A Review of Speckle Pattern Fabrication and Assessment for Digital Image Correlation

As a carrier of deformation information, the speckle pattern, or more exactly the random intensity distributions, which could be naturally occurred or artificially fabricated onto test samples’ surface, plays an indispensable role in digital image correlation (DIC). It is now well recognized that the accuracy and precision in DIC measurements not only rely on correlation algorithms, but also depend highly on the quality of the speckle pattern. Considering the huge diversity in test materials, spatial scales and experimental conditions, speckle pattern fabrication could be a challenging issue facing DIC practitioners. To obtain good speckle patterns suitable for DIC measurements, some key issues of fabrication methods and quality assessment of speckle patterns must be well addressed. To this end, this review systematically presents the speckle pattern classification and fabrication techniques for various samples and scales, as well as some typical quality assessment metrics.     

An Error Criterion in Digital Image Correlation for Unknown Deformation Fields and Its Application of Parameters Selection

Digital image correlation (DIC) is a widely used optical metrology for surface deformation measurement. In DIC, the square root of the mean square error (RMS error) and standard deviation error (SD error) are used as quantitative criteria in order to evaluate the accuracy and robustness of a DIC method\algorithm. However, RMS and SD error criteria are computed from prescribed and measured displacements, which indicates that the prescribed displacement fields must be precisely generated. Therefore, it is difficult to quantitatively evaluate the accuracy and robustness of an algorithm\method in practical DIC measurements because imposed displacements are unknown (that’s why DIC measurements are needed). Moreover, the accuracy of DIC measurements highly relies on parameters selection, especially the selections of subset size and shape function. In practice, the subset size and shape function are usually selected according to experience because there are numerous factors (e.g. the quality of speckle image, local displacement field) and uncertainties (e.g. noise level, out-of-plane motion, illumination lighting fluctuation during image capturing) that affect the parameters selection, which makes it difficult to select optimal parameters based on previous works which mainly focused on theoretical deduction in ideal condition. In this paper, an error criterion for evaluating the accuracy of practical DIC measurements with unknown displacements is proposed. Numerical experiments are used to validate the effectiveness and feasibility of the proposed criterion for accuracy evaluation. It is concluded that the square root of the sum of squared forward and backward displacements difference (SFBD) error has a significant positive linear correlation with the widely used SD error in most practical DIC measurements where the mismatch between the frequently-used first- and second-order shape functions and the actual field is usually small. Also, an application of the proposed criterion is presented by real experiments for subset size and shape function selections, which verifies that the proposed error criterion can be effectively used for DIC parameters selection.     

Recent Progress in Digital Image Correlation

In this paper, we report the following important progress recently made in the basic theory and practical implementation of digital image correlation (DIC) for deformation measurement. First, we answer a basic but confusing question to the users of DIC: what is a good speckle pattern for DIC? We present a simple, easy-to-compute yet effective global parameter, called mean intensity gradient, for quality assessment of the entire speckle pattern. Second, we provide an overview of various correlation criteria used in DIC for evaluating the similarity of the reference and deformed subsets, and demonstrate the equivalence of three robust and most widely used correlation criteria, i.e., a zero-mean normalized cross-correlation (ZNCC) criterion, a zero-mean normalized sum of squared difference (ZNSSD) criterion and a parametric zero-mean normalized sum of squared difference (PSSD_ab) criterion with two additional unknown parameters, which elegantly unifies these correlation criteria for subset-based pattern matching. Third, we describe an iterative least squares (ILS) algorithm for accurate subpixel motion detection, which is proved to be equivalent to the existing Newton–Raphson algorithm, but the principle and implementation of ILS algorithm is more straightforward and easier. Finally, to overcome the two limitations of existing subset-based DIC technique, we introduce a robust and generally applicable reliability-guided DIC technique, in which the calculation path is guided by the ZNCC coefficients of computed points, to determine the genuine full-field deformation of an object with complex shape.     

Deformation measurements by digital image correlation: Implementation of a second-order displacement gradient

This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

数字图像相关方法中散斑图的质量评价研究

在利用数字图像相关方法测量物体表面变形时,被测物体表面必需覆盖有灰度随机分布的散斑场,该散斑场作为试件表面变形信息的载体随试件一起变形。在实际情况下,不同的散斑场会显示出完全不同的灰度分布特征,并对数字图像相关方法的测量结果有着重要影响。因此如何定量评价散斑图的优劣是数字图像相关方法中一个重要的基本问题,也是该方法的使用者非常关心的问题。基于最近数字图像相关方法基本理论研究的进展,本文提出平均灰度梯度这一新参数用于散斑图质量的评价。为证实该参数的有效性,本文对五幅明显不同的散斑图进行了精确平移,并将数字图像相关方法测量的位移与预加的平移量进行比较,分析了位移测量结果的均值误差和标准差。结果显示位移测量结果的均值误差和标准差均与散斑图的平均灰度梯度有关,一个好的散斑图应该具有较大的平均灰度梯度。     

Mechanically Regularized FE DIC for Heterogeneous Materials

In situ tensile tests in a scanning electron microscope (SEM) have been conducted on a 8-layer 5-harness satin carbon fibre and epoxy matrix composite to observe the first stages of damage at the scale of fibres and matrix. A speckle pattern based on a suspension of alumina particles was applied onto the surface of the specimen to facilitate the use of digital image correlation (DIC). Local and finite element (FE) DIC are compared on pictures acquired during the tensile tests, with and without a speckle pattern. FE DIC with mechanical regularization was found to be the only approach able to measure displacement fields at a fine enough resolution in both cases. This method, initially created for homogeneous materials, was then adapted to heterogeneous materials. First, a microstructure consistent mesh was created and used for correlation purposes. Second, the difference between the mechanical properties of the constituents is taken into account in the mechanical regularization. Last, the accuracy of the method is analysed. The adaptation presented herein was proved to be able to measure displacement fields in the matrix between fibres with an error of 10 nm (a fifth of a pixel) and to detect the initiation of the first damage mechanisms by means of the mechanical residuals.

     

A Novel “Subset Splitting” Procedure for Digital Image Correlation on Discontinuous Displacement Fields

Digital Image Correlation (DIC) is an easy to use yet powerful approach to measure displacement and strain fields. While the method is robust and accurate for a variety of applications, standard DIC returns large error and poor correlation quality near displacement discontinuities such as cracks or shear bands. This occurs because the subsets used for correlation can only capture continuous deformations from the reference to the deformed image. As a result the regions around discontinuities are typically removed from the area of interest, before or after analysis. Here, a novel approach is proposed which enables the subset to split in two sections when a discontinuity is detected. This method enables the measurement of “displacement jumps”, and also of displacements and strains right by the discontinuity (for example a crack profile or residual strains in the wake). The method is validated on digitally created images based on mode I and mode II asymptotic displacement fields, for both sub-pixel and super-pixel crack opening displacements. Finally, an actual fracture experiment on a high density polyethylene (HDPE) specimen demonstrates the robustness of the method on actual images. Compared to other methods capable of handling discontinuities, this novel “subset-splitting” procedure offers the advantage of being a direct extension of the now popular standard DIC, and can therefore be implemented as an “upgrade” to that method.     

DIC-Based Surface Motion Correction for ESPI Measurements

Electronic Speckle Pattern Interferometry (ESPI) provides a sensitive technique for measuring surface deformations. The technique involves comparison of the speckle phase angles within surface images measured before and after material deformation. This phase angle comparison requires that the speckle positions be consistent in all images. A lateral shift between image sets of just one pixel substantially degrades ESPI measurements, while a shift of two or more pixels typically causes complete decorrelation and compromises the measurement entirely. To prevent such rigid body motions, the specimen and the optical system must be rigidly fixed. This requirement typically impedes use of the ESPI method in applications outside laboratories or where it is necessary to remove the specimen from the optical setup between ESPI measurements. Here, Digital Image Correlation (DIC) is used to track speckle motion caused by specimen displacement between ESPI phase stepped image sets. The measured image set can then be mathematically shifted to restore the original speckle locations, thereby recorrelating the ESPI measurement. Examples are presented where ESPI measurements are successfully made with specimen shifts over 60 pixels.     

基于退相关DIC的疲劳裂纹全局动态测量方法

工程材料和结构在反复荷载长期作用下容易发生疲劳开裂, 疲劳裂纹测量对于开展科学试验研究和工程问题分析都至关重要, 但现有方法无法实现高精度的疲劳裂纹全局动态测量. 本文基于数字图像相关(digital image correlation, DIC)技术, 合理利用DIC的退相关效应, 提出一种疲劳裂纹全局动态测量及可视化方法. 该方法首先在相机采集得到的裂纹图像内, 建立具备拓扑关系的目标点云结构, 并运用DIC亚像素算法得到裂纹区域位移场, 再基于零均值归一化互相关(zero-mean normalized cross correlation, ZNCC)计算结果剔除退相关的DIC目标点(灭点). 进一步通过“三生点”算法提取得到裂纹离散边界, 并采用最小二乘法将离散边界拟合为连续裂纹边界, 实现裂纹形态的几何重构, 最终自动计算得到裂纹长度和宽度的动态变化过程. 该方法原理清晰、理论简单, 易于实现. 开展数值模拟和钢节点疲劳试验, 对相关算法和图像采集参数进行了验证, 结果表明本文方法对疲劳裂纹边界的数字化重构误差在0.5个像素内, 基于重构结果计算得到的裂纹长度和宽度误差分别为0.46像素和0.08像素(类同于0.06 mm和0.01 mm), 并成功实现了对疲劳试验裂纹扩展形态的精细化动态测量及可视化. 研究成果证明了DIC技术用于疲劳裂纹全局动态测量及可视化的有效性, 并在测量精度、效率、成本等方面具有显著优势, 可在实验室测量和工程现场测试中推广应用.      

Absolute Nodal Coordinates in Digital Image Correlation

A great deal of progress has been made in recent years in the field of global digital image correlation (DIC), where higher-order, element-based approaches were proposed to improve the interpolation performance and to better capture the displacement fields. In this research, another higher-order, element-based DIC procedure is introduced. Instead of the displacements, the elements’ global nodal positions and nodal position-vector gradients, defined according to the absolute nodal coordinate formulation, are used as the searched parameters of the Newton–Raphson iterative procedure. For the finite elements, the planar isoparametric plates with 24 nodal degrees of freedom are employed to ensure the gradients’ continuity among the elements. As such, the presented procedure imposes no linearization on the strain measure, and therefore indicates a natural consistency with the nonlinear continuum theory. To verify the new procedure and to show its advantages, a real large deformation experiment and several numerical tests on the computer-generated images are studied for the standard, low-order, element-based digital image correlation and the presented procedure. The results show that the proposed procedure proves to be accurate and reliable for describing the rigid-body movement and simple deformations, as well as for determining the continuous finite strain field of a real specimen.     

基于数字图像体相关的物体内部三维位移场分析

在二维数字图像相关算法的基础上,推导了三维数字图像体相关算法,并应用于物体内部的三维位移场分析。用计算机模拟方法对SR-CT重建的物体内部三维图像施加已知变形,对变形前后三维数字图像进行体相关运算,获得三维位移场。在计算亚像素位移时,本文提出了一种三维的基于灰度梯度的算法,给出了梯度函数,阐述了数字模拟三维体相关的计算过程,通过数字模拟实验证明了算法的正确性和可靠性。     

Overview of High-temperature Deformation Measurement Using Digital Image Correlation

Background

Developments in digital image correlation (DIC) in the last decade have made it a practical and effective optical technique for displacement and strain measurement at high temperatures.

Objective

This overview aims to review the research progress, summarize the experience and provide valuable references for the high-temperature deformation measurement using DIC.

Methods

We comprehensively summarize challenges and recent advances in high-temperature DIC techniques.

Results

Fundamental principles of high-temperature DIC and various approaches to generate thermal environment or apply thermal loading are briefly introduced first. Then, the three primary challenges presented in performing high-temperature DIC measurements, i.e., 1). image saturation caused by intensified thermal radiation of heated sample and surrounding heating elements, 2) image contrast reduction due to surface oxidation of the heated sample and speckle pattern debonding, and 3) image distortion due to heat haze between the sample and the heating source, and corresponding countermeasures (i.e., the suppression of thermal radiation, fabrication of high-temperature speckle pattern and mitigation of heat haze) are discussed in detail. Next, typical applications of high-temperature DIC at various spatial scales are briefly described. Finally, remaining unsolved problems and future goals in high-temperature deformation measurements using DIC are also provided. 

Conclusions

We expect this review can guide to build a suitable DIC system for kinematic field measurements at high temperatures and solve the challenging problems that may be encountered during real tests.

     

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

Experimental and Numerical Methods for Exact Subpixel Shifting

An approach to quantifying the errors in digital image correlation (DIC) is presented using experimentally produced images. The challenge arises in creating exact subpixel shifted images in an experiment. This was accomplished via numerical binning of an ultra-high resolution image. The shifted images are then used for a preliminary analysis of 2D correlation software uncertainty and investigation of speckle pattern quality. Because it is often necessary to use numerically shifted images, for uncertainty quantification for instance, the optimum method of Fourier shifting is also presented.     

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.     

Subset-based local vs.finite element-based global digital image correlation:A comparison study

Being the two primary approaches for full-field kinematics measurements,both subset-based local digital image correlation(DIC) and finite element-based global DIC have been extensively studied.Nowadays,most commercial DIC systems employ local DIC algorithm because of its advantages of straight forward principle and higher efficiency.However,several researchers argue that global DIC can provide better displacement results due to the displacement continuity constraint among adjacent elements.As such,thoroughly examining the performance of these two different DIC methods seems to be highly necessary.Here,the random errors associated with local DIC and two global DIC methods are theoretically analyzed at first.Subsequently,based on the same algorithmic details and parameters during analyses of numerical and real experiments,the performance of the different DIC approaches is fairly compared.Theoretical and experimental results reveal that local DIC outperforms its global counterpart in terms of both displacement results and computational efficiency when element(subset) size is no less than 11 pixels.     

Displacement-Based Experimental Stress Analysis of a Circularly-Perforated Asymmetrical Isotropic Structure

This paper demonstrates the ability to determine the individual full-field components of stress, strain and displacement in finite asymmetrical engineering structures from recorded values of a single displacement component while not necessitating differentiation of the measured displacement data; a process which can be ill-conditioned and adversely influenced by data noise and quality. While the present approach of processing recorded displacements with a stress function is not new, previous cases have been restricted to symmetrical scenarios. Full-field displacements are measured here using the digital image correlation (DIC) method. As well as satisfying load equilibrium, the experimental results agree with those predicted using the finite element method (FEM).     

Measurement of deformations on concrete subjected to compression using image correlation

Because the nature of failure in concrete is complicated due to the material heterogeneity, a robust measuring method is essential to obtain reliable deformation data. A nondestructive displacement evaluation system using a digital image cross-correlation scheme, often called computer vision, is developed to make microscopic examinations of the fracture processes in concrete. This is a full-field measuring method that gives an accuracy within the micron range for a 100 mm × 75 mm viewing area. A feedback signal that combines the lateral and axial deformations provides a well-balanced imaging rate both before and after the peak load. Displacement vector diagrams or displacement contour maps of concrete reveal highly nonuniform deformations even in the elastic range. The processes of fracture in concrete are well defined at different deformation levels.