The application of fourier transform in regularized speckle photography

Two speckle patterns are recorded using a video camera corresponding to undisplaced and displaced states into the memory of a computer. After one pattern is added to another, the displacement of the measured points can be calculated by using the Fourier transform. The expression of displacement field is deduced for non-uniform displacement, and as an example, a rotatanle disc is tested for illustration. The results prove that the present method is promising.     

贴片散斑法及其应用

贴片散斑法将一种可剥离铝箔贴附在试件表面,经随机划痕制栅后,以其精细的光学结构和高度的反射本领,在白光或激光照射下,表面辐射率随机分布函数作为散斑场,采取直接记录手段,用全息底片对此作物体变形前后的两次曝光,所得到的散斑底片将包含宽广的空间频谱范围,且全场分析条纹清晰、灵敏度高、量程调节范围大。此方法不仅适用于各种材料的直接散斑法测量,具有经济、可靠、操作简便的特点,还能应用于平面及可展曲面构件的现场量测。     

基于单像素成像的微小位移测量方法

激光散斑位移测量法是一种重要的现代光学位移测量方法,由于受到图像传感器元件感光性能限制,难以在强干扰光条件下获得有效散斑场信息,进而无法获取位移场数据,因此,基于单像素成像技术,本文提出一种新的激光散斑位移测量方法:对散斑信息进行图案编码调制,并使用单像素探测器采集调制后的光强信息;利用Walsh-Hadamard Transformation(WHT)成像算法对散斑场图像进行重建;最后结合自相关算法确定物体的位移场信息。分别利用商业相机和单像素成像技术对散射介质的单轴微小位移进行测量,结果表明基于单像素成像技术的激光散斑位移测量技术可以获得较好的测量结果。相比于传统测量方法,基于单像素成像技术的激光散斑位移测量方法在复杂环境中具有一定的优势,可实现强光干扰下的位移场测量。     

基于空间光调制器获得空心光束的数值模拟和实验研究

光镊技术中,会聚的空心光束形成的能量光阱可用来捕获吸光性颗粒或操纵吸光性颗粒沿光轴方向运动。采用Gerchberg-Saxton(GS)算法计算所需相位,并将相位载入相位型空间光调制器来获得空心光束。为了提高会聚的空心光束能量,对空间光调制器相位屏进行预处理,叠加数字闪耀光栅位相,实现了将四个一级衍射谱闪耀至零级干涉极大位置,空心光束能量提高到原来的4.7倍。为了消除空间光调制器二维光栅结构所形成的零级谱亮斑以及高级谱的影响,在相位屏上加入球面波相位,使得空心光束衍射谱平面与零级谱平面的空间位置分离,并采用带通滤波器将空间光调制器的零级谱亮斑和高级谱滤掉。采用高度会聚透镜将所得空心光束会聚为微米尺寸,可应用于捕获吸光性颗粒。另外,利用离散傅立叶变换的平移原理实现空心光束实时平移,该方法可应用于实时操纵吸光性颗粒移动。     

Application of numerical and optical evaluation schemes for particle image velocimetry

Application of particle image velocimetry (PIV) techniques for measurement of fluid velocities typically requires two steps. The first of these is the photography step in which one or more exposures of a particle field are taken. The second step is the evaluation of the particle pattern and production of appropriate velocities. Each of these steps involves optimization which is usually specific to the experiment being conducted and there is significant interaction between photographic parameters and evaluation characteristics.Among the various evaluation techniques suggested for analysis of PIV images is the evaluation of the scattered interference pattern (Young's fringes) by numerical Fourier transform. An alternative to the numerical calculation of the Fourier transform of the Young's fringes has been suggested, using a modified liquid crystal television as an optical correlator to allow the transform to be performed optically. Both transform techniques are affected by the quality of the input function, specifically the Young's fringes.This paper will compare the performance of optical and numerical Fourier transform analysis of Young's fringes using speckle images. The repeatability and an estimate of the accuracy of the particle displacement will be shown for each method. A brief examination of the effects of small particle number density of PIV evaluation will also be presented. Finally, for a small part of an actual unsteady flow, the optical and numerical Fourier transform analysis methods will be compared.     

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) technique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measurements, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial tension experiments establish a surface displacement resolution of 1 μm over a 5×6 mm scale field of view for the airbrushed samples and 17 nm over a 100×100 μm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deformation fields generated around silica microspheres embedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.     

Analysis of Speckle Photographs by Subtracting Phase Functions of Digital Fourier Transforms

This paper presents a method for measuring displacements and strain in digital speckle photography that is an alternative to currently used correlation techniques. The method is analogous to heterodyne speckle photogrammetry wherein optical Fourier transforms were taken of individually recorded specklegrams and combined in a heterodyne interferometer where an electronic phase meter measured the phase differences between the two transforms. Here, digital photographs are recorded and Fourier transformed so that their phase functions can be subtracted and fitted to a linear function of the transform coordinates. The effect of different recording and processing parameters is investigated. It is found that incoherent speckles give better results than those formed by coherent laser light. In addition, image correlation is used to process an identical data set so that comparison of the two methods can be made.     

利用光学干涉条纹图相位分析测量纳米位移

Optical methods such as Twyman-Green interferometry, moiré interferometry, holographic interferometry and speckle interferometry are useful to measure displacement and strain in the full-field of structures. Recently phase analysis method of fringe patterns obtained by these optical methods becomes popular, and it provides accurate quantitative results in the full-field. In this paper, in order to measure displacement and strain, real-time or high-speed nano-meter displacement measurement methods developed by the authors are introduced. That is, (1) out-of-plane displacement analysis by Twyman-Green interferometry using integrated phase-shifting method using Fourier transform phase-shifting method, (2) simultaneous two-dimensional in-plane displacement analysis by moiré interferometry and (3) out-of-plane displacement analysis by phase-shifting digital holographic interferometry. The theories and applications are shown.     

Nano-meter Displacement Measurement by Phase Analysis of Fringe Patterns Obtained by Optical Methods

0Introduction Inordertomonitorthehealthofstructures,straingagesanddisplacementtransducersare usuallyused.Thereasonisthatmanyrulesorcodesforinspectionofstructuresrequiretousestrain gagesanddisplacementtransducers,anditiseasytousethem.However,thesemethodsarebasically one pointmeasurementmethods.Theyareexpensiveandtime consumingfordistributionanalysis.Opticalmethodssuchasgrating projection,geometricmoir啨,moir啨interferometry,holographic interferometryandspeckleinterferometryareusefultomeasuredi…     

三维物体形貌检测图像处理中的小波数字滤波技术

傅里叶变换轮廓术和相移法是投影栅法测物体三维形貌的两种重要方法。相移法需要精密的移相装置,且需采集一幅以上的图像,在应用中受到一定限制。而傅里叶变换轮廓术只需一幅图像便可计算出各点相位值,测量精度高,测量范围广,因而得到广泛运用。最大测量范围受到高度分布h(x,y)在与光栅线垂直向上变化率的限制,即面形变化剧烈的物体易产生相邻谱区的混合,不易测准。本文提出的基于小波数字滤波的傅里叶变换法,可以将物体的可测梯度提高3倍。因为利用小波技术对变形栅线图进行处理后,滤去了直流分量和高频分量,得到的相对栅线图只剩下基频分量。采用小波数字滤波与傅里叶变换轮廓术相结合的方法,用小波变换去除直流成分和高频成分,从而提高了物体的可测精度,降低了对滤波器的设计要求,能较好地将物体的相位信息分离出来。本文给出了这种算法的理论分析和计算机模拟试验的结果。     

Application of fourier analysis to the laser based interferometric strain/displacement gage

The laser based interferometric Strain/Displacement Gage (ISDG) measures the in-plane surface deformation between two small reflecting surface markers. When illuminated with a coherent beam of light, the reflected beams from the two markers form an interference pattern, and monitoring the shift of the fringe pattern allows strain in the gage section of a specimen to be directly measured. A minimum on the fringe pattern can be isolated and tracked as the test proceeds, but this technique utilizes only a small part of the optical signal and often requires a complex programming scheme. This paper presents the application of Fourier transform and phase shifting techniques to the use of the ISDG during microsample tensile testing. The Fourier transform samples the entire fringe pattern and greatly improves the optical signal to noise ratio, and the phase shifting fringe pattern analysis has proven to be more robust and less affected by speckle or optical noise than fringe pattern minimum tracking. This results in the ability to measure larger deformations with a system resolution of ∼5 microstrain and an uncertainty of ±15.5 microstrain. An example involving the microsample tensile testing of a MEMS related LIGA Ni specimen is included to demonstrate the utility of these new techniques.     

撞击载荷下数字散斑干涉法中位相的自动计量

在撞击载荷下的数字散斑干涉法（DSPI）中，本文联合应用加法和减法两种模式提出了位相测试技术，以矩形板对称轴承受撞击集中载荷为例，测量了位移场的位相分布，为了采集红宝石脉冲激光形成的数字散斑场，提出瞬态数字图像采集技术。     

云纹／光栅测试技术的几点讨论

本文用信号处理的方法系统地阐述了云纹／光栅测试技术。以面内云纹／光栅测试为例，首先说明了光栅是位移和变形信息的空间载体；位移和应变分别是对载体的相位和频率调制；而云纹现象则是试件栅频谱向零频处平移的结果或说云纹是对光栅载体信号解调的过程；进而讨论了云纹技术与光栅技术的本质区别。其次分析了云纹／光栅测试系统的性能，讨论了条纹分析方法及数字图象处理手段对云纹／光栅系统的测试精度、灵敏度、空间分辨率的影响。     

二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切（shearing horizontal, SH）波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂边界产生的能够自动满足直角边应力自由条件的散射波解，从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波中未知系数的无穷代数方程组，在满足计算精度的前提下通过有限项截断，得到相应有限代数方程组的解，最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况，结果表明了算法的有效实用性。     

Interaction of plane nonstationary waves with a thin elastic inclusion under smooth contact conditions

We solve the problem of determining the stress state near a thin elastic inclusion in the form of a strip of finite width in an unbounded elastic body (matrix) with plane nonstationary waves propagating through it and with the forces exerted by the ambient medium taken into account. We assume that the matrix is in the plane strain state, and the smooth contact conditions are realized on both sides of the inclusion. The method for solving this problem consists in using the integral Laplace transform with respect to time and in representing the stress and displacement images in terms of the discontinuous solution of Lamé equations in the case of plane strain. As a result, the initial problem is reduced to a system of singular integral equations for the transforms of the unknown stress and displacement jumps. To invert the Laplace transform, we use a numerical method based on replacing the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating the stress intensity factors (SIF) for the inclusion, which are used to study the SIF time-dependence and its influence on the values of the inclusion rigidity. We also studied the possibility of considering the inclusions of higher rigidity as absolutely rigid inclusions.     

Displacement measurements in the interior of 3-D bodies using scattered-light speckle patterns

Two new techniques making use of the scattered-light speckle pattern have been developed which yield the displacements on an arbitrary interior plane of a 3-D body. When a sheet of coherent light passes through a transparent 3-D body, a small fraction is scattered. This scattered light produces a speckle pattern in an imaging system. By recording two superimposed images of this speckle pattern, one before and one after body deformation, the displacements on the interior illuminated plane can be found. The technique of scattered-light photography uses a single illuminating beam and is sensitive to displacements greater than one speckle diameter, approximately 3 μm. Scattered-light speckle interferometry uses two illuminating beams and is sensitive to displacements greater than one half the wavelength of light being used, approximately 0.2 μm. With both techniques, the double-exposed speckle photograph is optically processed to yield displacement information. With both techniques, the maximum displacement measurable is limited by correlation requirements between the two speckle patterns. Experimental results are presented demonstrating the two new techniques.     

多相机3D-DIC及其在高温变形测量中的应用

将基于双目视觉的三维数字图像相关方法 (Three-dimension digital image correlation,3D-DIC)与多相机同步采集系统相结合,形成基于多相机的3D-DIC系统。依据三维空间误差(Three-dimensional residual,3Dresidual)最小原则,确定各点对应的最佳双目视觉系统,获得物体全场三维变形。以四相机3D-DIC系统为例,与测量精度达10~20nm的电子散斑干涉测量系统同时对平板的离面位移进行测量,并对测量得到的离面位移最大值进行了对比分析。结果显示,荷载较小时,四相机3D-DIC与电子散斑干涉测量系统误差稍大,最大达到2.7%;荷载增大,物体变形增大时,两种测量系统结果基本相同。文中讨论了四相机测量系统的不稳定对实验结果的影响。利用该四相机3D-DIC系统对镍合金不锈钢材料在高温场中的变形进行测量,获得了物体的三维变形场,并分析了材料的膨胀系数,得到了试件的热应变-温度曲线和膨胀系数随温度变化的关系式。     

DIC-Based Surface Motion Correction for ESPI Measurements

Electronic Speckle Pattern Interferometry (ESPI) provides a sensitive technique for measuring surface deformations. The technique involves comparison of the speckle phase angles within surface images measured before and after material deformation. This phase angle comparison requires that the speckle positions be consistent in all images. A lateral shift between image sets of just one pixel substantially degrades ESPI measurements, while a shift of two or more pixels typically causes complete decorrelation and compromises the measurement entirely. To prevent such rigid body motions, the specimen and the optical system must be rigidly fixed. This requirement typically impedes use of the ESPI method in applications outside laboratories or where it is necessary to remove the specimen from the optical setup between ESPI measurements. Here, Digital Image Correlation (DIC) is used to track speckle motion caused by specimen displacement between ESPI phase stepped image sets. The measured image set can then be mathematically shifted to restore the original speckle locations, thereby recorrelating the ESPI measurement. Examples are presented where ESPI measurements are successfully made with specimen shifts over 60 pixels.     

Approximate fundamental solutions and wave fronts for general anisotropic materials

The time-dependent differential equations of elastodynamics for homogeneous solids with a general structure of anisotropy are considered in the paper. A new method of computation of the fundamental solution for these equations is proposed. This method consists of the following. Applying the Fourier transformation with respect to space variables to these equations, we obtain a system of second order ordinary differential equations whose coefficients depend on Fourier parameters. Using the matrix transformations and properties of the coefficients, the Fourier image of the fundamental solution is computed. Finally, the fundamental solution is calculated by the inverse Fourier transformation to the obtained Fourier transform. The implementation and justification of the suggested method have been made by computational experiments in MATLAB. These experiments confirm the robustness of the suggested method. The visualization of the displacement components in general homogeneous anisotropic solids by modern computer tools allows us to see and evaluate the dependence between the structure of solids and the behavior of the displacement field. Our method allows users to observe the elastic wave propagation, arising from pulse point forces of the form e^mδ(x)δ(t), in monoclinic, triclinic and other anisotropic solids. The visualization of displacement components gives knowledge about the form of fronts of elastic wave propagation in Sodium Thiosulfate with monoclinic and Copper Sulphate Pentahydrate with triclinic structures of anisotropy.     

非对称铺层复合材料层合板的双稳态特性半解析研究

非对称铺层的复合材料层合板在存在热残余应力的情况下，具有双稳态性质．层合板的两个稳态之间仅需要一个适当的激励就可以互相转化，因此该结构在变体飞机上应用广泛．基于经典层合板理论，本文引入几何大变形建立了具有双稳态性质的复合材料层合板的能量泛函，提出了一个高阶的位移场函数，用瑞利里兹法推导出一组关于位移场函数系数的非线性方程组．结合牛顿迭代法和消元法求解非线性方程组，得到了层合板面外位移场．同时利用有限元软件ABAQUS，对复合材料层合板双稳态机理进行了数值模拟．选取了几组具有代表性的铺层进行计算，以有限元结果为基准，比较了本文的位移场结果与前人的结果，验证了高阶位移场函数的准确性．