Size-dependent reactivity of aluminum cluster cations toward water molecules

Using the autocorrelation of speckles in the deep Fresnel region is a novel approach to measuring surface parameters of a rough surface. In this letter, we construct a scanning system using a fibre-optic probe for detecting the speckle field with excellent resolution. By relating the autocorrelation function of the speckle intensity and the surface height with the Kirchhoff approximation theory, we realise the measurement of the surface parameters. Three parameters, i.e. the roughness w, the lateral correlation length ξ and roughness exponent α are extracted. We measure two sample surfaces in the experiment, and the results are consistent with those measured by atomic force microscope (AFM).     

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.     

Detection of a small defect on a rough surface

We report experimental results that show that the far-field correlation function is sensitive to a small local change in rough-surface geometry, where the speckle spatial correlation rather than the sample ensemble average is adopted. The angular cross-correlation function of the far-field speckles scattered by one-dimensional random rough surfaces is measured when a polarized beam of light is incident upon the rough surface from vacuum, where one part of the surface used is a thin dielectric film deposited upon a glass substrate and the other part is identical to the first except for a localized defect. We envisage application of this sensitivity property to inspection of a sample with a defect by means of speckle mapping.     

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     

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…     

Fractal Roughness Retrieval by Integrated Wavelet Transform

An integrated-wavelet-transform (IWT) approach is proposed for the study of scattering from slightly rough surfaces that manifest scaling properties over a finite domain of correlation lengths. Instead of collecting angle-resolved intensities, values of the irradiance integrated over increasing areas are used to enhance the contributions of small irradiances at large scattering angles and to reduce the coherent noise. In the case of self-similar surfaces, the scaling behavior of IWT allows investigation of the surface roughness at various length scales. For the realistic case of self-affine surfaces, IWT permits the evaluation of the scaling exponent of the autocorrelation and also offers a direct way to evaluate the necessary length scale of the surface profile.     

Fractal structure of digital speckle patterns produced by rough surfaces

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.     

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.     

Surface roughness measurements from coherent light scattering

Results are presented of surface roughness measurements obtained by applying Beckmann's theory on the scattering of electromagnetic waves from rough surfaces to the scattering of laser light from ground glass surfaces. Measurements of the variance of surface height obtained in several scattering geometries and also from stylus measurements are presented and shown to agree closely for each surface. Also results are presented which show that the usual assumption of a Gaussian form for the autocorrelation function of surface height does not apply to the surfaces being studied here.     

粗糙表面对散斑统计特性的影响

为研究高速摄影中激光相干噪声的影响因素,降低激光照明中散斑噪声对高速摄影成像质量的影响,对激光照射表面的粗糙程度与形成的散斑场统计特性之间的关系进行了研究。基于菲涅尔-基尔霍夫衍射原理,分析了高斯光束入射在随机粗糙表面上经反射形成的散斑图样,通过对大量散斑图样的数据统计,得出了激光散斑的信噪比、自相关函数、概率密度函数与入射表面粗糙度之间的变化关系。计算结果表明:粗糙度的增大使散斑场信噪比降低、相干程度减小、概率密度降低,即表面越粗糙散斑噪声越严重。     

基于多色散斑延长效应的表面粗糙度测量及影响因素分析

粗糙表面在多波长激光束照射下形成的多色散斑场显示出散斑延长效应,利用此效应可以测量表面粗糙度,并且测量结果在一定条件下不受粗糙表面横向特征的影响。通过模拟计算随机粗糙表面的多色散斑场,以空间平均的多色散斑场局部自相关函数研究了平均散斑延长率〈χ〉对表面轮廓均方根偏差σh的依赖关系,分析了测量系统因素,如入射激光波长组合、成像器件光敏单元尺寸和动态范围对测量结果的影响。结果表明,以空间平均的局部自相关函数代替集平均的散斑自相关函数描述多色散斑延长效应是有效的;为达到一定的粗糙度测量精度,应选择合适的入射激光波长组合和合适的成像器件光敏单元尺寸。     

Detection of a periodic structure embedded in surface roughness,for various correlation functions

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.     

Analysis of non-ergodic behaviour in spatio-temporal coherence properties of speckle light

Spatio-temporal coherence properties of light scattered by rough surfaces that leads to speckle fluctuations are analysed. It is demonstrated that the scattered light is non-ergodic with the disorder due to the scattering process. Although the mutual coherence matrix vanishes with isotropic polarization fluctuations, it is shown that spatio-temporal coherence properties can be described with interference experiments that can be obtained between different speckles of the scattered light. For non-singular scattering processes, the maximal value of the modulus of the Wolf degree of coherence is analysed in the spatial time domain. This approach is also applied to totally unpolarized incident light with an isotropic and spatially independent scattering process. The mean value and the standard deviation of the Wolf degree of coherence are then determined from the coherence properties of the incident light.     

弱散射体产生的菲涅耳极深区散斑场相位涡旋演化的实验研究

实验提取了弱散射体产生的菲涅耳极深区的散斑场.发现当散射距离一定时,弱散射体光场的相位分布特征随散射体的粗糙度的变化而变化;对于某一弱散射体,相位分布特征随散射距离的变化而变化;当弱散射体的粗糙度大到一定程度时,才产生相位涡旋现象;散射体表面上存在相位涡旋;弱散射体产生的相位涡旋的密度随散射屏粗糙度的增大而增大,还随散射距离的增大而增大.研究结果对于认识弱散射体的相位及相位涡旋分布特征随粗糙度和散射距离的演化具有重要意义,而且对于认识散斑场随散射距离的演化有一定的帮助.     

The dynamic angle-limited integrated scattering (DALIS) method for measuring scattering of light from optical surfaces with random roughness

A new and simple dynamic angle limited integrated scattering (DALIS) method is developed to examine optically smooth reflective surfaces with defined surface form. Our experimental results from two systems show advantages over conventional angle resolved scattering measurement (ARS) methods. By collecting scattered light in a given solid angle, our methods do not require a detection unit with an extremely large dynamic range. Unlike in the common ARS measurement method, here we use a simple linear translation stage to scan scattered light. The power spectrum density function and the autocorrelation function of the surface roughness can be recovered from the measured scattering pattern. This method can be applied to in-workshop inspection of optical polishing processes.     

Monostatic and bistatic statistical shadowing functions from a one-dimensional stationary randomly rough surface according to the observation length: I. Single scattering

When solving electromagnetic rough-surface scattering problems, the effect of shadowing by the surface roughness often needs to be considered, especially as the illumination angle approaches grazing incidence. This paper presents the Ricciardi-Sato, as well as the Wagner and the Smith formulations for calculating the monostatic and bistatic statistical shadowing functions from a one-dimensional rough stationary surface, which are valid for an uncorrelated Gaussian process with an infinite surface length. In this paper, these formulations are extended to include a finite surface length and any uncorrelated process. The inclusion of a finite surface length is needed to extend the single-reflection shadowing function to the more general multiple-reflection case, presented in the following companion paper. Comparisons of these shadowing functions with the exact numerical solution for the shadowing (using surfaces with Gaussian and Lorentzian autocorrelation functions for a Gaussian process) shows that the Smith formulation without correlation is a good approximation, and that including correlation only weakly improves the model. This paper also presents a method to include the shadowing effect in the electromagnetic scattering problem.     

随机表面散射光场的格林函数法与基尔霍夫近似的比较

从简谐光波满足的亥姆霍兹方程出发，将由格林定理得到的介质分界面上的积分方程转化为以表面上的光波及其导数为未知量的线性方程组，并对其进行数值求解，实现了光场的数值计算. 同时，由透射光场的格林函数积分得出了基尔霍夫近似下光场的表达式. 通过类比推导夫琅和费面上散斑场自相关函数的方法，提出了产生随机表面及其导数的傅里叶变换方法. 在此基础上，对采用基尔霍夫近似进行自仿射分形随机表面的散射光场数值计算的精确程度进行了研究. 发现在随机表面粗糙度比较小时，基尔霍夫近似的精度比较高；在粗糙度相同的情况下，表面的分形 关键词： 格林函数积分 基尔霍夫近似 自仿射分形随机表面     

Multiple scattering of plasmons at rough surfaces

We investigated the polarization and angle dependence of the scattered light intensity of surface plasma oscillations (SPO) propagating along rough silver surfaces. The rough silver films were prepared using the methods of pre-evaporating CaF₂ and silver on heated substrates. The scattered light intensity of both systems is explained by surface scattering effects. Differences of the light intensities between the rough silver films prepared by the two methods mainly were observed in “restlight intensities”, which cannot be described by first-order scattering theories. We explain these differences by higher order scattering effects.     

不稳定表面粗糙目标的太赫兹波段散射特性分析

研究了不同粗糙度下的非均匀和分区均匀不稳定表面粗糙导体目标在太赫兹波段的散射特性。区别于采用经验公式的建模方法,提出把随机粗糙面的建模理念应用到太赫兹波段的非均匀和分区均匀不稳定表面粗糙导体目标的建模中,用描述粗糙面的均方根高度和相关长度两个物理量来调节目标表面的粗糙度变化。提出表面粗糙目标的分类形式并给出具体模型,然后用随机高斯粗糙面来模拟非均匀和分区均匀不稳定粗糙目标的表面,再采用物理光学和等效电流相结合的方法来进行仿真计算,分别对不同入射角、不同频率和不同粗糙度的非均匀和分区均匀不稳定表面粗糙导体目标的太赫兹波散射特性进行分析,最后得出了相关的结论。