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.     

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.     

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.     

Digital speckle pattern interferometry (DSPI) with increased sensitivity: Use of spatial phase shifting

This paper presents a real-time digital speckle pattern interferometry system with twofold increase in sensitivity for the measurement of in-plane displacement and first order derivative of out-of-plane displacement (slope). Spatial phase shifting technique has been used for quantitative fringe analysis. The system employs a double aperture arrangement in front of the imaging system that introduces spatial carrier fringes within the speckle for spatial phase shifting. For in-plane displacement measurement, the scattered fields from the object are collected independently along the direction of illumination beams, and combined at the image plane. For slope measurement, a shear is introduced between the two scattered fields. Experimental results on an edge clamped circular plate subjected to in-plane rotation for in-plane displacement measurement and central loading for slope measurement are presented.     

3-D computer vision in experimental mechanics

Optical methods that give displacement or strain fields are now widely used in experimental mechanics. Some of the methods can only measure in-plane displacements/strains on planar specimens and some of them can give both in-plane and out-of-plane displacement/strain fields on any kind of specimen (planar or not). In the present paper, the stereovision technique that uses two cameras to measure 3-D displacement/strain fields on any 3-D object is presented. Additionally, a quite inclusive list of references on applications of stereovision (and 3-D DIC) to experimental mechanics is given at the end of the paper.     

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。     

Interferometric 3-D displacement measurement using wavefront analysis

We propose and demonstrate a novel interferometric technique for 3-D displacement measurement. The method is based on the analysis of the phase difference distribution measured when two coherent curved wavefronts originating from different locations interfere. Both the in-plane and out-of-plane displacements are found simultaneously from a single phase difference distribution. We find that our system could measure with an accuracy better than 1.5 μm for in-plane displacements and 36 μm for out-of-plane displacements over 1 mm range. This accuracy was limited by the output lens performance. Theoretical analysis reveals that sub-micron accuracy may be possible with more careful calibration.     

在电子散斑干涉中利用反相位法进行三维变形测量

提出一种可将离面位移与面内位移分离的三维位移计算方法。在双光束电子散斑干涉系统中增加一路参考光,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,分别计算相位分布,并对其中之一进行反相位计算。理论分析表明,对二路检测光所得到的相位进行相减运算,就能够较好地减少电子噪声的影响,分离面内位移场与离面位移,实现物体变形的三维测量。介绍该方法的原理,并利用典型实验证实了该方法的可行性。     

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.     

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.     

Multi-frequency lateral shear interferometer system for simultaneous measurement of thickness and three-dimensional shape

This Letter demonstrates a novel lateral shear interferometer system for simultaneous measurement of three-dimensional(3D) shape and thickness of transparent objects. Multi-frequency fringe patterns can be created by tilting mirrors at different inclination angles. With a single camera, the multi-frequency fringes are recorded in one image. The phase-shift of the fringes can be generated synchronously only by moving a plane-parallel plate along an in-plane parallel direction. According to the feature of transparent materials, the thickness and 3D shape can be reconstructed simultaneously based on the relationship between the in-plane displacement and their characteristics. The experiment was conducted on a thin transparent film subjected to a shearing force,which verifies the feasibility of the proposed system.     

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%。     

Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment

The determination of strain fields based on displacement components obtained via 2D-DIC is subject to several errors that originate from various sources. In this contribution, we study the impact of a non-perpendicular camera alignment to a planar sheet metal specimen's surface. The errors are estimated in a numerical experiment. To this purpose, deformed images - that were obtained by imposing finite element (FE) displacement fields on an undeformed image - are numerically rotated for various Euler angles. It is shown that a 3D-DIC stereo configuration induces a substantial compensation for the introduced image-plane displacement gradients. However, higher strain accuracy and precision are obtained - up to the level of a perfect perpendicular alignment - in a proposed “rectified” 2D-DIC setup. This compensating technique gains benefit from both 2D-DIC (single camera view, basic amount of correlation runs, no cross-camera matching nor triangulation) and 3D-DIC (oblique angle compensation). Our conclusions are validated in a real experiment on SS304.     

Influence of out-of-plane deformation and its elimination in white light speckle photography

The aim of this paper is to present the white light speckle method as a practical tool in metrology and to search for the optimum conditions for its application. In particular, the study provides evidence that the white light speckle technique is not exclusively sensitive to the in-plane components of displacement. Consequently, the interpretation of the Young's fringes as pure in-plane fringes is prone to inaccurate measurements. The errors so introduced are systematically analysed for various optical parameters. Some practical considerations are then pointed out to aid in the design of an error-tolerance limited white light displacement measurement system to suit a particular need. two complementary techniques are next proposed which promise to eliminate the influence of the out-of-plane movements on the measurement of the lateral components of displacement. The proposed methods not only allow an increase in the accuracy of in-plane measurements, but also permit mapping of the out-of-plane movements undergone by the object surface. The techniques presented, apply equally to coherent speckle photography where the same problems are manifest, and should pave the way for the application of these methods to concrete engineering problems.     

Automated fine grid technique for measurement of large-strain deformation maps

The fine grid technique has been a standard engineering tool for measuring large strains for many years. The sample surface is marked with a grid, and the deformation of this grid allows the deformation of the sample to be monitored. However, it has never been easy quantitatively to analyse the strain across the whole of a specimen's surface. We describe here an automated approach in which digitised images of a sample prepared with a grid are analysed by the Fourier transform method. This provides phase maps which, when unwrapped, yield planes representing the two in-plane specimen coordinates. An iterative technique follows these deforming planes from one frame to the next as the specimen deforms, allowing displacement fields to be calculated. Numerical differentiation gives strains across the specimen surface. Gerchberg iteration is used to provide immunity to errors resulting from holes or tears in the specimen surface. The method is demonstrated on a propellant simulant containing burn holes (a cylinder of diameter 10 mm; grid PITCH = 76 μm), loaded in compression across a diameter. All in-plane components of strain are calculated up to strains of approximately one-third. Displacement accuracy is of order 1 μm.     

融合散斑干涉技术的阵列式洛伦兹力微颗粒探测方法

提出了一种阵列式洛伦兹力微颗粒探测法,该方法结合了散斑干涉技术的全场位移测量、分辨率高等特性与洛伦兹力微颗粒探测法中探测量为矢量、可探测内部缺陷等优势,探索了一种实时、在线、原位的缺陷检测方法.针对阵列式洛伦兹力微颗粒探测法中阵列式排布的多个悬臂梁位移测量问题,设计了大剪切数字散斑干涉系统,使来自于被测悬臂梁和安装悬臂梁的横梁的反射光发生干涉,形成剪切干涉,通过对相位差进行分析获得悬臂梁的绝对位移,并且以洛伦兹力及悬臂梁末端的位移量为中间量建立了散斑干涉相位差与缺陷体积之间的关系.本文通过实验成功获得了悬臂梁全场位移量以及缺陷的体积,通过散斑干涉的方法测量悬臂梁位移量理论分辨率可达30 nm,这使洛伦兹力微颗粒探测法具备了微米级缺陷的探测能力.     

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.     

Realization of high sensitivity displacement field from moiré interferometer with rough phase shifting mechanism and pattern matching technique

In this study, phase shifting method is used to modify moiré system into micro moiré interferometer which can measure displacement field with highly improved sensitivity. Apart from existing micro moiré technique, a low cost and less precise translation stage with rough resolution (10 μm resolution) is adapted for the phase shifter. Least square algorithm is applied to estimate the arbitrary phase shifted amount and to minimize the errors induced by lowering the cost. Moreover, specimen grating is phase shifted instead of reference grating which enables simple construction from given moiré system. To compensate for rigid body in-plane translation of specimen that may occur during phase shifting, pattern matching algorithm is put into practice to ensure pixel correspondence for each phase shifted images. To verify the newly constructed micro moiré technique, local displacement fields of Fine pitch Ball Grid Array package and Wafer Level Chip Size Package with elevated sensitivity up to 26 nm per fringe was acquired.     

General model to predict and correct errors in phase map interpretation and measurement for out-of-plane ESPI interferometers

Out-of-plane configurations used in electronic speckle pattern interferometry (ESPI), introduce phase error interpretation in extended target objects due to spatial variation of the sensitivity vector. In this paper, a general model to predict and correct the displacement measurement error and error phase map interpretation taking into account the target shape, illumination geometry, and in-plane displacement information, is presented. This model generalizes and extends previous analyses with respect to the sensitivity vector variations. The model is based on a relationship between variable sensitivity vector and the constant one. The importance of illumination geometry and in-plane displacement as factors that introduce the biggest error in the interpretation of the phase map are stressed. An analysis with practical parameters using divergent and collimated beams is presented. In order to predict and correct the error of phase interpretation, the finite element method should be used to obtain in-plane proportional factors to build up the correction function. The analysis shows that the error can be large for common configurations even when using collimated beam. To compute the measurement directly from the phase map, a general sensitivity function taking into account the shape and in-plane displacement information is naturally obtained from the presented analysis.     

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%.