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.     

电子散斑干涉位移场分离技术及其在三维测量中的应用

提供了一种可将离面位移与面内位移分离的三维位移场测量方法.在双光束电子散斑干涉中增加参考光,使这一路参考光为两光束所共用.两束光各自独立地对变形物体进行测量,结合相移技术,可分别得到包含离面和面内位移信息的二幅位相图.只需简单的位相运算就能够将面内位移场与离面位移场分离.在竖直方向上,采用两光束对称照明被测物,直接测量面内位移竖直方向分量.本文将该技术应用到柴油机油泵测量上,得到了油泵的三维位移场.该技术为三维位移场的测量提供了一种新的有效途径,也为柴油机零部件的强度和刚度分析评价提供了新的方法.     

A modified moiré interferometer for three-dimensional displacement measurement

This paper presents a new optical interferometric system, MMI-T/G, composed of a modified four-beam moire interferometer and a Twyman/Green interferometer. The MMI-T/G system can measure threedimensional displacement fringe patterns with a single loading on the specimen, and the in-plane and out-of-plane displacement fields can be measured independently and defined clearly. The optical setup has the advantages of structural novelty, flexibility, and high fringe contrast. Moreover, the in-plane displacement sensitivity is twice of that of the normal moire interferometer. The measuring techniques to obtain the fringe patterns and displacement fields using the MMI-T/G system axe described. The experimental results of thermal displacement of an electronic device are shown.     

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.     

An autonomous surface discontinuity detection and quantification method by digital image correlation and phase congruency

Digital image correlation has been routinely used to measure full-field displacements in many areas of solid mechanics, including fracture mechanics. Accurate segmentation of the crack path is needed to study its interaction with the microstructure and stress fields, and studies of crack behaviour, such as the effect of closure or residual stress in fatigue, require data on its opening displacement. Such information can be obtained from any digital image correlation analysis of cracked components, but it collection by manual methods is quite onerous, particularly for massive amounts of data. We introduce the novel application of Phase Congruency to detect and quantify cracks and their opening. Unlike other crack detection techniques, Phase Congruency does not rely on adjustable threshold values that require user interaction, and so allows large datasets to be treated autonomously. The accuracy of the Phase Congruency based algorithm in detecting cracks is evaluated and compared with conventional methods such as Heaviside function fitting. As Phase Congruency is a displacement-based method, it does not suffer from the noise intensification to which gradient-based methods (e.g. strain thresholding) are susceptible. Its application is demonstrated to experimental data for cracks in quasi-brittle (Granitic rock) and ductile (Aluminium alloy) materials.     

On noise reduction in strain maps obtained with the grid method by averaging images affected by vibrations

Any image-based contactless measurement system has a limited resolution because of sensor noise. If the sensor is rigorously static with respect to the imaged object, a possibility is to reduce noise by averaging images acquired at different times. This paper discusses images of a pseudo-periodic grid used in experimental solid mechanics to give estimations of in-plane displacement and strain components of a deformed flat specimen. Because of the magnification factor which is employed, the grid images are often affected by residual vibrations, thereby invalidating the assumption that the sensor is static. The averaged grid image is thus a biased estimator of the unknown noise-free image. In spite of this, we prove that the retrieved displacement and strain components still benefit from noise reduction by time-averaging. A theoretical model is discussed, and experiments on real and synthetic data sets are provided.     

The effect of out-of-plane motion on 2D and 3D digital image correlation measurements

The effect of out-of-plane motion (including out-of-plane translation and rotation) on two-dimensional (2D) and three-dimensional (3D) digital image correlation measurements is demonstrated using basic theoretical pinhole image equations and experimentally through synchronized, multi-system measurements. Full-field results obtained during rigid body, out-of-plane motion using a single-camera vision system with (a-1) a standard f55mm Nikon lens and (a-2) a single Schneider–Kreuznach Xenoplan telecentric lens are compared with data obtained using a two-camera stereovision system with standard f55mm Nikon lenses.Results confirm that the theoretical equations are in excellent agreement with experimental measurements. Specifically, results show that (a) a single-camera, 2D imaging system is sensitive to out-of-plane motion, with in-plane strain errors (a-1) due to out-of-plane translation being proportional to ΔZ/Z, where Z is the distance from the object to the pin hole and ΔZ the out-of-plane translation displacement, and (a-2) due to out-of-plane rotation are shown to be a function of both rotation angle and the image distance Z; (b) the telecentric lens has an effective object distance, Z_eff, that is 50× larger than the 55 mm standard lens, with a corresponding reduction in strain errors from 1250 μs/mm of out-of-plane motion to 25 μs/mm; and (c) a stereovision system measures all components of displacement without introducing measurable, full-field, strain errors, even though an object may undergo appreciable out-of-plane translation and rotation.     

Two-dimensional strain measurement with ESPI

Optical techniques have been applied to the measurement of solid deformations in many instances. Practical difficulties with a particular technique can be overcome, in some circumstances, with attention to experimental detail. However, a common problem is the quantitative interpretation of the optical data thus obtained: this can be a time-consuming process and depends on the operator's skill. This paper describes an electronic speckle pattern interferometer that measures two in-plane displacement components simultaneously. The (phase-stepping) procedures implemented for automated displacement and strain analysis are described. Simultaneous measurement of the two displacement components is particularly important for shear strain measurement, because data from the two in-plane views must be combined. The accuracies of displacement and strain measurements are shown to be ±0·03 μm and ±6 μstrain, respectively. Results are presented for a compact tension specimen.     

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.     

Determining displacement and strain maps immune from aliasing effect with the grid method

Spatial aliasing may affect methods based on grid image processing to retrieve displacement and strain maps in experimental mechanics. Such methods aim at estimating these maps on the surface of a specimen subjected to a loading test. Aliasing, which is often not noticeable to the naked eye in the grid images, may give spurious fringes in the strain maps. This paper presents an analysis of aliasing in this context and provides the reader with simple guidelines to minimize the effect of aliasing on strain maps extracted from grid images.     

Exact analytical solution for free vibration of functionally graded micro/nanoplates via three-dimensional nonlocal elasticity

Using three-dimensional (3-D) nonlocal elasticity theory of Eringen, this paper presents closed-form solutions for in-plane and out-of-plane free vibration of simply supported functionally graded (FG) rectangular micro/nanoplates. Elasticity modulus and mass density of FG material are assumed to vary exponentially through the thickness of micro/nanoplate, whereas Poisson's ratio is considered to be constant. By employing appropriate displacement fields for the in-plane and out-of-plane modes that satisfy boundary conditions of the plate, ordinary differential equations of free vibration are obtained. Boundary conditions on the lateral surfaces are imposed on the analytical solutions of the equations to yield the natural frequencies of FG micro/nanoplate. The natural frequencies of FG micro/nanoplate are obtained for different values of nonlocal parameter and gradient index of material properties. The results of this investigation can be used as a benchmark for the future numerical, semi-analytical and analytical studies on the free vibration of FG micro/nanoplates.     

An alternative technique for extraction of in-plane displacement from an image plane hologram

The combination of image plane holography and speckle photography for measurement of 3-D displacements has been reported earlier. It has been observed that when we interrogate such a hologram by an unexpanded laser beam, in addition to the formation of Young's fringes in the direct diffracted beam, very bright side lobes are also generated. If the specimen has undergone any in-plane displacement, high contrast fringes appear in the side lobes. We have demonstrated that these fringes can be used to obtain a precise quantitative in-plane displacement of the object.     

X-ray scattering: A powerful probe of lattice strain in materials with small dimensions

X-ray diffraction was recognized from the early days as highly sensitive to atomic displacements. Indeed structural crystallography has been very successful in locating with great precision the position of atoms within an individual unit cell. In disordered systems, it is the average structure and fluctuations about it that may be determined. In the field of mechanics, diffraction may thus be used to evaluate elastic displacement fields. In this short overview, we give examples from recent work where X-ray diffraction has been used to investigate average strains in lines, films or multilayers. In small objects, the proximity of surfaces or interfaces may create very inhomogeneous displacement fields. X-ray scattering is again one of the best methods to determine such distributions. The need to characterize displacement fields in nano-structures together with the advent of third generation synchrotron radiation sources has generated new and powerful methods (anomalous diffraction, coherent diffraction, micro-diffraction, etc.). We review some of the recent and promising results in the field of strain measurements in small dimensions via X-ray diffraction.     

剪切散斑干涉术的统计分析

本文用统计光学方法分析了剪切散斑图的成象过程;散斑图的频谱分布以及全场滤波干涉条纹的形成.发现剪切散斑干涉条纹不仅与三维位移微分有关,而且与面内位移量有关.在此基础上又讨论了影响干涉条纹质量的有关因素,并作了实验验证.     

单模光纤相移DSPI测量二维面内位移的方法

本文提出将相移技术应用于2-D面内位移场的分离,用单模光纤相移数字散斑干涉计量技术快速、定量地同时测量2-D面内位移场。     

Study on Combined Method Based on 3-D ESPI

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Influence of in-plane displacement and strain components on slope fringe distributions in double-aperture speckle wedge-shearing interferometry

The influence of in-plane displacement and strain components on slope (first-order derivative of out-of-plane displacement component) fringe distributions in double-aperture speckle wedge-shearing interferometry is discussed in detail. The research results show that only the in-plane displacement component parallel to the centre line of double apertures has an influence on the slope fringe distributions. It is also shown that the in-plane strain components have no influence on the slope fringe distributions when utilising normal illumination and an axisymmetric system. A theoretical analysis and an experimental demonstration are given. The experimental results are in good agreement with the quantitative analysis.     

云纹干涉法面内位移测量的光栅补偿方法研究

运用光的干涉与衍射理论，导出了对称入射光路云纹干涉法面内位移计量的基本公式。针对云纹干涉法在实际应用中易引入刚体位移对真实面内位移干扰这一棘手问题，设计了定量补偿面内位移和变形的非对称光栅补偿光路系统。由于采用高灵敏度基准光栅调节的方法，比螺旋测微器等纯机械方法具有众多优越性。本文分析了该补偿方法对面内正应变条纹梯度和面内剪应变条纹梯度的补偿原理和具体实施过程。本方法大大提高了云纹干涉法面内位移计量和补偿的可靠性。     

Speckle interferometry methods for displacement and strain measurements using photorefractive crystal

Photorefractive crystals offer several attractive features such as high resolution and in situ processing. As the images are erasable, these crystals are suitable for read–write applications and hence find potential use in speckle photography, image processing and holography. The barium titanate (BaTiO₃) crystal as recording medium has been extensively used as a novelty filter for real-time in-plane displacement measurements employing two-beam coupling configuration. This paper presents new optical configurations in speckle shear photography to measure in-plan displacement and the strain in real time using BaTiO₃ crystal as recording medium. Speckle photography studies are made using a simple two-beam coupling configuration. In speckle shear photography, a diffused object illuminated with two parallel narrow laser beams is imaged inside the crystal, and a pump beam is added at this plane. The speckle patterns due to each beam and the pump beam produce index gratings. When the object is deformed, the speckle patterns shift consequently. We now have four speckle fields: two generated from the interaction of pump beam with the index gratings and two pertaining to deformed states directly transmitted through the crystal. Thus, the fields from respective points on the object interfere after passage through the crystal and produce the Young's fringe patterns. Due to strain, the fringes in each pattern are of different width and orientation, resulting in the generation of a Moiré pattern. The strain is obtained from the width and orientation of the fringes in the Moiré pattern. The experiments are conducted on a specimen with a notch, which is subjected to tensile loading. The in-plane displacement is measured separately in another experiment. The above studies are carried out at Nd–Yag laser.     

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%.