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.     

人工局域表面等离激元诱导的超透射

利用有限元方法研究了理想导体薄膜中齿状孔阵列在微波频段的超透射现象.齿状结构的引入使得孔阵列的透射谱发生红移,在更深的亚波长区实现全透射.近场分析表明分布在齿状孔上的局域态对红移起了关键作用.研究发现单个齿孔支持人工局域表面等离激元多极子模式,与超透射相关的是偶极子模式.该研究方案可以推广到红外与太赫兹频段.     

Image pre-filtering for measurement error reduction in digital image correlation

In digital image correlation, the sub-pixel intensity interpolation causes a systematic error in the measured displacements. The error increases toward high-frequency component of the speckle pattern. In practice, a captured image is usually corrupted by additive white noise. The noise introduces additional energy in the high frequencies and therefore raises the systematic error. Meanwhile, the noise also elevates the random error which increases with the noise power. In order to reduce the systematic error and the random error of the measurements, we apply a pre-filtering to the images prior to the correlation so that the high-frequency contents are suppressed. Two spatial-domain filters (binomial and Gaussian) and two frequency-domain filters (Butterworth and Wiener) are tested on speckle images undergoing both simulated and real-world translations. By evaluating the errors of the various combinations of speckle patterns, interpolators, noise levels, and filter configurations, we come to the following conclusions. All the four filters are able to reduce the systematic error. Meanwhile, the random error can also be reduced if the signal power is mainly distributed around DC. For high-frequency speckle patterns, the low-pass filters (binomial, Gaussian and Butterworth) slightly increase the random error and Butterworth filter produces the lowest random error among them. By using Wiener filter with over-estimated noise power, the random error can be reduced but the resultant systematic error is higher than that of low-pass filters. In general, Butterworth filter is recommended for error reduction due to its flexibility of passband selection and maximal preservation of the allowed frequencies. Binomial filter enables efficient implementation and thus becomes a good option if computational cost is a critical issue. While used together with pre-filtering, B-spline interpolator produces lower systematic error than bicubic interpolator and similar level of the random error. Cubic B-spline interpolator can achieve comparable efficiency as bicubic interpolator, while quintic B-spline interpolator requires about 1.5 times the running time.     

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.     

Critical process of extraordinary optical transmission through periodic subwavelength hole array: Hole-assisted evanescent-field coupling

We present a new explanation of the extraordinary optical transmission through subwavelength hole array in metal films. By using the classical coupled-wave theory, we analyzed the coupling process between light and the surface plasmons wave on metal films with hole array. The analysis shows clearly the physical mechanism of extraordinary optical transmission. The calculation demonstrates that, instead of energy flux directly passing through the holes, the electromagnetic modes could exchange energy by overlapping the evanescent fields under the assistance of hole array. The periodicity of the array provides the momentum-matching condition to present the transmission peaks. The theory exhibits a good agreement with the experimental results reported in every detail.     

含有侧孔阵列圆柱管的发声频谱

利用末端导纳匹配方法和格林函数方法,对含有侧孔的律管进行了声学谱分析,得到了均匀侧孔长管在两个音阶上的共振频谱。发现了随有效管长的均匀递减,其发声频率的递增是不均匀的。主要共振效应发生在离吹孔最近的侧孔处,随着共振频率的升高,气流更加集中地在第一侧孔辐射能量,次共振几乎可以忽略。附管上的侧孔对共振频率影响甚微,但是对音色、音强以及各侧孔的透射率都有一定的影响。该理论给出的共振频率与数值模拟结果符合地很好,第一音阶和第二音阶的平均偏差分别为5.03%和2.23%。由此认为末端导纳匹配方法适用于各类含有侧孔的管状发声物声学特性的研究。      

Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes

We show that extraordinary light transmission of periodic subwavelength hole arrays, generally attributed to surface-plasmon resonances, is strongly influenced by the hole shape. Both experiments and calculations, based on a Fourier modal method, demonstrate that a shape change from circular to rectangular increases the normalized transmission by an order of magnitude while the hole area decreases. Moreover, the spectra exhibit large redshifts (approximately 2500 cm(-1)). A comparison with the transmission of isolated holes shows that shape resonances of the rectangular holes play a dominant role.     

随机分布的多圆孔的夫琅禾费衍射场分布研究

采用蒙特卡罗方法先对随机分布的多圆孔构成的衍射屏进行了分析计算,并与单个圆孔的衍射场进行了比较,结果表明,多圆孔的衍射场与单个小圆孔的衍射场有相同的条纹形状和条纹半径,但多圆孔衍射场的能量比单个圆孔的衍射场能量明显增加,同时场强变化不均匀,有叠加噪声的效果,在衍射艾里斑的中心处有一个强亮点.然后对大圆孔内随机分布着的小圆屏构成的衍射屏进行分析,得到了与多圆孔衍射类似的结论,这些结论与实验结果一致.     

Nodal densities of planar gaussian random waves

The nodal densities of gaussian random functions, modelling various physical systems including chaotic quantum eigenfunctions and optical speckle patterns, are reviewed. The nodal domains of isotropically random real and complex functions are formulated in terms of their Minkowski functionals, and their correlations and spectra are discussed. The results on the statistical densities of the zeros of the real and complex functions, and their derivatives, in two dimensions are reviewed. New results are derived on the nodal domains of the hessian determinant (gaussian curvature) of two-dimensional random surfaces.     

时间序列散斑干涉场中相位函数的计算

散斑干涉或电子散斑干涉计量应用于连续运动或变形物体时,就会产生一个时变的散斑干涉场,通过摄像系统连续地采集这一时变散斑场,可获得一系列时间序列散斑干涉图,通过对序列散斑图上各点在时间轴上光强值的变化进行分析,提出了一种基于时间序列的分析方法,用以提取干涉场的相位值,进而获得物体全场变形信息。     

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.     

Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances

By using the rigid full-vectorial three-dimensional finite-difference time-domain method, we show that the enhanced transmission through a metallic film with a periodic array of subwavelength holes results from two different resonances: (i) localized waveguide resonances where each air hole can be considered as a section of metallic waveguide with both ends open to free space, forming a low-quality-factor resonator, and (ii) well-recognized surface plasmon resonances due to the periodicity. These two different resonances can be characterized from electromagnetic band structures in the structured metal film. In addition, we show that the shape effect in the enhanced transmission through the Au film with subwavelength holes is attributed to the localized waveguide resonance.     

Compressed ghost imaging based on differential speckle patterns

We propose a compressed ghost imaging scheme based on differential speckle patterns,named CGI-DSP.In the scheme,a series of bucket detector signals are acquired when a series of random speckle patterns are employed to illuminate an unknown object.Then the differential speckle patterns(differential bucket detector signals) are obtained by taking the difference between present random speckle patterns(present bucket detector signals) and previous random speckle patterns(previous bucket detector signals).Finally,the image of object can be obtained directly by performing the compressed sensing algorithm on the differential speckle patterns and differential bucket detector signals.The experimental and simulated results reveal that CGI-DSP can improve the imaging quality and reduce the number of measurements comparing with the traditional compressed ghost imaging schemes because our scheme can remove the environmental illuminations efficiently.     

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.     

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.     

Chladni figures in Andreev billiards

We study wave functions and their nodal patterns in Andreev billiards consisting of a normal-conducting (N) ballistic quantum dot in contact with a superconductor (S). The bound states in such systems feature an electron and a hole component which are coherently coupled by the scattering of electrons into holes at the S-N interface. The wave function “lives” therefore on two sheets of configuration space, each of which features, in general, distinct nodal patterns. By comparing the wave functions and their nodal patterns for holes and electrons detailed tests of semiclassical predictions become possible. One semiclassical theory based on ideal Andreev retroreflection predicts the electron- and hole eigenstates to perfectly mirror each other. We probe the limitations of validity of this model both in terms of the spectral density of the eigenstates and the shape of the wavefunctions in the electron and hole sheet. We identify cases where the Chladni figures for the electrons and holes drastically differ from each other and explain these discrepancies by limitations of the retroreflection picture.     

Observation of speckle pattern formation in transparent nonlinear random media

We report on the experimental observation of speckle formation from a transparent crystal formed by a random distribution of nonlinear domains. The angular distribution of second-harmonic light generated by a transparent strontium barium niobate crystal is measured for different diameters of the fundamental beam and crystal thicknesses. Distinct manifestations of speckle pattern formation are found in these experiments. By using a theoretical Green's function formalism, we explain the reported observations as a result of the linear interference among the second-harmonic waves generated in all directions by each of the nonlinear domains forming the nonlinear crystal.     

带缝隙矩形腔的屏蔽效能传输线法修正及扩展分析

为研究入射电磁波与缝隙参量对矩形腔体屏蔽效能的影响,提出基于透射定律结合等效传输线方法对腔体的电磁屏蔽特性进行分析。详细推导了经缝隙透射进腔体内的电场,将透射电场作为等效电压源并对传统的传输线模型进行了修正,使之能计算任意方位入射的电磁波及缝隙偏离体壁中心时的情况;并对此方法的计算公式进行了扩展,使其能分析不同形状、孔阵、孔距及损耗等参量对腔体屏蔽效能的影响。研究表明:缝隙位于体壁中心时的屏蔽效能比靠近体壁边沿时差;相对入射角和方位角而言,极化角对腔体的屏蔽效能影响较大;在保持孔阵总面积不变的情况下,通过减小孔径来增加孔的数目或增大孔间距都可提高腔体的屏蔽效能;屏蔽体内损耗因子越大,则对腔体内的谐振频率抑制效果越明显。通过与腔体内谐振频率理论值、数值方法结果的比对分析表明,修正和扩展的解析方法结果可信,且利于各参量对腔体屏蔽效能的分析,适用范围更广。