基于数字图像相关的三维刚体位移测量方法

基于三维位移测量在工程技术领域的必要性和重要性,开展了单摄像机和数字图像相关相结合的三维刚体位移测试方法的研究.基于图像位移场矢量中心和斜率与面内和离面位移的分别对应关系,采用最小二乘拟合法分离图像位移场的常量项与一次项,据此,可实现物体三维位移分量的有效分离.以针孔摄像机成像模型为基础,开展了数值模拟及硅片平移实验,发展了与三维刚体位移对应的散斑图模拟方法,验证了基于仿射变换的相关迭代法的精度和适用性.数值模拟与实验结果验证了数字图像相关方法用于实现物体三维刚体化移重构的可行性和优越性,最大测量误差为5%.     

Determination of displacement distributions in bolted steel tension elements using digital image techniques

Digital imaging methods have found a great interest in various engineering fields to study stress-deformation characteristics of materials. Recent enhancements in visual instrumentation with the availability of cost-effective hardware and software products make the digital imaging techniques a viable tool to replace direct strain or displacement measurement methods in engineering applications. In this study, deformation characteristics of bolted steel connections are investigated by calculating in-plane displacement distributions using digital image correlation method (DIC). Validation of the method is presented by comparing the strains measured in standard tension specimens using electrical resistance strain gages and the DIC method. Finite element analysis of the connection specimen is also performed to compare the in-plane displacement distributions calculated from both methods. Results from the validation process indicate that the strains obtained from the DIC method compare well with the results of strain gages. The findings also indicate that the displacement distributions calculated from the finite element method may differ from those of the DIC method in terms of distribution pattern, and the location and magnitude of the extreme values of displacements. It is suggested that the proposed method can be used to determine the in-plane displacement distributions for the bolted connections, hence to evaluate their deformation characteristics under loading.     

基于单摄像机的三维位移测试方法

基于三维位移测量手段在工程技术领域的必要性和重要性,开展了基于单摄像机和数字图像相关的三维位移测试方法研究.基于图像位移场矢量中心和斜率与面内和离面位移的分别对应关系,采用Savitzky-Golay(SG)微分滤波器分离图像位移子区内的常数项与一次项,可实现物体三维位移分量的有效分离.以针孔摄像机成像模型为基础,开展了相应的数值模拟实验及悬臂梁端部受载的实验,发展了与三维线性变形对应的散斑图模拟方法,验证了基于二阶位移模式的牛顿-拉夫森迭代法的精度和适用性.数值模拟与实验结果均验证了三维位移测试方法用于实现物体三维位移重构的可行性和优越性.     

Single-step scanner-based digital image correlation (SB-DIC) method for large deformation mapping in rubber

The incremental digital image correlation (DIC) method has been applied in the past to determine strain in large deformation materials like rubber. This method is, however, prone to cumulative errors since the total displacement is determined by combining the displacements in numerous stages of the deformation. In this work, a method of mapping large strains in rubber using DIC in a single-step without the need for a series of deformation images is proposed. The reference subsets were deformed using deformation factors obtained from the fitted mean stress-axial stretch ratio curve obtained experimentally and the theoretical Poisson function. The deformed reference subsets were then correlated with the deformed image after loading. The recently developed scanner-based digital image correlation (SB-DIC) method was applied on dumbbell rubber specimens to obtain the in-plane displacement fields up to 350% axial strain. Comparison of the mean axial strains determined from the single-step SB-DIC method with those from the incremental SB-DIC method showed an average difference of 4.7%. Two rectangular rubber specimens containing circular and square holes were deformed and analysed using the proposed method. The resultant strain maps from the single-step SB-DIC method were compared with the results of finite element modeling (FEM). The comparison shows that the proposed single-step SB-DIC method can be used to map the strain distribution accurately in large deformation materials like rubber at much shorter time compared to the incremental DIC method.     

Precision verification of a simplified three-dimensional DIC method

The traditional three-dimensional (3D) digital image measurement technique uses at least two images captured from different positions to determine the 3D coordinate of an object. One disadvantage of this method is that the mechanical and optical properties of the image capture devices are not fully identical, and the calibration procedure is quite complicated. This paper introduces a simplified 3D digital image correlation (DIC) method, in which only one image capture device is used. The theoretical measurement error equation is derived and experimentally verified. Experimental results show that distortion correction plays an important role in the improvement of measurement precision. After a radial distortion correction, the measurement precision of the object distance can reach 0.0043%. The optimal camera spacing should be set from 1/50 to 1/30 of the object distance, to obtain a satisfactory precision.     

Digital speckle pattern interferometry (DSPI) with increased sensitivity: Use of spatial phase shifting

This paper presents a real-time digital speckle pattern interferometry system with twofold increase in sensitivity for the measurement of in-plane displacement and first order derivative of out-of-plane displacement (slope). Spatial phase shifting technique has been used for quantitative fringe analysis. The system employs a double aperture arrangement in front of the imaging system that introduces spatial carrier fringes within the speckle for spatial phase shifting. For in-plane displacement measurement, the scattered fields from the object are collected independently along the direction of illumination beams, and combined at the image plane. For slope measurement, a shear is introduced between the two scattered fields. Experimental results on an edge clamped circular plate subjected to in-plane rotation for in-plane displacement measurement and central loading for slope measurement are presented.     

Strain field estimation based on digital image correlation and radial basis function

Two methods based on digital image correlation (DIC) and radial basis function (RBF) were proposed to obtain the accurate strain field in this paper. One is a combined method. RBF was applied to remove the noisy discrete displacement data first. After that, the strain was computed by a local least-squares algorithm. The other is a partial derivative of RBF (PD-RBF) based strain estimation method which integrated denoising with differential process. The effectiveness and accuracy of the proposed methods were verified through two numerical simulation experiments. A practical application on the normal strain measurement of an aluminum alloy beam under symmetric four-point bending via an outer loading frame was also presented. The measurement results are in good accordance with the data obtained by strain gauges. Furthermore, a shape parameter selection method based on rate of convergence was suggested. The new method simplifies the choice of the good shape parameter.     

斜光轴面内位移测量的数字散斑相关法研究

以工程环境中远距离位移和位移场的光学测量为研究课题,分析了远距离斜光轴成像时,像模糊和成像位置变化对白光数字散斑相关方法产生的影响,给出了这两种影响的误差理论计算公式。提出使用参考测量技术克服斜光轴成像位置变化带来影响,给出一种新的远距离斜光轴高精度测量面内位移的方法,在2～50m处作静载挠度测量,其最大相对误差小于1％,测量精度在实验室环境和工程测量环境中都得到了验证。该方法无需共轴光路的测量环境要求,特别适用于桥梁、高速公路立交桥的静载挠度测量等工程应用。使用高速图像采集卡,该方法可应用于斜光轴动态位移测量,拓展了数字散斑相关方法的应用范围。     

A fast digital image correlation method for deformation measurement

Fast and high-accuracy deformation analysis using digital image correlation (DIC) has been increasingly important and highly demanded in recent years. In literature, the DIC method using the Newton-Rapshon (NR) algorithm has been considered as a gold standard for accurate sub-pixel displacement tracking, as it is insensitive to the relative deformation and rotation of the target subset and thus provides highest sub-pixel registration accuracy and widest applicability. A significant drawback of conventional NR-algorithm-based DIC method, however, is its extremely huge computational expense. In this paper, a fast DIC method is proposed deformation measurement by effectively eliminating the repeating redundant calculations involved in the conventional NR-algorithm-based DIC method. Specifically, a reliability-guided displacement scanning strategy is employed to avoid time-consuming integer-pixel displacement searching for each calculation point, and a pre-computed global interpolation coefficient look-up table is utilized to entirely eliminate repetitive interpolation calculation at sub-pixel locations. With these two approaches, the proposed fast DIC method substantially increases the calculation efficiency of the traditional NR-algorithm-based DIC method. The performance of proposed fast DIC method is carefully tested on real experimental images using various calculation parameters. Results reveal that the computational speed of the present fast DIC is about 120-200 times faster than that of the traditional method, without any loss of its measurement accuracy     

基于相移偏折法的高反射表面面形测量技术

利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性.     

High-efficiency and high-accuracy digital image correlation for three-dimensional measurement

The computational efficiency and measurement accuracy of the digital image correlation (DIC) have become more and more important in recent years. For the three-dimensional DIC (3D-DIC), these issues are much more serious. First, there are two cameras employed which increases the computational amount several times. Second, because of the differences in view angles, the must-do stereo correspondence between the left and right images is equivalently a non-uniform deformation, and cannot be weakened by increasing the sampling frequency of digital cameras. This work mainly focuses on the efficiency and accuracy of 3D-DIC. The inverse compositional Gauss–Newton algorithm (IC-GN²) with the second-order shape function is firstly proposed. Because it contains the second-order displacement gradient terms, the measurement accuracy for the non-uniform deformation thus can be improved significantly, which is typically one order higher than the first-order shape function combined with the IC-GN algorithm (IC-GN¹), and 2 times faster than the second-order shape function combined with the forward additive Gauss–Newton algorithm (FA-GN²). Then, based on the features of the IC-GN¹ and IC-GN² algorithms, a high-efficiency and high-accuracy measurement strategy for 3D-DIC is proposed in the end.     

Single-lens 3D digital image correlation system based on a bilateral telecentric lens and a bi-prism: Systematic error analysis and correction

Recently, we proposed a single-lens 3D digital image correlation (3D DIC) method and established a measurement system on the basis of a bilateral telecentric lens (BTL) and a bi-prism. This system can retrieve the 3D morphology of a target and measure its deformation using a single BTL with relatively high accuracy. Nevertheless, the system still suffers from systematic errors caused by manufacturing deficiency of the bi-prism and distortion of the BTL. In this study, in-depth evaluations of these errors and their effects on the measurement results are performed experimentally. The bi-prism deficiency and the BTL distortion are characterized by two in-plane rotation angles and several distortion coefficients, respectively. These values are obtained from a calibration process using a chessboard placed into the field of view of the system; this process is conducted after the measurement of tested specimen. A modified mathematical model is proposed, which takes these systematic errors into account and corrects them during 3D reconstruction. Experiments on retrieving the 3D positions of the chessboard grid corners and the morphology of a ceramic plate specimen are performed. The results of the experiments reveal that ignoring the bi-prism deficiency will induce attitude error to the retrieved morphology, and the BTL distortion can lead to its pseudo out-of-plane deformation. Correcting these problems can further improve the measurement accuracy of the bi-prism-based single-lens 3D DIC system.     

Quality assessment of speckle patterns for DIC by consideration of both systematic errors and random errors

The performance of digital image correlation (DIC) is influenced by the quality of speckle patterns significantly. Thus, it is crucial to present a valid and practical method to assess the quality of speckle patterns. However, existing assessment methods either lack a solid theoretical foundation or fail to consider the errors due to interpolation. In this work, it is proposed to assess the quality of speckle patterns by estimating the root mean square error (RMSE) of DIC, which is the square root of the sum of square of systematic error and random error. Two performance evaluation parameters, respectively the maximum and the quadratic mean of RMSE, are proposed to characterize the total error. An efficient algorithm is developed to estimate these parameters, and the correctness of this algorithm is verified by numerical experiments for both 1 dimensional signal and actual speckle images. The influences of correlation criterion, shape function order, and sub-pixel registration algorithm are briefly discussed. Compared to existing methods, method presented by this paper is more valid due to the consideration of both measurement accuracy and precision.     

High-accuracy and real-time 3D positioning,tracking system for medical imaging applications based on 3D digital image correlation

This paper presents a system for positioning markers and tracking the pose of a rigid object with 6 degrees of freedom in real-time using 3D digital image correlation, with two examples for medical imaging applications. Traditional DIC method was improved to meet the requirements of the real-time by simplifying the computations of integral pixel search. Experiments were carried out and the results indicated that the new method improved the computational efficiency by about 4–10 times in comparison with the traditional DIC method. The system was aimed for orthognathic surgery navigation in order to track the maxilla segment after LeFort I osteotomy. Experiments showed noise for the static point was at the level of 10⁻³ mm and the measurement accuracy was 0.009 mm. The system was demonstrated on skin surface shape evaluation of a hand for finger stretching exercises, which indicated a great potential on tracking muscle and skin movements.     

Two wavelength simultaneous DSPI and DSP for 3D displacement field measurements

A novel optical system is proposed that implements digital speckle pattern interferometry (DSPI) and digital speckle photography (DSP) simultaneously using two wavelength illumination of an object for simultaneous measurement of all three components of the displacement vector field. A collimated red light illuminates both the object and a reference surface in a DSPI configuration which is sensitive to out-of-plane displacement field while a blue light illuminates the object in a DSP configuration which is sensitive to in-plane displacement fields. A color 3-CCD camera records the red and blue lights individually through its red and blue channels, respectively. Two reference images and one image in the deformed state of the object are required for quantitative measurement. Experimental results are presented to validate the system.     

On the use of the digital image correlation method for heterogeneous deformation measurement of porous solids

In this paper, several crucial issues arising from the application of the digital image correlation (DIC) method to the measurement of heterogeneous deformation of porous solids are discussed. To handle samples with complex geometry, the performance of the two commonly employed DIC methods, namely the subset-based DIC and the finite-element based DIC methods are first evaluated and compared. A combined DIC approach and an adaptive DIC approach suitable for samples with discontinuities/holes are then proposed. Aluminum plates with circular holes subject to compressive loading are employed to evaluate the accuracy of the proposed methods. It has been found that in addition to other factors such as the number of pixels and speckle size, the orientation of the camera lens also plays an important role on the measurement accuracy. A calibration method for the adjustment of camera orientation is proposed, which leads to a good agreement between the experimentally measured displacements and finite element simulation results. Another finding of the presented work is that for relatively stiff specimens, the deformation of the loading system itself must be considered in order to obtain an accurate displacement.     

数字图像相关中基于位移场局部最小二乘拟合的全场应变测量

为了从含噪声的位移场中计算得到可靠的应变场,提出一种基于位移场局部最小二乘拟合的全场应变求解方法。介绍了数字图像相关方法的原理,阐述了基于位移场局部最小二乘拟合的全场应变求解方法,并讨论了计算区域边界、孔洞及裂纹附近区域等情况下的应变计算。对均匀变形和中心带圆孔的薄铝板拉伸实验的计算结果表明,该方法能有效地从原始位移场数据中提取全场应变信息。在均匀变形情况下应选择大的应变计算窗口,计算结果更逼近真值;在非均匀变形情况下,如果位移场中包含较强的噪声,则应选择较大的应变计算窗口,而位移场精度很高时可选择更小的应变计算窗口。     

Accuracy of stress measurement by Laue microdiffraction (Laue‐DIC method): the influence of image noise,calibration errors and spot number

Laue microdiffraction, available at several synchrotron radiation facilities, is well suited for measuring the intragranular stress field in deformed materials thanks to the achievable submicrometer beam size. The traditional method for extracting elastic strain (and hence stress) and lattice orientation from a microdiffraction image relies on fitting each Laue spot with an analytical function to estimate the peak position on the detector screen. The method is thus limited to spots exhibiting ellipsoidal shapes, thereby impeding the study of specimens plastically deformed. To overcome this difficulty, the so‐called Laue‐DIC method introduces digital image correlation (DIC) for the evaluation of the relative positions of spots, which can thus be of any shape. This paper is dedicated to evaluating the accuracy of this Laue‐DIC method. First, a simple image noise model is established and verified on the data acquired at beamline BM32 of the European Synchrotron Radiation Facility. Then, the effect of image noise on errors on spot displacement measured by DIC is evaluated by Monte Carlo simulation. Finally, the combined effect of the image noise, calibration errors and the number of Laue spots used for data treatment is investigated. Results in terms of the uncertainty of stress measurement are provided, and various error regimes are identified.     

Accuracy evaluation of optical distortion calibration by digital image correlation

Due to its convenience of operation, the camera calibration algorithm, which is based on the plane template, is widely used in image measurement, computer vision and other fields. How to select a suitable distortion model is always a problem to be solved. Therefore, there is an urgent need for an experimental evaluation of the accuracy of camera distortion calibrations. This paper presents an experimental method for evaluating camera distortion calibration accuracy, which is easy to implement, has high precision, and is suitable for a variety of commonly used lens. First, we use the digital image correlation method to calculate the in-plane rigid body displacement field of an image displayed on a liquid crystal display before and after translation, as captured with a camera. Next, we use a calibration board to calibrate the camera to obtain calibration parameters which are used to correct calculation points of the image before and after deformation. The displacement field before and after correction is compared to analyze the distortion calibration results. Experiments were carried out to evaluate the performance of two commonly used industrial camera lenses for four commonly used distortion models.     

Comparison of subset-based local and FE-based global digital image correlation: Theoretical error analysis and validation

Subset-based local and finite-element-based (FE-based) global digital image correlation (DIC) approaches are the two primary image matching algorithms widely used for full-field displacement mapping. Very recently, the performances of these different DIC approaches have been experimentally investigated using numerical and real-world experimental tests. The results have shown that in typical cases, where the subset (element) size is no less than a few pixels and the local deformation within a subset (element) can be well approximated by the adopted shape functions, the subset-based local DIC outperforms FE-based global DIC approaches because the former provides slightly smaller root-mean-square errors and offers much higher computation efficiency. Here we investigate the theoretical origin and lay a solid theoretical basis for the previous comparison. We assume that systematic errors due to imperfect intensity interpolation and undermatched shape functions are negligibly small, and perform a theoretical analysis of the random errors or standard deviation (SD) errors in the displacements measured by two local DIC approaches (i.e., a subset-based local DIC and an element-based local DIC) and two FE-based global DIC approaches (i.e., Q4-DIC and Q8-DIC). The equations that govern the random errors in the displacements measured by these local and global DIC approaches are theoretically derived. The correctness of the theoretically predicted SD errors is validated through numerical translation tests under various noise levels. We demonstrate that the SD errors induced by the Q4-element-based local DIC, the global Q4-DIC and the global Q8-DIC are 4, 1.8–2.2 and 1.2–1.6 times greater, respectively, than that associated with the subset-based local DIC, which is consistent with our conclusions from previous work.