The phenomenon of simplified scattering from rough surfaces to reflection in fractional space

In this paper, the scattering of incident plane waves from rough surfaces has been modeled in a fractional space. It is shown how wave scattering from a rough surface could correspond to a simple reflection problem in a fractional space. In an integer dimensional space, fluctuations of the surface result in wave scattering, while in the fractional space, these fluctuations are compensated by the geometry of space. In the fractional space, reflection is equivalent to scattering from the integer dimensional space. Comparing scattered wave functions from different self-affine rough surfaces in the framework of the Kirchhoff theory with the results from the fractional space, we see good agreement between them.     

Scattering of electromagnetic radiation by surfaces with a fractal relief

The scattering indicatrix of electromagnetic waves for different types of rough surfaces and angles of incidence is calculated using the Kirchhoff scalar theory. The rough surfaces are modelled by a two dimensional Weierstrass function. The scattering index for a rough surface with a fractal relief is found to have a complicated structure with intensity bursts in directions quite far from the direction of mirror reflection.     

A Study of Optical Backscattering Enhancement from One-Dimensional Rough Surface Using Monte Carlo Method

In this paper, according to Kirchhoff approximation, the optical backscattering enhancement of one-dimensional random rough surface, which includes fractal rough surfaces and random rough surfaces with Gaussian and exponential correlation simulated by Monte Carlo method, is obtained. It is shown that backscattering enhancement of random rough surfaces will increase with increasing the rms height of rough surface for a given correlation length. The angle width of backscattering enhancement is directly proportional to incident wavelength and inverse proportional to correlation length of rough surface. Complex phase of scattering field from superposed rough surface is uniformly distributed, none of the directions is of more overweight. The backscattering enhancement is also studied by wavelet analysis. The numerical results show good consistent with that of the relative references.     

Explicit results for wave scattering and transmission through a rough fluid-fluid interface

This paper describes an analysis of reflection and transmission of acoustic waves from an imperfectly reflecting, rough fluid-fluid interface within the Kirchhoff approximation. It presents the results of calculations of the coherent and diffuse field. This work is motivated by the fact that few explicit results of the characteristics of the scattered and transmitted wave field exist in the literature for this problem. For the problem of interest, the surface reflection coefficient depends at each point upon the local angle between the incident wave and the rough surface. For surfaces with statistically independent local surface position and gradient, coherent field calculations show that the correction to constant reflection coefficient analyses is simply a multiplicative factor that depends upon the statistical characteristics of the surface gradient, sound speed and density ratio across the surface. This multiplicative factor is interpreted as an average reflection or transmission coefficient, <R> and <T>, respectively. The principle differences between these results and constant reflection coefficient analyses occur when waves impinge upon regions with higher sound speeds, where total internal reflection may occur. While the wave characteristics of smooth or constant reflection coefficient surfaces change abruptly in the vicinity of the angle of total internal reflection, the average reflection coefficient exhibits a much smoother dependence upon angle of incidence or sound speed ratio for rough surfaces. It is also shown that the direction of maximum diffuse scattering moves relative to its value were the reflection coefficient constant.     

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。     

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。     

Three-Component Model for Bidirectional Reflection Distribution Function of Thermal Coating Surfaces

We present a bidirectional reflection distribution function(BRDF) model for thermal coating surfaces based on a three-component reflection assumption,in which the specular reflection is given according to the microfacet theory and Snell's law,the multiple reflection is considered Nth cosine distributed,and the volume scattering is uniformly distributed in reflection angles according to the experimental results.This model describes the reflection characteristics of thermal coating surfaces more completely and reasonably.Simulation and measurement results of two thermal coating samples SR107 and S781 are given to validate that this three-component model signiScantly improves the modeling accuracy for thermal coating surfaces compared with the existing BRDF models.     

Matching conditions in atomistic-continuum modeling of materials

A new class of matching conditions between the atomistic and continuum regions is presented for the multiscale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and at the same time minimize the reflection of phonons at the interface. These matching conditions can be made adaptive if we choose appropriate weight functions. Applications to dislocation dynamics and friction between two-dimensional atomically flat crystal surfaces are described.     

Surface reverberation spectrum of underwater sound

A general formulation is derived for the power spectrum of fluctuations in the signal received by way of reflection from a rough sea surface, in terms of an arbitrary wavenumber-frequency spectrum of the surface waves and an arbitrary source directivity function. The formulation is then applied to the specific case of backscatter for which the extreme cases of acoustically slightly rough and very rough sea surfaces are examined in detail. The results of the analysis are compared with experiments, and with the somewhat more restricted results of other theoretical work.     

随机起伏冰面三维声散射的Kirchhoff近似数值计算模型

针对随机起伏冰面的声散射问题,建立了随机起伏冰面三维声散射的Kirchhoff近似数值计算模型。利用Delaunay三角剖分方法对随机起伏冰面进行三角面元剖分,然后采用Z-buffer算法进行面元的遮挡消隐,得到处于声波照射亮区的面元,最后采用Gordon面元积分的板块元方法计算得到随机起伏冰面的散射强度。数值计算模型中,将冰面认为是局部阻抗表面,直接代入起伏冰面局部反射系数进行散射声场的计算,避免了解析计算模型中对反射系数的近似处理。对比分析了数值和解析计算模型在小粗糙起伏冰面、大粗糙起伏冰面及不同声波入射角和不同声波频率时的散射强度。相比解析模型计算结果,数值模型计算结果与实测结果更吻合。     

Simplified Method to Estimate Millimeter-Wave Reflection from Rough Surfaces

Two-dimensionally sinusoidal model is used to establish a simplified method to estimate millimeter-wave reflection from rough surfaces. A very simple result is derived for engineering design.     

随机粗糙表面超声双透射研究

基于Fresnel近似及相屏近似理论建立了随机粗糙表面的声波双透射信号损失理论模型,提出采用指数替代法消除非线性积分项实现双透射信号损失的简单解析解。研究表明,观透射信号损失不仅与粗糙高度有关,而且与声波传播路径即缺陷深度有关。     

Investigation of surface topology of printed nanoparticle layers using wide‐angle low‐Q scattering

A new small‐angle scattering technique in reflection geometry is described which enables a topological study of rough surfaces. This is achieved by using long‐wavelength soft X‐rays which are scattered at wide angles but in the low‐Q range normally associated with small‐angle scattering. The use of nanometre‐wavelength radiation restricts the penetration to a thin surface layer which follows the topology of the surface, while moving the scattered beam to wider angles preventing shadowing by the surface features. The technique is, however, only applicable to rough surfaces for which there is no specular reflection, so that only the scattered beam was detected by the detector. As an example, a study of the surfaces of rough layers of silicon produced by the deposition of nanoparticles by blade‐coating is presented. The surfaces of the blade‐coated layers have rough features of the order of several micrometers. Using 2 nm and 13 nm X‐rays scattered at angular ranges of 5°≤θ≤ 51° and 5°≤θ≤ 45°, respectively, a combined range of scattering vector of 0.00842 Å^?1≤Q≤ 0.4883 Å^?1 was obtained. Comparison with previous transmission SAXS and USAXS studies of the same materials indicates that the new method does probe the surface topology rather than the internal microstructure.     

高平均功率光纤激光技术基础: (2) 谐振腔

概述光纤激光谐振腔的基本结构、主要组件及其功能,介绍高功率光纤激光谐振腔的发展现状。以光纤光栅为研究载体分析谐振腔时空频域多维特性。从中心波长、线宽和形态三个方面介绍谐振腔输出光谱特性调控的机理、方法与研究进展;从本征模与反射谱的关联角度介绍谐振腔输出模式调控的机理、方法与研究进展;介绍谐振腔瞬态时域特性建模的最新成果,指出时频特性的关联及其对非线性效应产生的影响。最后介绍两种无腔结构的高功率光纤激光。     

Light scattering by complex ice-analogue crystals

Angle-dependent light-scattering measurements on single ice analogues crystals are described. Phase functions and degree of linear polarization are measured for electrodynamically levitated crystals. A procedure for randomizing particle orientation during levitation is demonstrated. The dependence of scattering on the shape, complexity and surface roughness of the crystals is examined. The phase functions from complex crystals with smooth surfaces show little dependence on shape. There is close agreement between the measured functions and the analytic phase function for ice clouds. However, rosettes with rough surfaces have qualitatively different phase functions, with raised side and back scattering. The asymmetry parameter is typically about 0.8±0.04 and 0.63±0.05 for smooth and rough crystals, respectively. The 22° halo peak is present for smooth rosettes and aggregates but absent for rough rosettes. Two-dimensional scattering patterns from several crystals in fixed orientations are also shown. The results suggest that it may be possible to use such patterns to discriminate not only between crystals of different shape but also to obtain some information on surface properties.     

Scattering by an object above a randomly rough surface from a fast numerical method: Extended PILE method combined with FB-SA

In this paper, a fast exact numerical method, based on the method of moments, is developed to calculate the scattering by an object above a rough surface. N. Déchamps et al. have recently developed the PILE (Propagation-Inside-Layer Expansion) method for a stack of two one-dimensional rough interfaces separating homogeneous media. This method allows us to calculate separately and exactly the multiple scattering contributions inside the layer. This is done with a decomposition by block of the impedance matrix (the inverse of the impedance matrix of each interface and two coupling matrices are involved). The purpose of this paper is to extend the PILE method to the more general case of two illuminated surfaces and to apply it to an object located above a rough surface. In addition, to invert a matrix of large size, the Forward–Backward Spectral Acceleration (FB-SA) approach of complexity 𝒪(N) proposed by Chou and Johnson is applied. The new method, extended PILE combined with FB-SA, is tested on Perfectly Conducting (PC) circular and elliptic cylinders located above a rough surface (dielectric or PC) obeying a Gaussian process with Gaussian and exponential height autocorrelation functions.     

相位解码的时-空重建算法

基于相位映射的三维传感技术对几何形状和拓扑结构复杂或表面梯度很大的物体进行绝对相位测量及相位重建仍然是一个困难的问题。近年来国际上提出了一种时间维度相位重建算法可以对此提供一种解决方案。然而,该算法对结构光照明系统提出了很高的要求,当系统无法满足算法要求时,重建结果存在严重的噪声。针对这一问题,提出了一种利用分段函数构造的相位解码的时空重建算法。该算法在相位重建过程中同时考虑时间维度和空间维度相位的相对关系,使得空间频率非严格按指数增长的条纹序列可以得到正确的重建,消除了跳变边界的相位模糊问题,从而可以更加有效地解决深度表面不连续和存在相互孤立物表面拓扑结构的景物相位重建问题。实验结果证明了此算法的可行性和有效性。     

Light reflection from finite conductors with a Gaussian random roughness using Kirchhoff and geometric optics approximations

A comparison between exact solutions and two approximate models, Kirchhoff approximation (KA) and geometric optics approximation (GOA), for reflection from random Gaussian rough conductive metallic surfaces for three regimes of correlation length in both cases of polarization TM and TE has been reported. The phenomenon of excitation of surface plasmons (SPs) has been shown only at TM polarization for KA. The domains of validity of both approximate models have been quantified. It is shown that accuracy and efficiency of any approximate method depended of various parameters: surface roughness, polarization, SPs effects, wavelength, and surface materials. KA is efficient for weakly rough surfaces with correlation length greater than wavelength, but when rms height increases GOA is more suitable than KA. Excitation of SPs is observed only at TM-polarized light, only for weakly rough surfaces with correlation length less than wavelength using KA and not GOA.     

Discrete dipole approximation simulations of light reflection from flat non-transparent particles with rough surfaces

We study light reflection from flat particles with rough surfaces and fractal statistics of topography. Discrete dipole approximation method is used to solve the problem of light scattering. Refractive indices corresponding to a metal and a transient material with conductive properties are taken. The sizes of particles are much larger than the wavelength of incident light and the roughness scales are larger, comparable to and smaller than the wavelength. The influence of the fractal dimension parameter and the amplitude of heights of random topography on reflectance and on the angular profile of the specular reflection peak is considered. Our calculations demonstrate that topography amplitude is very important for reflectance and fractal dimension is responsible for the angular dispersion of the specular reflection peak.     

小掠射角下高斯谱粗糙海面反射损失建模

在散射能量基本为前向散射且集中在“镜面反射”方向的情况下,粗糙海面反射损失建模是声呐信号传播建模必不可少的一部分,尤其对于中远距离下浅海或者存在表面声道的水声环境,小掠射角(10°以内)下的粗糙海面反射损失建模尤为重要。首先基于高斯谱粗糙海面模型,通过高海况下的声传播试验数据处理分析了粗糙海面边界条件下的Ramsurf声传播模型的有效性,进而以Ramsurf声传播模型为基准,在小掠射角下,比较分析了Kirchhoff近似(KA)海面反射损失模型和小斜率近似(SSA)海面反射损失模型,数值计算结果表明,在小掠射角下SSA海面反射损失模型与Ramsurf计算结果较为吻合,是比较精确的海面反射损失模型。