Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

Effects of imaging properties on dynamic speckles produced by a set of moving phase screens

Space-time correlation functions have been derived for the time-varying intensities of speckle patterns in image space produced by a series of moving random-phase screens. The time-correlation length, which measures the changing rate of intensity fluctuations, is evaluated from the correlation functions to examine the effects of the imaging properties on the temporal behaviour of the speckles resulting from the multiple scattering. It is shown that the average velocity and velocity dispersion of the phase screens can be measured from the time-correlation length by using imaging systems which have a small and a large point spread at the front focal plane of the systems, respectively. Theoretical results for the relationship between the focal position of the imaging lens and the time-correlation length are also presented.     

Experimental study of the angular correlation function in the double passage of waves through a one-dimensional random phase screen

Abstract

Experimental results are presented for the angular correlation function of far-field speckle patterns scattered in the double passage of waves through a one-dimensional random phase screen. The experiment for the correlation measurement was set up to use a CCD camera to obtain the image of the speckle patterns in the scattering directions for each given angle of incidence; the cross-correlation function is then calculated from the digitized images. The theoretical analysis of the motion of the speckle as the source is moved, as given by Escamilla, is verified experimentally. It is found that in contrast with the memory effect line of speckle motion, the speckle pattern produced in the region of observation tracks the backscattering direction.     

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.     

‘1001’ correlations in random wave fields

Abstract

Correlations in Gaussian speckle patterns are discussed for the intensity and the phase, as well as for the real and imaginary parts of the wavefunction. Application of the sampling theorem to the wave field is described, and five topologically mandated deterministic rules are enumerated that constrain many aspects of the field structure. A brief overview is given of wave-field correlation matrices containing several million coefficients.     

Velocity measurement using the time-space cross-correlation of speckle patterns

The vector velocity measurement of the in-plane object motion based on the dynamic properties of speckle patterns is conducted. The time-space cross-correlation function of speckle intensity variations is used to determine the magnitude and direction of the in-plane object velocity. Theoretical and experimental studies of the speckle correlation technique for the determination of the in-plane object velocity are discussed and the vector velocities of the diffuse object are displayed as a two-dimensional image.     

Diagnostics of two-dimensional fractal structures using scanning coherent beams

A method of studying two-dimensional random structures such as amplitude screens with fractal properties using scanning focused and wide collimated beams is discussed. An analysis is made of the interrelation between the parameters of the structure functions of the intensity fluctuations detected at a fixed observation point and the structural characteristics of the particular screens. Results of experimental investigations of model samples of random amplitude screens with fractal properties are presented. Zh. Tekh. Fiz. 67, 101–112 (November 1997)     

弱散射屏的像面散斑自相关函数特性的实验研究

在对随机弱散射屏进行表面参数的原子力显微镜测量和建立了门积分取样平均的随机光强自相关函数测量系统的基础上,对弱散射屏在严格像面和离焦像面上产生的散斑自相关函数进行了测量。发现在严格像面上,散斑平均颗粒的大小随表面粗糙度增加而减小,且光强自相关函数次极大的相关间隔宽度随粗糙度增加而减小;而次极大的超伏随粗糙度的增大而增大;在离焦像面上,离焦量的增加使光强的自相关函数下降变得平滑,并使极小值点和次极大点变得不明显或者消失。     

Velocity measurement of the diffuse object based on time-differentiated speckle intensity fluctuations

This paper proposes a new velocity measuring method for a moving diffuse object on the basis of the autocorrelation of time-differentiated speckle intensity fluctuations. The theoretical background and experimental verification of this method are given. The correlation length of time-differentiated speckle intensity fluctuations is defined by the point at which the correlation becomes zero. By means of the correlation length the object velocity is found to be accurately measured.     

Measurement of surface roughness properties using speckle patterns with non-gaussian statistics

The surface roughness properties (i.e. the rms surface roughness and the correlation length) of strong diffuse objects are investigated by using the speckle patterns which obeys the non-gaussian statistics. The intimate linear relation is found to exist between the rms surface roughness of objects and the maximum contrast obtained from the varying curves of the average image speckle contrast as a function of the point spread of an optical imaging system. The correlation length of surface roughness of objects is related to the averaged intensity distribution of speckle patterns produced at the far-field diffraction plane. It now becomes clear that the rms roughness and the correlation length of strong diffuse objects are determined, respectively, from the maximum speckle contrast at the image plane and the averaged speckle intensity distribution at the far-field diffraction plane.     

Photon statistics and speckle visibility spectroscopy with partially coherent X‐rays

A new approach is proposed for measuring structural dynamics in materials from multi‐speckle scattering patterns obtained with partially coherent X‐rays. Coherent X‐ray scattering is already widely used at high‐brightness synchrotron lightsources to measure dynamics using X‐ray photon correlation spectroscopy, but in many situations this experimental approach based on recording long series of images (i.e. movies) is either not adequate or not practical. Following the development of visible‐light speckle visibility spectroscopy, the dynamic information is obtained instead by analyzing the photon statistics and calculating the speckle contrast in single scattering patterns. This quantity, also referred to as the speckle visibility, is determined by the properties of the partially coherent beam and other experimental parameters, as well as the internal motions in the sample (dynamics). As a case study, Brownian dynamics in a low‐density colloidal suspension is measured and an excellent agreement is found between correlation functions measured by X‐ray photon correlation spectroscopy and the decay in speckle visibility with integration time obtained from the analysis presented here.     

Speckle photography applied to statistical analysis of turbulence

A speckle photographic technique is used for visualizing the planar distribution of the refractive deflection angles of light transmitted through the compressible turbulent flow. Both double and single (prolonged) exposure speckle photography are applied for statistical analysis of such flows. Using single (prolonged) exposure speckle photography (SPESP), instantaneous quantitative measurement of 2-D distribution of turbulence intensity in a flame is performed. Anisotropy of turbulence is visualized by a diffraction halo form and quantitatively evaluated by measuring the diffraction halo diameters. Using double exposure speckle photography (DESP), quantitative visualization of the planar distribution of the refractive deflection angles of the light transmitted through the compressible turbulent flow is done. Turbulent structures are visible in the patterns of the deflection angles isolines. The 2-D correlation functions of these deflection angles are constructed and analyzed. The 3-D density correlation functions are evaluated using the Erbeck–Merzkirch integral transformation.     

地面对激光雷达信号散射的统计研究

从理论角度研究了利用高斯光束照射远场目标时,激光散斑的统计特性.导出了散射光场的自相关函数和光强度的二阶矩的解析表达式,计算了激光散斑的面积.研究表明:在接收面上,光强的分布与目标表面高度的相关长度和均方根高度密切相关,激光散斑面积和散斑光强的相关系数只与激光束腰的尺度有关,与目标的均方根高度和相关长度无关. 关键词： 激光散斑 自相关函数 高斯分布 协方差     

Statistical properties of the dynamic dichromatic laser speckle

The statistical properties of dynamic elongated speckle patterns produced in the far-field diffraction region by a moving diffuse object under illumination of the dichromatic laser beam are experimentally investigated by means of a correlation method. The experimental results show that the correlation length of the normalized autocorrelation function of time-varying dichromatic speckle intensity fluctuations depends strongly on the fibrous radial structure of elongated speckle patterns. The qualitative discussions are given for the experimental results.     

基于一阶及二阶灰度梯度的散斑图质量评价方法

散斑图质量对数字图像相关(DIC)方法的测量精度具有重要的影响。以平均灰度梯度这一传统的散斑图质量评价参数作为基础,提出了一种新的评价参数——平均一阶及二阶灰度梯度商,该参数同时考虑了一阶和二阶灰度梯度。从整体上来说,一阶灰度梯度的曲面比较光滑,而一阶及二阶灰度梯度商的曲面比较粗糙。采用Zhou等人提出的方法制作了80张模拟散斑图,对这些模拟散斑图的传统参数和提出参数进行了计算。结果表明:当散斑半径相同时,随着散斑数量的增加,两种参数均先增加,后减小;当散斑数量一定时,二者均有一个峰值;散斑半径越大,提出参数的峰值越大,而传统参数的峰值越小。对提出参数的峰值所对应的4张散斑图进行了多次连续平动,并使用DIC方法测量了测点的水平位移。结果表明,在提出参数越大的散斑图上测点的水平位移误差越小,在一定程度上验证了提出参数的正确性。     

Statistical Properties of Laser Speckles Generated from Far Rough Surfaces

The statistical properties of speckle patterns generated from far rough surfaces, under illumination of a Gaussian beam, are investigated. The surface roughness dependence of the first- and second-order moments of intensity is theoretically investigated, and their analytical expressions have been derived and presented. The analysis indicates that the mean intensity distribution on the receiver plane is closely related to the ratio of the lateral correlation length to the surface root mean square (rms) height. On the other hand, the speckle size and the correlation degree of the speckle intensities are found to be independent of the parameter characterizing the roughness of a surface, and are only determined by the laser beam waist.     

Development of Matlab filtering techniques in digital speckle pattern interferometry

In interferometric fringe pattern analysis, specular and speckle fringe patterns are the two main divisions. While specular fringes are characterized by quality fringes, speckle (that obtains due to the diffuse scattering of the coherent radiation from an optically rough surface) fringe patterns are characterized by noisy fringes. This paper concentrates on this aspect and the Matlab based filtering methods to improve the quality of speckle fringe patterns by developing the appropriate software. Further, the newly developed software “Macurv” will be presented which can give the second order derivative (curvature) fringe information. A software with several functions is written using Matlab. The objective of the software is to provide a more effective way for the post-processing of speckle interferometric fringes. The algorithm and functions of the developed software “Macurv” will be explained.     

Tuning the intensity statistics of random speckle patterns

Speckle patterns are a fundamental tool in a variety of physical and optical applications. Here, we investigate a method of precisely tuning the intensity statistics of random speckle patterns into a desirable pattern that possesses the same spatial correlation length and similar statistics distribution. This tuning mechanism relies on the derivation of the transform function and transmission matrix, which achieves different contrasts while maintaining the same average value or energy level. The statistics properties of the generated speckle patterns are further investigated by analyzing the standard deviation under different fitting parameters. Precisely tuning the intensity statistics of random speckle patterns could be useful for both fundamental research and practical applications, such as microscopy, imaging, and optical manipulation.     

Statistical properties of the sum of two partially correlated speckle patterns

The probability density function and average contrast of the sum of two speckle patterns produced with various intensity ratios and correlation conditions have been experimentally investigated. The experimental results are compared with the theoretical ones obtained by Barakat and Goodman. Comparison shows excellent agreement between the experimental and theoretical results.     

Optical velocimetry: a method using two shifted speckle patterns

A new optical method for measuring the lateral velocity of a diffuse object is presented. The speckle pattern, originated by the surface under coherent illumination, is imaged into a linear photodiode array. The scanning time of the array is selected to detect two slightly shifted speckle patterns. By processing the intensity distributions, the velocity of the surface is derived. Some experimental results are shown.