Quality assessment of speckle patterns for digital image correlation

Digital image correlation (DIC) is an optical–numerical full-field displacement measuring technique, which is nowadays widely used in the domain of experimental mechanics. The technique is based on a comparison between pictures taken during loading of an object. For an optimal use of the method, the object of interest has to be covered with painted speckles. In the present paper, a comparison is made between three different speckle patterns originated by the same reference speckle pattern. A method is presented for the determination of the speckle size distribution of the speckle patterns, using image morphology. The images of the speckle patterns are numerically deformed based on a finite element simulation. Subsequently, the displacements are measured with DIC-software and compared to the imposed ones. It is shown that the size of the speckles combined with the size of the used pixel subset clearly influences the accuracy of the measured displacements.     

Whole-field thickness strain measurement using multiple camera digital image correlation system

Three Dimensional digital image correlation(3D-DIC) has been widely used by industry, especially for strain measurement. The traditional 3D-DIC system can accurately obtain the whole-field 3D deformation. However, the conventional 3D-DIC system can only acquire the displacement field on a single surface, thus lacking information in the depth direction. Therefore, the strain in the thickness direction cannot be measured. In recent years, multiple camera DIC (multi-camera DIC) systems have become a new research topic, which provides much more measurement possibility compared to the conventional 3D-DIC system. In this paper, a multi-camera DIC system used to measure the whole-field thickness strain is introduced in detail. Four cameras are used in the system. two of them are placed at the front side of the object, and the other two cameras are placed at the back side. Each pair of cameras constitutes a sub stereo-vision system and measures the whole-field 3D deformation on one side of the object. A special calibration plate is used to calibrate the system, and the information from these two subsystems is linked by the calibration result. Whole-field thickness strain can be measured using the information obtained from both sides of the object. Additionally, the major and minor strain on the object surface are obtained simultaneously, and a whole-field quasi 3D strain history is acquired. The theory derivation for the system, experimental process, and application of determining the thinning strain limit based on the obtained whole-field thickness strain history are introduced in detail.     

高温下数字图像相关散斑最优成像探究

为了测量材料在高温甚至超高温下的力学性能,采用数字图像相关方法,并研究其在高温下的最优成像。采取不同的散斑制作方法,同时加入不同颜色的高温漆,在不同的温度节点,外加不同光源及相应的滤波片,采集并观察图像是否具有良好的对比度。普通的单色光源在800℃以后会逐渐失效,无法获取图像,而紫外光在1 200℃时依然可以获取较好的图像,且直接利用试件本身颜色作为底色效果更佳。采用紫外光照明可以实现DIC在高温环境下的测量。同时利用黑色或者蓝色散斑直接喷涂在试件上有着最佳的对比度,要优于常规的散斑制作方法。     

Incremental calculation for large deformation measurement using reliability-guided digital image correlation

Conventional digital image correlation (DIC) technique using a fixed reference image provides high-accuracy measurements but normally fails when serious decorrelation effect occurs in the deformed images due to large deformation, serious illumination fluctuations or other reasons. In this paper, an incremental reliability-guided digital image correlation (RG-DIC) technique, by combining the recently developed RG-DIC technique and an automatic reference image updating scheme, is proposed for large deformation measurement. In the incremental RG-DIC technique, a seed point is defined in the original reference image and searched in the deformed images, if the estimated correlation coefficient is larger than a preset threshold, which means no serious decorrelation effect exists in the deformed image, the RG-DIC technique is used to continue correlation analysis to obtain full-field displacements. Otherwise, the image recorded just before the current deformed image is chosen as an updated reference image to proceed with correlation analysis. Afterwards, the incremental displacements extracted by comparing the current deformed image and the updated reference image can be cumulated to determine the overall deformation. The effectiveness of the proposed technique is demonstrated by retrieving the full-field deformation of a foam sample subjected to large compressive deformation.     

Strain field denoising for digital image correlation using a regularized cost-function

In digital image correlation (DIC), the widely used forward-additive Newton–Raphson (FA-NR) algorithm and the recently introduced equivalent but more efficient inverse-compositional Gauss–Newton (IC-GN) algorithm are capable of providing both displacements and displacement gradients (strains) for each calculation point. However, the obtained displacement gradients are seriously corrupted by various noises, and for this reason these directly computed strains are usually considered as useless information and therefore discarded. To extract strain distributions more accurately, much research efforts have been dedicated to how to smooth and differentiate the noisy displacement fields using appropriate numerical approaches. In this contribution, contrary to these existing strain estimation approaches, a novel and alternative strain estimation approach, based on denoising the noisy strain fields obtained by FA-NR or IC-GN algorithm using a regularized cost-function, is proposed. The effectiveness and practicality of the proposed strain estimation technique is carefully examined using both computer-simulated images with imposed homogeneous and inhomogeneous deformation, and experimentally obtained images. Experimental results reveal that the strains obtained by the proposed method are comparable to those determined by post-processing of the displacement fields using conventional pointwise least squares strain estimation approach.     

Full-field digital image correlation with Kriging regression

A full-field Digital Image Correlation (DIC) method with integrated Kriging regression is presented in this article. The displacement field is formulated as a best linear unbiased model that includes the correlations between all the locations in the Region of Interest (RoI). A global error factor is employed to extend conventional Kriging interpolation to quantify displacement errors of the control points. An updating strategy for the self-adaptive control grid is developed on the basis of the Mean Squared Error (MSE) determined from the Kriging model. Kriging DIC is shown to outperform several other full-field DIC methods when using open-access experimental data. Numerical examples are used to demonstrate the robustness of Kriging DIC to different choices of initial control points and to speckle pattern variability. Finally Kriging DIC is tested on an experimental example.     

A space-time approach in digital image correlation: Movie-DIC

A new method is proposed to estimate arbitrary velocity fields from a time series of images acquired by a single camera. This approach, here focused on a single spatial plus a time dimension, is specialized to the decomposition of the velocity field over rectangular shaped (finite-element) bilinear shape functions. It is therefore assumed that the velocity field is essentially aligned along one direction. The use of a time sequence over which the velocity is assumed to have a smooth temporal change allows one to use elements whose spatial extension is much smaller than in traditional digital image correlation based on successive image pairs. This method is first qualified by using synthetic numerical test cases, and then applied to a dynamic tensile test performed on a tantalum specimen. Improvements with respect to classical digital image correlation techniques are observed in terms of spatial resolution.     

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     

Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns

This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such “designer patterns” are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 µε are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.     

Study of optimal subset size in digital image correlation of speckle pattern images

This paper investigates the effect of subset size, associated with image pattern quality and subset displacement functions, on the accuracy of deformation measurements by digital image correlation(DIC). A concept of subset entropy is introduced in this work to quantify the subset image pattern quality for DIC analysis and its effectiveness was demonstrated by experimental studies. By employing white-light images with almost uniform subset entropy and first-order displacement functions, the effect of subset size on DIC analysis was investigated for the deformation cases of translation, uniform deformation, and simulated quadratic deformation, respectively. The results show that the chosen subset size must be large enough for precise displacement measurements when subset displacement functions match underlying actual deformation. On the other hand, optimal subset size in DIC for nonhomgeneous deformation measurements appears as a result of a tradeoff between the influence of random errors and systematic errors.     

A weighting window applied to the digital image correlation method

In the digital image correlation method, two steps are used to calculate the displacements of tested images. The first step is to locate the integer-pixel displacement, and the next one is to compute the sub-pixel displacement based on the first step. The benefit from the computation method for the integer-pixel displacement is that its results directly affect the displacement accuracy of each point in tested images. In this paper, a new method is developed to calculate the displacement fields between two images taken before and after deformation of an object. A new correlation function with a weighting factor related to the position of each point in the image is taken into account. The analysis and experimental results confirm the validity of the new method. In addition, the calculation results from our method have more accuracy than that of the traditional one.     

Application of iteration and finite element smoothing technique for displacement and strain measurement of digital speckle correlation

In this paper, an improved method for measuring displacement in digital speckle correlation technology, which is based on an iterative and spatial-gradient algorithm, is developed. After obtaining full-field displacement, both finite element method and 2D generalized cross-validation (GCV) algorithm are adopted for smoothing the displacement field, and then the strain field can be obtained from the smoothed displacement field. The method is estimated by simulated speckle patterns and three-point bending experiment. All the results show the improved method can obtain a reasonable estimation of displacement and strain fields in digital speckle correlation method.     

Assessment of speckle-pattern quality in digital image correlation based on gray intensity and speckle morphology

In digital image correlation (DIC), speckle patterns are generated on the surface of a specimen to resolve uniqueness issues. Thus, speckle patterns significantly affect the accuracy of image correlation. To assess the quality of speckle patterns, the standard deviation of gray intensities within each speckle (SDGIS) is introduced as a new metric. On the basis of the cumulative distribution of SDGIS, speckle-pattern quality measurement (ρ) is proposed, which integrates the features of gray intensity and speckle morphology. Twelve speckle patterns are generated by changing the spraying time and nozzle sizes of an airbrush because these are associated with the speckle volume fraction and speckle size, respectively. In addition, three displacement fields are used to investigate the effects of speckle patterns on the accuracy of the DIC results. For the 12 speckle images associated with the three displacement fields, the correlation results demonstrate that the proposed speckle-pattern quality measurement is inversely proportional to the averaged error of the subset method. This is statistically confirmed by evaluating the correlation coefficient and p-value. Furthermore, the error of the subset method is more affected by speckle patterns than the subset size when the subset size is sufficiently large.     

Measuring thickness change of transparent plate by electronic speckle pattern interferometry and digital image correlation

The thickness change of transparent plates was measured by electronic speckle pattern interferometry (ESPI) method and digital image correlation (DIC) method. An out-of-plane ESPI system was developed based on the Michelson interferometer, and a new thickness measurement method was designed, which is on the basis of Snell's law of refraction and DIC. The main principles and experimental procedures of these two methods were presented. The thickness change of polymethyl specimens under uniaxial tensile loading were measured by the optical techniques and compared with each other. The results reveal that the data obtained with DIC method achieve better linearity than ESPI.     

A novel 2nd-order shape function based digital image correlation method for large deformation measurements

Compared with the traditional forward compositional matching strategy, the inverse compositional matching strategy has almost the same accuracy, but has an obviously higher efficiency than the former in digital image correlation (DIC) algorithms. Based on the inverse compositional matching strategy and the auxiliary displacement functions, a more accurate inverse compositional Gauss-Newton (IC-GN2) algorithm with a new second-order shape operator is proposed for nonuniform and large deformation measurements. A theoretical deduction showed that the new proposed second-order shape operator is invertible and can steadily attain second-order precision. The result of the numerical simulation showed that the matching accuracy of the new IC-GN2 algorithm is the same as that of the forward compositional Gauss-Newton (FC-GN2) algorithm and is relatively better than in IC-GN2 algorithm. Finally, a rubber tension experiment with a large deformation of 27% was performed to validate the feasibility of the proposed algorithm.     

Kalman filter based initial guess estimation for digital image correlation

In applications digital image correlation based algorithms often present a basis for analysis of movement/deformation of bodies. The sequence of the obtained images is analyzed for this purpose. Especially, in cases when the body׳s movement/deformation between two successive images is significant, the initial guess can have a major influence on the execution speed of the algorithm. In the worst case it can even cause the divergence of the algorithm. This was the inspiration to develop a new and unique approach for an accurate and reliable determination of an initial guess for each image pixel. Kalman filter has been used for this purpose. It uses past measurements of observed variable(s) for calculations. Beside that it also incorporates state space model of the actual system. This is one of the most important advantages provided by Kalman filter. The determined initial guess by the proposed method is actually close to the true one and it enables fast convergence. Even more important property of this approach is the fact that it is not path-dependant because each image pixel, which is defined in ROI, is tracked through the sequence of images based on its own past measurements and general state space model. Consequently, the proposed method can be used to analyze tasks where discontinuities between image pixels are present. The applied method can be used to predict an initial guess where reference and deformed subsets are related by translational and rotational motion. The advantages mentioned above are verified with numerical and real experiments. The experimental validations are performed by NR (Newton–Raphson) approach which is the most widely used. Beside NR method the presented algorithm is applicable for other registration methods as well. It is used as an addition for calculation of initial guesses in a sequence of deformed images.     

Evaluation and improvement of digital image correlation uncertainty in dynamic conditions

Dealing with a moving target causes a motion effect (i.e. blurring) on the acquired images. This factor is an important source of measurement uncertainty while exploiting the Digital Image Correlation (DIC) technique. Therefore, the present study aims to evaluate and improve DIC uncertainty in dynamic conditions in the case of translating target. The study focuses on 2D DIC. In the case of 3D DIC similar problems arise, and therefore a complete understanding of two dimensional conditions will be of great help for further studies which deal with 3D conditions. The whole work can be divided into two main parts. In the first part, two different methods to simulate the motion effect on a reference image are proposed, discussed and validated. These methods allow simulating the acquired images in a real dynamic test and estimating the measurement uncertainty caused by the motion effect. The validation is performed by conducting several harmonic vibration tests with an electromagnetic shaker. In the second part of the study a numerical technique is proposed to estimate the motion effect present in an acquired image. This technique gives two main advantages. First of all, since the motion effect itself has a known influence on the uncertainty of measurement (first part of the study), we can predict the DIC׳s uncertainty by just having an acquired image. Furthermore, this numerical technique is used in the last part of this work to improve the performances of DIC in dynamic applications. In this way the bias error and the uncertainty of measurements were considerably decreased.     

基于单幅数字散斑投影及图像相关的离面振动测量

采用单幅数字散斑图投影及高速数字图像采集技术,研究了动态离面位移的测量。采用商用液晶投影仪将计算机产生的模拟散斑图投影到待测动态变形物体表面,由高速数字图像采集设备摄取并保存变形散斑图,采用时间序列数字图像相关软件计算出物体表面各点随时间变化的离面位移。这种方法用于振动分析时不仅可以获得振型分布,而且还可以获得各点的振幅值。与现有的激光频闪照相测振及激光多普勒测振等方法相比,具有光学系统简单,可全场定量测量。悬臂梁振动实验结果证实了该方法的有效性。     

Digital speckle correlation method with compensation technique for strain field measurements

In the strain field measurements, especially in large strain field measurements, the correlation coefficient values obtained by the digital speckle correlation method are usually very low due to the relative pixel movement of the subset. The measuring error, therefore, is increased. A primary method, that is called compensation algorithm, is introduced for improving the correlation coefficient. A flow scheme with the compensation algorithm of our software is developed and some improved techniques for reducing the calculation time and error are discussed in the paper. After obtaining a set of displacement data with high correlation coefficient, a de-noise wavelet processing is adopted. It is obvious that the measuring accuracy of the strain field is better then before. A strain field of testing experiment is performed with this compensation technique. The correlation coefficients can increase from 0.70 to 0.99, which will be of much benefit for the improvements of the measuring accuracy.     

Digital image correlation with gray gradient constraints: Application to spatially variant speckle images

As a carrier of local deformation information, speckle pattern inside a subset is usually crucial for surface displacement acquisition based upon a digital image correlation (DIC) method, since both accuracy and precision of DIC method are closely related to the amount of speckle information in a subset. Although some comprehensive theoretical frameworks have been developed to estimate the quality of local speckle patterns, it is still a great challenge how to effectively integrate the subset speckle information into the well-developed correlation criteria used for DIC. By means of a well-designed square window function, we here propose the concept of continuous subset in order to modulate subset size in a continuously derivable manner. Afterwards, we further develop a new constrained zero-normalized sum-of-squared differences (CZNSSD) criterion and construct the corresponding iterative algorithm, based on which the subset size involved can be automatically determined according to the necessary amount of speckle information. Numerical results of synthetic speckle images indicate that the set of algorithm can enhance the accuracy and precision of displacement measurement, especially for spatially variant speckle images.