A comparison of 2D and 3D digital image correlation for a membrane under inflation

Three-dimensional (3D) digital image correlation (DIC) is becoming widely used to characterize the behavior of structures undergoing 3D deformations. However, the use of 3D-DIC can be challenging under certain conditions, such as high magnification, and therefore small depth of field, or a highly controlled environment with limited access for two-angled cameras. The purpose of this study is to compare 2D-DIC and 3D-DIC for the same inflation experiment and evaluate whether 2D-DIC can be used when conditions discourage the use of a stereo-vision system. A latex membrane was inflated vertically to 5.41 kPa (reference pressure), then to 7.87 kPa (deformed pressure). A two-camera stereo-vision system acquired top-down images of the membrane, while a single camera system simultaneously recorded images of the membrane in profile. 2D-DIC and 3D-DIC were used to calculate horizontal (in the membrane plane) and vertical (out of the membrane plane) displacements, and meridional strain. Under static conditions, the baseline uncertainty in horizontal displacement and strain were smaller for 3D-DIC than 2D-DIC. However, the opposite was observed for the vertical displacement, for which 2D-DIC had a smaller baseline uncertainty. The baseline absolute error in vertical displacement and strain were similar for both DIC methods, but it was larger for 2D-DIC than 3D-DIC for the horizontal displacement. Under inflation, the variability in the measurements were larger than under static conditions for both DIC methods. 2D-DIC showed a smaller variability in displacements than 3D-DIC, especially for the vertical displacement, but a similar strain uncertainty. The absolute difference in the average displacements and strain between 3D-DIC and 2D-DIC were in the range of the 3D-DIC variability. Those findings suggest that 2D-DIC might be used as an alternative to 3D-DIC to study the inflation response of materials under certain conditions.     

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.     

Calibration and correction of lens distortion for two-dimensional digital speckle correlation measurement

Lens distortion practically presents in optical imaging system using in two-dimensional digital speckle correlation measurement (2D-DSCM) system, and gives rise to additional errors in the displacement and strain measurement. Camera calibration procedure is performed to obtain the coefficients of radial distortion and tangential distortion. The corrected displacement fields can be calculated using the distortion coefficient. The influence of distortion on displacement and strain measurement errors in experiment is further discussed. The three-point bending test result shows that the camera lens calibration method can effectively eliminate the effect of lens distortion and improve displacement and strain measurement accuracy.     

An experimental method for eliminating effect of rigid out-of-plane motion on 2D-DIC

The out-of-plane motion is one of the most important factors that affect the precision of two-dimensional digital image correlation (2D-DIC). In this paper, a novel solution is presented to improve conventional 2D-DIC by eliminating the effect of out-of-plane motion, including translation and rotation. Firstly, an experimental technique using two projected laser strips is proposed to measure the out-of-plane motion of a planar specimen. A theoretical model is then established to predict the pseudostrains caused by out-of-plane motion based on the pin-hole imaging model. Using the measured out-of-plane displacement, the captured deformed images used in 2D-DIC are amended to eliminate the effect of out-of-plane motion by the theoretical model. Finally, two experiments were conducted to validate the effectiveness of the proposed method. Results indicate that application of the proposed method can effectively eliminate the errors caused by out-of-plane motion.     

Investigation of Portevin-Le Chatelier effect in 5456 Al-based alloy using digital image correlation

A variety of experimental methods have been proposed for Portevin-Le Chatelier (PLC) effect. They mainly focused on the in-plane deformation. In order to achieve the high-accuracy measurement, three-dimensional digital image correlation (3D-DIC) was employed in this work to investigate the PLC effect in 5456 Al-based alloy. The temporal and spatial evolutions of deformation in the full field of specimen surface were observed. The large deformation of localized necking was determined experimentally. The distributions of out-of-plane displacement over the loading procedure were also obtained. Furthermore, a comparison of measurement accuracy between two-dimensional digital image correlation (2D-DIC) and 3D-DIC was also performed. Due to the theoretical restriction, the measurement accuracy of 2D-DIC decreases with the increase of deformation. A maximum discrepancy of about 20% with 3D-DIC was observed in this work. Therefore, 3D-DIC is actually more essential for the high-accuracy investigation of PLC effect.     

三维时域散斑动态干涉测量系统的集成化设计

三维电子散斑干涉技术（3D ESPI）具有非接触、高精度、高灵敏度和全场测量等优点,被广泛应用于许多领域。为了实现非接触动态全场三维测量,设计并建立了一个紧凑、完备的三维测量系统。用一个多波长光纤耦合激光器代替3个独立光源,产生的离面、面内散斑干涉图仅用一台彩色CCD相机就能捕捉和处理;整个测量系统采用笼式结构,具有高度的灵活性和稳定性;对基于小波变换的相位展开算法进行了编程,实现了被测物体三维位移信息的完整提取。实验证明该测量系统可以实时获取被测物体的三维位移,在测量实验中,获得的三维位移值17.68 μm、36.23 μm、13.85 μm,相比于实际位移值18.1 μm、36.4 μm、14.0 μm它们的绝对误差分别为0.42 μm、0.17 μm、0.15 μm,相对误差分别为2.3%、0.5%、1.1%。     

New method to characterize mesoscopic range and very small strain with using multi-wave X-ray diffraction

A new technique to observe mesoscopic-range strain fields (up to several hundreds of nm) is proposed, using modulation of the crystal-truncation-rod (CTR) scattering caused by Bragg reflection. This technique is particularly sensitive to small, long-range strain fields near crystal surfaces and interfaces, which are usually difficult to be discriminated by using Bragg reflection. A simple interpretation can be made for the modulation profile: the technique is physically simple with a few parameters fitted to the data and, independently of any model, is able to determine the total displacement due to mesoscopic strain field for depths up to several hundreds of nanometers. We applied this method to a Si(0 0 1) wafer whose surface is covered with a thermal oxide layer 3 nm thick. On the basis of the expressions we obtained for the modulation profile a least-squares fitting was carried out to give a result that under the oxide layer there exists a total displacement of −0.16 Å. It was also revealed from the visibility of the modulation profile that the total displacement has a static fluctuation of at least ±0.13 Å in the lateral direction. The new method can be used for the correction of the errors of the X-ray standing wave (XSW) method produced by strained layers near crystal surfaces.     

Measuring Microscopic Deformations with Digital Image Correlation

This paper describes a feasibility study of a high magnification full field deformation measurement system. The system consists of an image acquiring and analysis system and an optical metallurgical microscope. It can be used to determine in-plane surface deformations at magnifications up to 2000 pixels/mm. Images from an optical microscope are acquired by using a CCD camera and a digitizing board, and stored in a microcomputer. The surface displacement field is determined by using the digital image correlation method. Displacement gradients on the surface are computed after smoothing the displacement data. By performing a number of experiments and analyzing them, sources of errors in the system and their magnitudes are determined. Methods to minimize these errors are also discussed. It is realized that the system has every potential of quantifying in-plane surface displacement fields and the strains on the surfaces of specimens used in the research areas of micromechanics of solids. © 1997 Elsevier Science Ltd. All rights reserved.     

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.     

Microscopic 3-D displacement field measurements using digital speckle photography

A technique to measure object shape and 3-D displacement fields in micro-scale is offered by microscopic stereo digital speckle photography. The displacement of the random features that are often present on many engineering surfaces when viewed in a microscope is measured with the system, using image correlation. In this paper the equipment, physical model and calibration routines are described. The technique can be applied for sub-mm sized objects of arbitrary shape for small deformation fields. As a verifying experiment, an in-plane rotation of a flat calibration plate is presented. The expected in-plane errors are shown to be less than 0.1 μm and the corresponding out-of-plane errors about three times larger. As a pilot experiment, micro-structural paper expansion is studied, when exposed to humidity. The scaling properties of the microscope as well as the sampling criteria and reliability of the system are discussed in detail.     

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.     

Hysteresis compensation of piezoelectric actuators: The modified Rayleigh model

In this study, we develop a novel modified Rayleigh model for hysteresis compensation in piezoelectric actuators. Piezoelectric actuators suffer from hysteresis, in large drive fields of more than 100 V, which can result in serious displacement errors. The typical phenomenological approach is to use the Rayleigh model; however, this model gives more than 10% difference with experiments at the large electric fields of more than 1 kV/mm. Furthermore, there are no studies that apply the Rayleigh model to the compensation of precision actuators, such as stack actuators; it has only been applied in the study of the physical properties of piezoelectric materials. Therefore, we propose a modified Rayleigh model, in which each coefficient is defined differently according to whether the field is increasing or decreasing to account for asymmetry at the high fields. By applying a computer-based control from an inverse form of this modified Rayleigh model, we show that we can compensate for hysteresis to reduce the position error to less than five percent. This model has the merits of reducing complicated fitting procedures and of saving computation time compared to the Preisach model. Specifically, this model cannot only predict the hysteresis curves in all local fields using only one fitting procedure, but also make it possible to control the displacement of various piezo-based actuators without expensive sensors, based on the charge-based model.     

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.     

Study on Combined Method Based on 3-D ESPI

The finite element method (FEM),whether the calculation is accurate or not,depends closely on object boundary condition.If the three dimensional displacement of the object obtained in experiment is regarded as its boundary condition,a new method combining the results of experiment and calculation,called combined method (CM),is formed.The combined method possess advantages of experiment and calculation.It can correct calculation and improve the accuracy of FEM.Accordingly it has more practicability.In this paper,the three dimensional displacement fields of a typical beam loaded at three points are tested by using 3-D electric speckle pattern interferometry (ESPI).Using the experimental results as boundary condition the whole three-dimensional displacement fields can be calculated by FEM.The beam′s three-dimensional displacement fields obtained by FEM agree very well with those obtained by experiment.This proves that the combined method is effective and practicable.     

Study on Combined Method Based on 3-D ESPI

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A stereoscopic digital speckle photography system for 3-D displacement field measurements

Stereoscopic digital speckle photography offers a technique to measure object shapes and 3-D displacement fields in experimental mechanics. The system measures the displacement of a random white light speckle pattern, which somehow is present on the object surface, using digital correlation. This paper describes a general physical model for stereo imaging systems. A camera calibration algorithm, which takes the distortion in the lenses into account, is also presented and evaluated by real experiments. Standard deviations of small deformations as low as 1% of the pixel size for in-plane deformations and 6% of the pixel size for the out-of-plane component are reported. Using the calibration algorithm described, the main source of errors is random errors originating from the correlation algorithm.     

结合稳健中国余数定理的合成孔径声呐多子带运动补偿算法

针对运动误差过大导致基于相位的时延估计发生模糊的问题,提出了一种多子带处理和稳健中国余数定理结合的合成孔径声呐运动补偿方法。该方法利用前后两帧回波在多个子频带上的相位差获得模糊时延估计,再根据模糊时延之间的关联性,应用稳健中国余数定理估计真实的时延,最后通过所估计的时延对原始回波进行校正。湖试数据处理结果表明该方法能精确补偿运动误差对成像的影响,进行运动补偿后,包裹目标成像结果的方位向虚假目标被有效消除,且目标的轮廓也变得更加清晰;对线缆目标的成像结果进行斜距向剖面分析,剖面图的-3 dB宽度由运动补偿前的9.05个像素点缩小为运动补偿后的2.06个像素点,线缆目标的聚焦程度明显增强。      

A novel technique for measuring 3D deformation of adhesively bonded single lap joint

An easy-to-implement yet practical single-camera microscopic stereo-digital image correlation(stereo-DIC) technique is proposed for surface three-dimensional(3D) deformation measurement of singe lap joint(SLJ) samples subjected to mechanical loads. The basic principles, optical configurations and implementation procedures of the proposed technique are described in detail. Compared with existing single-camera 2D-DIC technique, which has been regularly used for in-plane deformation measurement of a SLJ specimen, the proposed technique offers the special merit of simultaneously determining all the three displacement components by simply adding two additional optical elements to existing single-camera 2D-DIC systems. The accuracy and effectiveness of the proposed technique is demonstrated by measuring the 3D deformation of a SLJ specimen subjected to quasi-static tensile loads.     

Straightness Measurement Using Laser Diode and CCD Camera

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多程放大器光束空间分布的优化设计

This paper focuses on measuring straightness of large-scale dimension by using laser diode fiber alignment, diffraction imaging technique and a CCD camera. In this method, we use a laser diode fiber alignment beam as the datum reference of straightness, deviation of the measured from this datum, can be detected by a CCD camera directly. Also a novel image processing algorithm is presented. The experiment result shows that the measurement range of L (m), the measurement accuracy of the system is 3+2.3×10-6L(\mm).