,最大误差小于4%,且具有极强的抗噪能力.这为显微干涉测量提供了有效的相位恢复新手段.     

Deformation and profile measurement using the digital projection grating method

This paper presents a digital projection grating method for full field measurement of out-of-plane deformation and shape of an object. Two grating patterns on an object before and after deformation are captured by a CCD camera and stored in a computer. With the aid of Fast Fourier Transform (FFT) and signal demodulating techniques, a wrapped phase map is generated. The phases are expanded in the range of 0–2π and compared with the resulting moiré pattern. An unwrapping procedure is used to obtain a continuous phase. In addition, a digital method for fractional fringe multiplication is also developed. Results on deformation and object profile measurements are presented.     

散斑剪切干涉条纹特性的实验研究

本文通过位移位相存在的真实性实验、小孔滤波的必要性实验、位移梯度的解相关性实验,证实了散斑剪切于涉术的条纹是由物体变形所引起的“位移位相”和“位移微分位相”以及由位移和位移微分共同决定的“附加位相”之和的余弦条纹。实验证实这种余弦条纹的分布,随着滤波孔的位置而变化,它的衬比随着位移和位移梯度的增大而下降。特别是,当在象面上一点相遇的两个物点的象面散斑位移之差的模值大于散斑的直径时,两者相遇的象点上的条纹消失。     

Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers

This paper presents a method that can recover absolute phase pixel by pixel without embedding markers on three phase-shifted fringe patterns, acquiring additional images, or introducing additional hardware component(s). The proposed three-dimensional (3D) absolute shape measurement technique includes the following major steps: (1) segment the measured object into different regions using rough priori knowledge of surface geometry; (2) artificially create phase maps at different z planes using geometric constraints of structured light system; (3) unwrap the phase pixel by pixel for each region by properly referring to the artificially created phase map; and (4) merge unwrapped phases from all regions into a complete absolute phase map for 3D reconstruction. We demonstrate that conventional three-step phase-shifted fringe patterns can be used to create absolute phase map pixel by pixel even for large depth range objects. We have successfully implemented our proposed computational framework to achieve absolute 3D shape measurement at 40 Hz.     

Simultaneous estimation of unwrapped phase and phase derivative from a closed fringe pattern

We propose a new approach for the direct estimation of the unwrapped phase from a single closed fringe pattern. The fringe analysis is performed along a given row/column at a time by approximating the phase with a weighted linear combination of linearly independent basis functions. Gaussian radial basis functions with equally distributed centers and a fixed variance are considered for the phase approximation. A state space model is defined with the weights of the basis functions as the state vector elements. Extended Kalman filter is effectively utilized for the accurate state estimation. A fringe density estimation based criteria is established to select whether the phase estimation is performed in a row by row or column by column manner. In the seed row/column decided based on this criteria, the optimal basis dimension is computed. The proposed method effectively renders itself in the simultaneous estimation of the phase and the phase derivative. The proposed phase modeling approach also allows us to successfully demodulate the low density fringe patterns. Simulation and experimental results validate the practical applicability of the proposed method.     

Superfast 3D absolute shape measurement using five binary patterns

This paper presents a method that recovers high-quality 3D absolute coordinates point by point with only five binary patterns. Specifically, three dense binary dithered patterns are used to compute the wrapped phase; and the average intensity is combined with two additional binary patterns to determine fringe order pixel by pixel in phase domain. The wrapped phase is temporarily unwrapped point by point by referring to the fringe order. We further developed a computational framework to reduce random noise impact due to dithering, defocusing and random noise. Since only five binary fringe patterns are required to recover one 3D frame, extremely high speed 3D shape measurement can be achieved. For example, we developed a system that captures 2D images at 3333 Hz, and thus performs 3D shape measurement at 667 Hz.     

Nanoscale deformation measurement by using the hybrid method of gray-level and holographic interferometry

This study extends the use of holographic interferometry to measure the nanoscale out-of-plane displacement with high surface resolution. It is noted that if the deformation is less than half of the optical wavelength, it is hard to find an obvious fringe pattern. Under such a situation, in general, the phase shift method is used. However, it needs to take more than 3 images for phase shifting and phase reconstruction In this paper, a more simple hybrid method of gray-level and holographic interferometry is used to extract fringe skeletons, in which it just needs to take one or two images for the normal deformation measurement directly, even if there exists no obvious fringe pattern. The displacement field with high surface resolution can also be obtained. The proposed method yielded a theoretical precision of 0.15 nm for out-of-plane displacement with a monochromatic CCD camera of 10-bit gray scale (1024 gray scales) sensitivity and microscale surface resolution for millimeter scale object with 640×480 pixels image resolution by an He–Ne LASER (632.8 nm wavelength) light source. The gray-level method is proposed to calculate the non-obvious interferometry fringe by traditional holographic interferometry hologram, and the result showed that this method works for this purpose.     

基于时域小波变换相位提取的三维形貌测量

提出基于时域小波变换的连续振动物体相位提取方法,恢复连续振动物体的瞬时三维形貌。将小波变换用于序列影栅云纹相位分析中,对连续振动物体的序列影栅图像进行处理,利用小波变换的多分辨力特点,对各点的灰度变化进行连续复小波变换,通过提取小波脊所对应的相位,得到各点相对于基准光栅的完整相位调制信息,从而获取运动物体的瞬时三维形貌。利用该方法对连续振动悬臂梁进行了分析,得到连续振动悬臂梁的瞬时速度及瞬时三维形貌,再现了悬臂梁的连续振动过程。为研究动态物体瞬时特性提供了一种新的方法。     

Evaluation of residual deformations generated by a pulsed ion implanter using interferometric phase measurement

A Fourier transform method of holographic fringe pattern analysis is applied to measure surface residual deformations generated by a pulsed ion implanter. The technique uses a fixture that makes it possible to remove the specimen and put it back into the same position after being implanted. The phase information from interferograms extracted by means of the Fourier transform method is unwrapped using an algorithm based on cellular automata. Results computed from the application of a numerical model are compared with those determined experimentally and a reasonable agreement is obtained.     

Demodulation of a single interferogram based on continuous wavelet transform and phase derivative

A novel method based on continuous wavelet transform (CWT) and guidance of phase derivative is developed to measure the phase of a single fringe pattern which contains closed fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT which has the capability of better noise reduction and thus increases the resolution of measurement significantly. To further reduce the noise, the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. The proposed method also identifies any ambiguous point in a non-monotonous fringe pattern by directly tracking an inflexion point from an unwrapped phase map without the use of a carrier. The algorithm developed is validated by computer simulation and experimental results. Based on micro interferometry the experimental results for both static and dynamic deformations of a micro structure demonstrate that the proposed method is an effective tool for the analysis of closed fringe patterns and subsequent deformation measurement. However, the proposed technique is limited to measurement of surface which is relatively smooth compared to the mean wavelength of the light source. In addition, prior knowledge of the sign of surface slope is required in cases where a spatial carrier is not available or adaptable.     

基于条纹等值线相关的散斑条纹图处理新方法

在数字散斑干涉术中,通常由物体变形前后得到的两幅原始散斑场用相减方法来得到条纹图,并由相移后的多幅(三幅以上)条纹图来求取相位场。介绍了一种基于条纹等值线相关的条纹图生成新方法,并在此基础上提出了基于单幅干涉条纹图的相位场提取新方法和基于条纹等值线相关的单步相移新方法。实验结果表明,该方法具有良好的结果和发展前景。     

基于载频条纹相位分析的畸变测量和校正

为了对图像畸变进行测量和校正,利用纵向朗奇(Ronchi)载频条纹作为测量模板,通过成像系统获取畸变光栅条纹.运用傅里叶变换对畸变条纹图像进行频谱分析、滤波提取基频信息,直接从畸变图像的中心无畸变区域提取理想条纹像信息.通过相位分析提取包裹相位并解包,获得畸变光栅条纹的径向畸变相位分布规律.将该分布规律转化为径向位置畸变分布规律,并结合双线性插值灰度重建对畸变图像进行校正.实验结果证明该方法是有效的.