Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns

This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such “designer patterns” are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 µε are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.     

纳米磁流体动态散斑干涉场的奇异场分布

通过对由纳米磁流体运动引起的双扫描激光散斑干涉光场及其变化做拉盖尔-高斯滤波下的傅里叶变换,获得动态散斑干涉图对应的光学涡旋分布及变化特征。分析认为,光学涡旋分布及变化对应着由纳米磁微粒及其团族的运动所引起的动态散斑变化。当纳米磁微粒聚集到分散的过程中,动态激光散斑光场的奇异场分布发生相应变化,说明了磁流体运动过程对应涡旋密度有先大后小,再由小变大的两个变化;并且光学涡旋密度高,对应较小颗粒的散斑场,磁流体处于稳态的状况;光学涡旋密度低,对应较大颗粒的散斑场,对应着磁流体激烈的运动。研究结果体现了奇异场分布变化和纳米磁流体动后趋稳的过程存在对应关系。     

Studies on the statistical properties of phase difference of speckle fields

According to the relations between the phase and the complex speckle amplitude, a phase angle is constructed to estimate the free standard deviation of phase difference of speckle fields. The relative accurate amending expression of evaluating the free standard deviation of phase difference is derived for the Gaussian speckle fields. The statistical properties of phase difference are studied for the Gaussian speckle fields of diffraction fields. The theoretical values of the free standard deviation of phase difference for the case of fully developed speckle fields are compared with the numerical values of the free standard deviation which are calculated from the Gaussian theory of the fully developed speckle fields.     

Improvement of the sensitivity in velocity sensing using dynamic speckles

Dynamic speckle patterns can be used for imaging of relative velocity of moving objects in fields of biomedical and mechanical measurements. In spite of the widespread use of this method, the effect of speckle size on velocity sensing has not fully been estimated so far. In addition, effects of speckle contrast and random noises on the sensitivity of velocity sensing have not been investigated yet. In the present study, we estimated condition of image processing of speckle patterns for reducing effects of random noises with relation to linearity and sensitivity in velocity sensing. We further introduced binarization of the speckle pattern to improve the sensitivity in velocity sensing. Experiments were conducted for sample models using a diffusive plate and fluid flows to confirm the feasibility of the proposed method.     

Controlling the evolution of nondiffracting speckle by complex amplitude modulation on a phase-only spatial light modulator

In this work we investigate the structure of nondiffracting speckle fields, both experimentally and theoretically. We are able to produce very good agreement between the experimentally recorded and theoretically calculated fields by using complex amplitude modulation on a phase-only spatial light modulator to implement controlled ring-slit experiments for the generation of nondiffracting speckle fields. The structure of the nondiffracting speckle due to binary and continuous phase modulations for both a uniform and a normal distribution is investigated. We find that we are able to engineer whether the nondiffracting field will appear as speckle or a structured zero-order Bessel beam by adjusting the standard deviation in the distribution. Having the ability to control where in the spectrum, from fully-developed nondiffracting speckle to a symmetric zero-order Bessel beam, the nondiffracting field will exist can prove to be a useful resource in the non-destructive testing of materials.     

空间散斑场捕获大量吸光性颗粒及其红外显微观测

光镊技术被广泛应用于捕获和操纵微纳米尺寸颗粒,主要包括捕获水中透明性颗粒和空气中吸光性颗粒两种类型.本文用激光束照射毛玻璃散射片,透射光经透镜会聚后在透镜的像平面附近产生了主观散斑场.该散斑场为空间分布,包含大量的亮斑和暗斑.大量由亮斑包围的暗斑如同一个个空间能量陷阱,被用来捕获大量的吸光性墨粉颗粒,被捕获颗粒的尺寸约2—8μm,密度约1—2 g/cm3.采用红外显微镜拍摄到空间散斑场捕获颗粒的红外像,红外图像显示被捕获颗粒吸光后温度升高,证实了空间散斑场捕获吸光性颗粒的机理为光泳力原理.     

Statistics of Gaussian Speckles with Enhanced Fluctuations

Some first-order statistics of speckle fields obeying the complex Gaussian probability density are investigated with the special emphasis on a possibility for the speckle contrast to exceed unity. It is shown that such enhanced fluctuations of speckle fields are generated when the probability density of the complex amplitude is non-circular with the vanishing mean. This means that Gaussian speckles having the contrast of unity are not necessarily fully developed speckles. Some practical situations producing such enhanced fluctuations in speckle fields are discussed.     

Statistical properties of the phase difference between two interfering speckle fields in speckle interferometry

The statistical properties of the phase difference between the two interfering partially correlated and partially developed speckle fields were studied experimentally as a function of the intensity correlation coefficient. The gaussian statistics are assumed for the formation of speckle fields in the diffraction region and the correlation coefficient between the two speckle intensities is used to evaluate the phase difference. The standard deviation of the phase difference can be uniquely determined in the fully developed speckle field from the correlation coefficient of the two speckle intensities. However, it was found in the partially developed speckle field that the standard deviation of the phase difference between the two speckle fields cannot be uniquely determined from the correlation coefficient of the two speckle intensities.     

Theoretical study on the statistical properties of phase difference between two interfering speckle fields

The statistical properties of phase difference between two interfering speckle fields are studied theoretically with the general expression of the free standard deviation of the phase difference of speckle fields. The experimental results of the standard deviations of phase difference between two interfering partially developed speckle fields in the diffractive region [Opt. Quantum Electron. 19 (1987) 59] are studied and discussed theoretically with the general expression of the free standard deviation of phase difference of speckle fields. The theoretical standard deviations of phase difference for the case of two interfering fully developed Gaussian speckle fields are compared with that which are numerically calculated from the Gaussian theory.     

Singularities in speckled speckle

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 10(4) for experimentally realistic source parameters.     

The development of full field interferometric methods for fluid velocimetry

The development of full field interferometry as a velocimetry technique in experimental fluid mechanics from its inception in 1977 to the present is discussed. In 1977, holographic interferometry (HI) was applied for the first time to measure the velocity field in a liquid flow. It was not until 1998 that the first application to a gaseous flow was reported. The only kind of speckle interferometry that has been applied to measure velocity fields so far is digital speckle pattern interferometry (DSPI). It was in 1999 that DSPI was demonstrated both in a liquid and a gaseous flow.     

Assessment of speckle-pattern quality in digital image correlation based on gray intensity and speckle morphology

In digital image correlation (DIC), speckle patterns are generated on the surface of a specimen to resolve uniqueness issues. Thus, speckle patterns significantly affect the accuracy of image correlation. To assess the quality of speckle patterns, the standard deviation of gray intensities within each speckle (SDGIS) is introduced as a new metric. On the basis of the cumulative distribution of SDGIS, speckle-pattern quality measurement (ρ) is proposed, which integrates the features of gray intensity and speckle morphology. Twelve speckle patterns are generated by changing the spraying time and nozzle sizes of an airbrush because these are associated with the speckle volume fraction and speckle size, respectively. In addition, three displacement fields are used to investigate the effects of speckle patterns on the accuracy of the DIC results. For the 12 speckle images associated with the three displacement fields, the correlation results demonstrate that the proposed speckle-pattern quality measurement is inversely proportional to the averaged error of the subset method. This is statistically confirmed by evaluating the correlation coefficient and p-value. Furthermore, the error of the subset method is more affected by speckle patterns than the subset size when the subset size is sufficiently large.     

Fields of a viscous fluiid without shear and rotation

It is shown that in Einstein's theory of gravitation conformally flat gravitational fields of a viscous fluid without shear and rotation are analogous to the fields of an ideal fluid with a conformally flat space-time. Thus, the fluid particles in such fields move along geodesics, and the three-dimensional hypersurfaces determined by the sections x⁰=const are spaces of constant curvature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–40, January, 1981.     

An effective method for reducing speckle noise in digital holography

An effective method for reducing the speckle noise in digital holography is proposed in this paper.Different from the methods based on classical filtering technique,it utilizes the multiple holograms which are generated by rotating the illuminating light continuously.The intensity images reconstructed by a series of holograms generated by rotating the illuminating light possess different speckle patterns.Hence by properly averaging the reconstructed intensity fields,the speckle noises can be reduced greatly.Experimental results show that the proposed method is simple and effective to reduce speckle noise in digital holography.     

高斯型弱散射屏产生的像面散斑场的分布特性研究

弱散射屏产生的远场散斑由一个中央亮斑和一个分布于亮斑周围而与正态散斑类似的散斑结构, 根据弱散射屏远场的散斑图样, 人们假设弱散射屏产生的像面散斑为均匀背景与正态散斑两者相干叠加的结果, 但这种假设与实际像面散斑存在歧异, 基于上述情况, 本文利用4f高通滤波光学成像系统, 研究了高斯型弱散射屏产生的像面散斑场的统计特性, 得出只有表面均方根粗糙度与入射光波的波长相差不多时上述假设才是可行的结论. 关键词： 弱散射屏 f光学成像系统')" href="#">4f光学成像系统 像面散斑     

电子显微镜散斑照相技术

提出了一种新颖的人工亚微米/纳米散斑制作技术.采用超声波分散亚微米/纳米颗粒,然后利用范德华力、静电力和毛细力将其吸附在试件表面.在特定分辨率的扫描电镜下,物体表面的亚微米/纳米颗粒可以看作是亚微米/纳米散斑.此外,发展了一种测量面内亚微米/纳米级变形的电子显微镜散斑照相技术.详细介绍了人工制作亚微米/纳米散斑和电子显微镜散斑照相技术,实验验证了技术的可行性     

Some properties of the gravitational fields of a hydrodynamical fluid and dust

Conditions are obtained on the four velocity of the particles of a medium in the gravitational fields of a hydrodynamical fluid and dust, and the nature of the motion of the medium in these fields is investigated. It is shown that the gravitational fields of a hydrodynamical fluid and dust do not admit conformal mapping onto Einstein spaces which are not conformally flat spaces (spaces of constant curvature).     

Microparticle column geometry in acoustic stationary fields

Particles suspended in a fluid will experience forces from stationary acoustic fields. The magnitude of the force depends on the time-averaged energy density of the field and the material properties of the particles and fluid. Forces acting on known particles smaller than 20 microm were studied. Within a 500 kHz acoustic beam generated by a plane-piston circular source, observations were made of the geometry of the particle column that is formed. Varying the acoustic energy altered the column width in a manner predicted by equations for the primary acoustic radiation force from scattering of particles in the long-wavelength limit. The minimum pressures required to trap gas, solid, and liquid particles in a water medium at room temperature were also estimated to within 12%. These results highlight the ability of stationary acoustic fields from a plane-piston radiator to impose nano-Newton-scale forces onto fluid particles with properties similar to biological cells, and suggest that it is possible to accurately quantify these forces.     

A new formula for fringe localization in holographic interferometry

Holographic interferometry generally involves the interference of two or more speckle fields reflected from or transmitted through a diffused object. The visibility of the resulting fringes depends on the degree of coherence of the interfering speckle fields. Through a statistical analysis it is found that the degree of coherence of speckle fields is essentially a function of the relative speckle displacement and average speckle size. The analysis leads to a new physical model for holographic interferometry. With this model the problem of fringe formation and localization may be analyzed and formulated in terms of speckle movement. A new formula for ideal fringe localization is then derived from the analysis. Furthermore, a localization factor V_c, i.e. the visibility of the holographic fringes, is introduced to analyze the partial fringe localization in holographic interferometry, which is of practical interest to most researchers.     

参考光干涉提取复振幅的散斑统计函数的实验研究

由散斑场和参考光的干涉图样提取散斑场复振幅、相位和强度的数值分布,并对其统计特性进行实验研究,消除了散斑场强度统计函数特别是概率密度函数的传统测量方法中噪声引起的偏差,并实现了散斑场复振幅和相位统计特性的实验研究.通过对不同散射角处散斑场的研究发现随着散射角度的增大散斑颗粒逐渐呈现出横向展宽的现象,且其平均宽度表现为各向异性,但是其概率密度函数并没有发生变化,与小角度情况一样属于圆形高斯散斑场. 关键词： 散斑 概率密度 干涉