Accuracy enhancement of digital image correlation with B-spline interpolation

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting version is employed to enhance the accuracy of DIC analysis. Theories are introduced, and simulation results are presented to illustrate the effectiveness of the method as compared with the common bicubic interpolation.     

Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique

The aim of this work is to investigate the sources of errors related to digital image correlation (DIC) technique applied to strain measurements. The knowledge of such information is important before the measured kinematic fields can be exploited. After recalling the principle of DIC, some sources of errors related to this technique are listed. Both numerical and experimental tests, based on rigid-body motion, are proposed. These tests are simple and easy-to-implement. They permit to quickly assess the errors related to lighting, the optical lens (distortion), the CCD sensor, the out-of-plane displacement, the speckle pattern, the grid pitch, the size of the subset and the correlation algorithm. The errors sources that cannot be uncoupled were estimated by amplifying their contribution to the global error. The obtained results permit to address a classification of the error related to the used equipment. The paper ends by some suggestions proposed in order to minimize the errors.     

Delamination and damage studies of composite materials using phase-shifting interferometry

Composite materials offer a unique advantage over conventional engineering materials in that structural properties can be tailored to suit specific applications. However, the inherent anisotropy and the discrete layer-by-layer fabrication method of composite materials lead to mechanical behavior and failure characteristics that are quite different from those of homogeneous materials. Consequently, failure modes such as delamination in polymer matrix composites and matrix cracking and damage in ceramic matrix materials prohibit these materials from being used in conventional engineering structures, as well as making their characterization in the laboratory difficult. In this paper, an experimental photomechanics technique called phase-shifting moiré interferometry is described. This technique is capable of providing analysts and designers (both material and structural) with detailed displacement and strain fields near discontinuities in these materials. The technique allows high resolution measurements of in-plane surface displacements to be made without introducing global smoothing errors, thus preserving the integrity of data near cracks, discontinuities and material interfaces. In this paper, the advantages of phase-shifting moiré interferometry will be illustrated through several problems involving composite materials.     

Multi-camera digital image correlation method with distributed fields of view

A multi-camera digital image correlation (DIC) method and system for measurements of large engineering objects with distributed, non-overlapping areas of interest are described. The data obtained with individual 3D DIC systems are stitched by an algorithm which utilizes the positions of fiducial markers determined simultaneously by Stereo-DIC units and laser tracker. The proposed calibration method enables reliable determination of transformations between local (3D DIC) and global coordinate systems. The applicability of the method was proven during in-situ measurements of a hall made of arch-shaped (18 m span) self-supporting metal-plates. The proposed method is highly recommended for 3D measurements of shape and displacements of large and complex engineering objects made from multiple directions and it provides the suitable accuracy of data for further advanced structural integrity analysis of such objects.     

Numerical investigation on thermal properties at Cu-Al interface in micro/nano manufacturing

A hybrid model by integrating TTM (two-temperature model) and MD (molecular dynamics) is proposed to investigate the properties on interface of dissimilar materials under thermal flux conditions. This model can describe the electron phonon coupling and phonon scattering at the interface of different metals easily. By comparing the Cu-Cu interface and Cu-Al interface, the atoms of the Cu-Cu interface at different sides tend to move together; while, the atoms displacements of Cu and Al are opposite along the interface, which may cause stress and voids at the interface. Moreover, the propagation mechanisms of nanocracks and the corresponding change of temperature distribution and thermal flux are investigated. The results show that the interfaces of dissimilar materials are prone to crack initiations, leading to delaminations because of the high temperature. All these are useful for understanding the deformation and failure of the interfaces structures. It implies a potential method for design and analysis of interface structure in micro/nano manufacturing.     

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     

Thermal stresses in box-type laser packages

The effect of Au coating on thermally induced stresses in box-type semiconductor laser packages was investigated by a finite-element method (FEM). The simulated results showed that Invar–Invar joints with Au coating have maximum stresses two times higher than joints without Au coating. This is due to the different coefficients of the thermal expansion (CTE) between dissimilar materials of Invar and Au, resulting in higher stresses. Maximum stresses were also found to be increased as the Au thickness increased. This effect is attributed to the increase in the thermal gradient in the welded region provided by the increased thermal conduction of the thicker Au coating layer. These results suggest that both the difference in CTE between dissimilar materials and higher thermal conduction of Au coating layer have an important impact on thermally induced stresses for optoelectronic packages having laser-welded Au coated materials.     

A digital image correlation method for fatigue test experiments

In this paper, a method based on the digital image correlation (DIC) technique is proposed to monitor the crack growth process during a cyclic fatigue test. Stroboscopic illumination is used to acquire DIC speckle pattern images while the test sample is dynamically loaded. The proposed DIC algorithm uses the fact that the load is periodic to increase the accuracy of the displacement field estimates (a sinusoidal fitting method is introduced for this purpose). Using the appropriate post-processing both the crack lengths and the stress intensity factors can be estimated in function of the number of fatigue cycles. A validation test case on an aluminum U-profile will be presented in the paper.     

Quantification of a Ti(CxN1−x) based multilayer by Auger Electron Spectroscopy

Auger Electron Spectroscopy (AES) is an analytical technique sensitive to the surface of materials and providing elemental and chemical composition of conductive samples. The excellent spatial resolution and its quantification possibilities, even for light elements, make AES a commonly used technique to investigate surface and interfaces.TiN-like materials have a wide range of applications depending on their stoichiometry, but their composition is still complex (or at least not straightforward) to determine because of a strong overlapping of the Ti LMM with the N KLL Auger transitions. This quantification problem can be circumvented using computerised calculations as target factor analysis (TFA) to estimate the different nitrogen and titanium contributions in this peaks overlap. However, a more simple method, based on the study of Ti LMM and Ti LMV area ratio of pure TiN and TiC reference samples, is described in this paper and can be used to obtain the atomic composition of any titanium nitride based compound, whatever the complexity of the material. This method is an alternative to easily quantify TiN-like compounds by AES.As an illustration, a Ti(C_xN_1−x) based multilayer deposited on a hardmetal substrate was investigated. This quantification method was successfully used to evidence three different layers and the diffusion phenomenon at the interfaces between the layers. This study was completed with a quantitative SIMS depth profile that the high sensitivity and depth resolution allowed to measure the small variations of composition lower than the uncertainty of AES.     

An improved method for shape measurement using two-dimensional digital image correlation

Shape measurement is a significant application of digital image correlation (DIC). An improved method that combines a rotatable plane mirror is proposed to measure the shape of an immovable object. In this method, two images, one before and the other after rotating the plane mirror, are obtained and then in-plane translation which related to the shape of the detected object can be calculated by the use of two-dimensional digital image correlation (2D DIC). The relationship between the in-plane translation and the shape of the object is described. Experimental results show that the proposed method is feasible for shape and distance measurement with high accuracy.     

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.     

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.     

微分干涉相衬显微镜中偏光棱镜设计

微分干涉相衬显微测量术在生物医学、材料科学等领域中有广泛应用 ,其中偏振分光棱镜设计是关键技术之一。对应用于微分干涉相衬显微系统中的偏振分光棱镜 Nomarski棱镜的主要参数之间的关系进行分析 ,并做了设计计算 ,得出了一些有实用价值的结论 ,使 Nomarski棱镜的设计更简便 ,有利于促进微分干涉相衬显微测量术在我国的推广应用     

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.     

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.     

A linear least squares approach for evaluation of crack tip stress field parameters using DIC

In the present work, an experimental study is carried out to estimate the mixed-mode stress intensity factors (SIF) for different cracked specimen configurations using digital image correlation (DIC) technique. For the estimation of mixed-mode SIF׳s using DIC, a new algorithm is proposed for the extraction of crack tip location and coefficients in the multi-parameter displacement field equations. From those estimated coefficients, SIF could be extracted. The required displacement data surrounding the crack tip has been obtained using 2D-DIC technique. An open source 2D DIC software Ncorr is used for the displacement field extraction. The presented methodology has been used to extract mixed-mode SIF׳s for specimen configurations like single edge notch (SEN) specimen and centre slant crack (CSC) specimens made out of Al 2014-T6 alloy. The experimental results have been compared with the analytical values and they are found to be in good agreement, thereby confirming the accuracy of the algorithm being proposed.     

Performance of iterative gradient-based algorithms with different intensity change models in digital image correlation

Digital image correlation (DIC) is a non-contact and powerful tool for whole-field displacement and strain measurement in modern optical metrology. In the DIC technique, the gradient-based algorithm is one of the most commonly used sub-pixel registration algorithms due to its effectiveness and accuracy. Thus, this algorithm has been further investigated and improved by many researchers to increase its accuracy. In the existing gradient-based algorithms, there are three relation models for the gray level intensity of a point in the undeformed and deformed images: namely the constant intensity model, the linear intensity change model and the non-linear intensity change model. However, little quantitative investigation has been conducted to compare their performance. In this paper, three iterative gradient-based algorithms are given using the corresponding intensity change model and the iterative least squares (ILS) solving method. The accuracy, robustness and computational efficiency of the three algorithms for intensity variation are investigated through numerical simulation experiments. The experimental results reveal that the algorithm generated using the non-linear intensity change model is the most accurate, robust and efficient of the three algorithms and the algorithms generated using the linear and non-linear intensity change models have approximately the same accuracy when the intensity variation is small between undeformed and deformed images.     

Path-independent digital image correlation with high accuracy,speed and robustness

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy.     

Perspectives of cross-sectional scanning tunneling microscopy and spectroscopy for complex oxide physics

Complex oxide heterostructure interfaces have shown novel physical phenomena which do not exist in bulk materials. These heterostructures can be used in the potential applications in the next generation devices and served as the playgrounds for the fundamental physics research. The direct measurements of the interfaces with excellent spatial resolution and physical property information is rather difficult to achieve with the existing tools. Recently developed cross-sectional scanning tunneling microscopy and spectroscopy (XSTM/S) for complex oxide interfaces have proven to be capable of providing local electronic density of states (LDOS) information at the interface with spatial resolution down to nanometer scale. In this perspective, we will briefly introduce the basic idea and some recent achievements in using XSTM/S to study complex oxide interfaces. We will also discuss the future of this technique and the field of the interfacial physics.     

Effects of discontinuous magnetic permeability on magnetodynamic problems

A novel approximation technique using Lagrange finite elements is proposed to solve magneto-dynamics problems involving discontinuous magnetic permeability and non-smooth interfaces. The algorithm is validated on benchmark problems and is used for kinematic studies of the Cadarache von Kármán Sodium 2 (VKS2) experimental fluid dynamo.