Scaling reduction of the contrast of fractal speckles detected with a finite aperture

It is known that speckle patterns with fractal properties, called fractal speckles, are produced by illuminating a diffuser with the coherent light having the intensity distribution obeying a negative power law. One of key properties of fractal speckles is the spatial correlation function obeying a negative power law, which implies that such speckles have scaling properties. In detecting fractal speckles, the effect of the spatial integration is inevitable in most cases since they have speckle grains of various scales including very fine ones. To evaluate this effect, in this paper, the contrast of spatially integrated intensity distributions is investigated theoretically and experimentally for fractal speckles. The results show that the contrast reduction with the size of the detector aperture obeys a negative power function related with the exponent of the intensity correlation coefficient of fractal speckles.     

Speckle characteristics of simulated deep Fresnel region under shadowing effect

After the three-dimensional self-affine fractal random surface simulation, we use the optical scattering theory to calculate the deep Fresnel region speckle(DFRS) under consideration of the more strict shadowing effect. The evolution of DFRS with the scattering distance and the intensity probability distribution are studied. It is found that the morphology of the scatterer has an antisymmetric relationship with the intensity distribution of DFRS, and the effect of micro-lenses on the scattering surface causes the intensity probability distribution of DFRS to deviate from the Gaussian speckle in the high light intensity area.     

Measurements of femtosecond temporal speckle field of a random medium

The femtosecond temporal speckle field of a random medium is studied theoretically and experimentally. Femtosecond temporal speckle arises from the interference of multiple randomly scattered electric fields. The femtosecond temporal speckle field is measured with a cross-correlation frequency-resolved optical gating method. The spatial average of the speckle field yields a smooth transmitted profile. The speckle field is a circular complex Gaussian variable because the scattered light beams from different trajectories have no correlation with each other. The field and the intensity profiles of individual speckle spots fluctuate randomly in time. The ensemble average of the temporal intensity profiles converges, thereby yielding the photon travel time probability distribution function.     

Computer-generated holograms for producing fractal speckles

When a diffuser is illuminated by the coherent light with a negative power-law distribution, fractal speckles are produced in the far-field diffraction region. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles, which implies that they may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. To have fractal speckles with satisfactory statistical properties, it is required to produce a power-law illumination profile with high quality. In this paper, we report on the computer-generated holograms for producing power-law intensities on the basis of the method of stationary phase, with the error-reduction algorithm combined with to suppress strong ringing of the intensity.     

Correlation and fractal properties of speckles in the extremely deep Fresnel diffraction region

Based on the Kirchhoff approximation and the theoretical analysis of the random light fields,the speckle intensity distributions in the extremely deep Fresnel diffraction region are simulated.The fractal property of the speckles as well as the relation between the speckle intensity distribution and the corresponding random surface is investigated.We design a microscope system to detect experimentally the speckles in the extremely deep Fresnel diffraction region,and the experimental results prove the conclusions drawn from our simulations.     

Near-field speckles produced by random self-affine surfaces and their contrast transitions

By use of a numerical calculation based on Green's integral equation, we study the near-field speckles produced by the random self-affine fractal surfaces of a dielectric medium. The speckle intensities evolve considerably in the near-field region, and the local fluctuations in them disappear before they have traversed the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near field and in the neighborhood non-near-field regions depends on lateral correlation length xi and roughness exponent alpha of the random surfaces.     

运动界面上反射超声散斑空间运动的研究

在Kirchhoff 衍射理论的基础上，应用随机信号相关原理，推导了作刚体运动的界面上反射超声散斑在空间运动时，保持其复振幅相关的必要条件.由此得到超声散斑的空间运动公式.界面、超声散斑和超声接收探头之间的相对运动，导致界面孔径的改变.分析表明，在保持界面孔径相关的条件下，界面所允许的最大平移量和转角值，与声源位置、接收用聚焦探头的数值孔径、超声入射角以及观察角有关.应用数字相关技术和三维扫描信号采集系统，根据散斑场子集相关系数的单峰性质，对超声散斑空间运动公式进行了实验验证.实验结果表明，理论分析所得的 关键词： 超声散斑 相关原理 空间运动     

大散射角散斑场中有关相位奇异新特性的研究

利用散斑场和参考光的干涉提取散斑场复振幅和相位, 研究了不同散射角下散斑场相位的分布规律以及相位奇异处光波复振幅实部零值线和虚部零值线夹角、光强等值线离心率的统计特性. 在大散射角散斑中发现了一种新的相位奇异现象, 即相位奇异线; 研究了相位在跨越奇异线时的突变规律及涡旋状相位的分布特征, 发现在相位奇异线处存在着呈双曲线或抛物线状的光强等值线.     

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.     

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.     

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.     

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.     

空间平均的角度散斑相关粗糙度测量模拟研究

角度散斑相关是一种不受表面粗糙度轮廓的间距特性影响的粗糙度幅度参量测量方法,它的数学模型通常建立在集平均的基础上。通过模拟计算随机粗糙表面的远场散斑场,以散斑图面上的空间平均代替常规的集平均来计算角度散斑相关系数,并应用集平均的数学模型反演粗糙度参量。结果证实了这种空间平均角度散斑相关粗糙度测量方法的有效性,在同一表面只需对少数个区域进行测量并对测得的粗糙度参量取平均,即可获得足够的测量精度。对于Rq大于2.0μm的表面,测量相对误差小于15%。根据最佳测量条件,该方法适用于大粗糙度表面。     

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

Abstract

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.     

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.     

Experimental measurements of non-Gaussian scattering by a fractal diffuser

We report measurements of the statistics of intensity scintillations of 10.6 μm CO₂ radiation scattered by a two-dimensional fractal phase screen. The surface profile of the phase screen is measured and shown to have a Hausdorff-Besicovitch dimension of approximately 1.4. Measurements of the on-axis intensity fluctuations as a function of illuminated spot size in both the Fresnel and Fraunhofer region are presented. This fractal scatterer does not produce the high contrast values found in speckle patterns of smoothlyvarying surfaces. Both direct and heterodyne detection results are reported. Measurements of the average intensity as a function of angle are also presented, and illustrate the failure of theoretical models which assume a Gaussian phase autocorrelation function.     

Digital Speckle Photography of Subpixel Displacements of Speckle Structures Based on Analysis of Their Spatial Spectra

We have investigated the capabilities of the method of digital speckle interferometry for determining subpixel displacements of a speckle structure formed by a displaceable or deformable object with a scattering surface. An analysis of spatial spectra of speckle structures makes it possible to perform measurements with a subpixel accuracy and to extend the lower boundary of the range of measurements of displacements of speckle structures to the range of subpixel values. The method is realized on the basis of digital recording of the images of undisplaced and displaced speckle structures, their spatial frequency analysis using numerically specified constant phase shifts, and correlation analysis of spatial spectra of speckle structures. Transformation into the frequency range makes it possible to obtain quantities to be measured with a subpixel accuracy from the shift of the interference-pattern minimum in the diffraction halo by introducing an additional phase shift into the complex spatial spectrum of the speckle structure or from the slope of the linear plot of the function of accumulated phase difference in the field of the complex spatial spectrum of the displaced speckle structure. The capabilities of the method have been investigated in natural experiment.     

激光散斑时间漂移效应研究

报道了激光散斑时间漂移效应.引入了散斑模型,接收面上散斑场复振幅的强度和位相的统计性质证明了模型的合理性.基于此模型和相关算法,模拟了所有可能导致激光散斑时间漂移效应的物理因素的影响.模拟结果显示两个因素起主要作用.通过巧妙地改变VCSEL和CCD的工作状态,也证明了两个因素其主要作用,即激光器对表面的加热引起的表面膨胀和CCD的热效应带来的噪声增加.相比之下,其他因素仅仅会带来散斑图像的微小变化.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

Dipole radiation of a charged particle moving along a fractal trajectory

The dipole radiation of a charged particle moving along a closed fractal trajectory with constant velocity is studied. It is found that the spectrum intensity of the radiation is displaced to the high frequency region when reducing the spatial scale of the fractal trajectory and tends to zero if the trajectory is a true fractal.