Scattered-light properties of diffraction gratings

One of the many calibrations performed for a scientific-quality spectrometer is the characterization of its scattered-light properties. The scattered light can arise from any optical surface, and light leaks or scattering from baffles can also contribute to the instrumental stray-light level. For a diffraction-grating spectrometer the primary contribution to instrumental scattered light has been found to be the scattered light from the grating. The results from measuring the scattered-light properties of 10 diffraction gratings are discussed along with the application of these results in analyzing the total scattered light measured for three spectrometers. It has been found from these measurements that there are two components of the grating scattered light: a Lorentzian-type component and a constant background component. The Lorentzian component is predicted from the diffraction theory for a grating, and the constant background component is consistent with Rayleigh scattering from the microscopic surface im erfections. It was also discovered that multiple replicas of gratings from the same master grating exhibit significantly more scattered light than the preceding replica by factors of 1.1-2.     

Scattering from rough inhomogeneous media: splitting of surface and volume scattering

The intensity scattered by particles randomly placed beneath a rough interface is studied with rigorous simulations. It is shown that the angular intensity pattern is close to that obtained by adding the intensity scattered by particles under a flat surface to that scattered by a rough homogeneous surface whose permittivity is evaluated with an effective-medium theory. This heuristic splitting rule is accurate for a large range of parameters that are well beyond any perturbative treatment.     

Three-dimensional reconstruction of dielectric objects by the coupled-dipole method

We present an inversion procedure for electromagnetic scattering, based on the powerful and flexible technique called the coupled-dipole method combined with an optimization algorithm. This method permits us to realize imaging of dielectric objects whose dimensions are comparable with the incident wavelength and is shown to be efficient with corrupted data (scattered electric field). The feasibility of this method is shown in a synthetic example in which the scattered field is corrupted with Gaussian noise. Two methods are used to invert the scattered field to recover the refractive index of the medium: a conventional matrix inversion and an iterative method.     

Extremely asymmetrical scattering of optical waves in nonuniform periodic Bragg arrays

The extremely asymmetrical scattering (EAS) of bulk and guided electromagnetic waves in nonuniform periodic Bragg arrays with steplike variations of the grating amplitude is analyzed theoretically by means of a recently developed approach based on allowance for the diffractional divergence of the scattered wave. Arrays of finite and infinite widths are investigated. It is shown that, for thin nonuniform arrays, EAS has the same pattern as for uniform arrays with mean grating amplitude. On the contrary, for wide nonuniform arrays, the scattered wave amplitudes are well determined by local values of the grating amplitude. In this case, the energy of the scattered wave is shown to concentrate mainly in regions with smaller grating amplitude. The sensitivity of EAS to small imperfections of periodic arrays is investigated theoretically. The physical explanation of the observed effects is based on the diffractional divergence of the scattered wave.     

Numerical evaluation of droplet sizing based on the ratio of fluorescent and scattered light intensities (LIF/Mie technique)

The dependence of fluorescent and scattered light intensities from spherical droplets on droplet diameter was evaluated using Mie theory. The emphasis is on the evaluation of droplet sizing, based on the ratio of laser-induced fluorescence and scattered light intensities (LIF/Mie technique). A parametric study is presented, which includes the effects of scattering angle, the real part of the refractive index and the dye concentration in the liquid (determining the imaginary part of the refractive index). The assumption that the fluorescent and scattered light intensities are proportional to the volume and surface area of the droplets for accurate sizing measurements is not generally valid. More accurate sizing measurements can be performed with minimal dye concentration in the liquid and by collecting light at a scattering angle of 60° rather than the commonly used angle of 90°. Unfavorable to the sizing accuracy are oscillations of the scattered light intensity with droplet diameter that are profound at the sidescatter direction (90°) and for droplets with refractive indices around 1.4.     

Scattering of SH waves by an arc-shaped interface crack between a cylindrical magneto-electro-elastic inclusion and matrix with the symmetry of 6 mm

Summary Investigated are the scattered field properties of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material in this paper. The debonding region is modeled as an arc-shaped interface crack with magneto-electrically permeable surfaces. By expressing the scattered fields as the wave function expansions with unknown coefficients, the mixed boundary value problem is first reduced to a set of dual series equations. Then the dislocation density function is introduced as an unknown to transform the dual series equations to a Cauchy singular integral equation of the first type, which can be solved numerically. Finally, the scattered field intensity factor, the scattered far field pattern and scattered cross section are obtained. The effects of incident direction, crack opening angle and material combination on the properties of both near fields and far fields are respectively examined graphically. The solution of this problem is relevant to ultrasonic nondestructive detection of the debonding between two dissimilar magneto-electro-elastic materials and is expected to have applications to the question of how dynamic loading can lead to growth of debonds.     

双层弹性-非弹性封闭腔体的内部声场研究

从球坐标中声波波动方程出发，利用本征函数展开方法和界面边界条件，导出了双层弹性封闭球壳的内部散射声场表达式。对于单位源强度的点声源，本文计算了分别由弹性/粘弹性和弹性/吸声材料组成的双层封闭球壳的内部散射声压随频率的变化关系。计算结果表明，粘弹性材料和吸声材料在某些频段对散射声压有十分明显的抑制作用。     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.     

Developments in the design of a spectroscopic scanning electron microscope

This paper develops the design of a spectroscopic scanning electron microscope (SEM), one that can combine the acquisition of high image resolution with the capture of the full energy spectrum of scattered electrons. The proposal is based upon the use of segmented magnetic sector plates to both deflect the primary beam and at the same time provide energy dispersion for the scattered electrons. Simulations of the design are carried out via numerical direct ray tracing. They predict that the spectroscopic SEM should be able to acquire the whole energy spectrum of scattered electrons in parallel, captured by a single multi-channel detector. They also predict that first-order focusing at the detector plane can be achieved, and that collection of the scattered electrons can be made with high transport efficiency, close to 100%.     

Pulse distortion of a scattered chirped pulse

We have studied the time-dependent properties of a chirped short pulse when the pulse is scattered by a spherical particle. We used generalized Lorentz-Mie formulas to study the scattered electrical field and pulse distortion. Plane wave Gaussian pulses of different chirps with a constant pulse-filling coefficient l(0) = 1.98 have been studied. A morphology-dependent resonance causes a prolonged trailing edge (small scattering angle) and oscillations (large scattering angle) in the scattered pulse. When frequency sweeping superimposes on a morphology-dependent resonance, the pulse chirp affects the scattered pattern and distorts the scattered intensity. Multisecondary pulses are generated because of the pulse chirp and even subsecondary pulses occur if the incident pulse is deeply chirped. The pulse widths of secondary and subsecondary pulses are shorter than those of an incident pulse.     

Scattering of SH waves by an arbitrarily orientated closed crack

The 2D problem of a time-harmonic plane shear horizontal (SH) wave scattered by a finite closed crack in an isotropic material is presented in the paper. The crack is arbitrarily orientated with regard to the incident wave. A spring model based on the assumption that the traction components on the crack surfaces are linearly related to the crack opening displacement (COD) is used to model the closed crack. The problem is formulated in a set of boundary integral equations which contains the CODs as unknowns. Numerical examples are presented for the CODs, elastodynamic stress intensity factors, and the scattered displacement field for various parameters, such as spring stiffness, crack sizes and crack orientations. The results show that both the crack closure and orientation have significant effects on the scattered displacement field for the closed crack.     

Inverse scattering from phaseless measurements of the total field on open lines

A new solution approach to inverse scattering from aspect-limited phaseless measurements of the total field is introduced and discussed. In analogy with the case of measurements on closed curves [J. Opt. Soc. Am. A21, 622 (2004)], the procedure splits the problem into two different steps. In the first step, amplitude and phase of the scattered field are estimated from only amplitude information of the total field. By properly extending the concept of reduced radiated field to the case of scattered fields (as a function of both illumination and measurement variables) and taking advantage of the properties of the square amplitude distribution of the total field, criteria are given for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step, starting from the scattered fields estimated in the previous step. Numerical examples are provided to assess the effectiveness of the whole chain in the presence of noise-corrupted data and the relevance of the representation introduced for the scattered fields.     

Scattering from anisotropic plasma-coated PEMC cylinder buried beneath a slightly rough surface

A general theoretical formulation is done to calculate the field scattered by perfect electromagnetic conductor (PEMC) cylinder coated with anisotropic plasma material. It is buried below a slightly rough surface. Spectral plane wave representation of fields and small perturbation method are used to calculate multiple reflections between coated cylinder and rough surface. To validate the present formulation, scattered field from a PEMC cylinder coated with double negative (DNG) material is obtained from the present formulation. Scattering pattern of non coated PEC/PEMC cylinder or coated with isotropic material can also be obtained by the proper selection of physical parameters such as anisotropy, admittance of PEMC cylinder and permittivity of hosting medium. Analytical expressions of scattered field for a sinusoidal rough surface are given along with their physical interpretation to get a good insight. Effect of geometrical and physical parameters on scattering pattern is observed.     

Effects of cellular fine structure on scattered light pattern

Biological cells are complex in both morphological and biochemical structure. The effects of cellular fine structure on light scattered from cells are studied by employing a three-dimensional code named AETHER which solves the full set of Maxwell equations by using the finite-difference time-domain method. It is shown that changes in cellular fine structure can cause significant changes in the scattered light pattern over particular scattering angles. These changes potentially provide the possibility for distinguishability of cellular intrastructures. The effects that features of different intrastructure have on scattered light are discussed from the viewpoint of diagnosing cellular fine structure. Finally, we discuss scattered light patterns for lymphocyte-like cells and basophil-like cells.     

Scattering of SH-waves by an interface cavity

Summary. The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.     

Wave Scattering from Fractal Surfaces

Abstract

In this paper, a normalized band-limited Weierstrass function is presented for modelling 2D fractal rough surfaces. Some conventional statistical parameters, namely the root mean square and the correlation length of rough surfaces, are used to assess between fractal parameters and the roughness of surfaces. An analytic solution of the scattered light field from these fractal surfaces is derived based on Kirchhoff theory. Three statistical parameters, namely the average scattering coefficient, the average intensity of scattered field, and the root mean square of scattered field, are introduced to study the influence of various fractal parameters on the scattered field by theoretical analysis and numerical calculations.     

Special visual effect of art glazes explained by the radiative transfer equation

We present the first modeling of the light scattered by a paint layer in a bidirectional configuration. The studied medium is composed of small concentrated pigments embedded in an oil binder. The color is modulated by changing the number of paint layers, called glazes. The radiative transfer equation is established for incoherent light scattered by the pigments with use of a collimated illumination. The equation is solved by use of the auxiliary function method. This new method, applied here for the first time to a practical case, allows for exact computations of the scattered flux for any incident and collected directions. Spectroscopic and goniometric measurements are implemented in bidirectional and back-scattered configurations. The excellent agreement between the measurement and the simulation validates the assumptions used for the glaze model and proves the effectiveness of the auxiliary function method.     

基于神经网络的三角形网格智能重建

探讨了曲面密集三维散乱点数据的三角网格智能重建方法。建立了基于自组织特征映射神经网络的三角网格构建模型。该模型利用神经元对曲面散乱点的学习和训练来模拟曲面上的点与点之间的内在关系,结点连接权矢量集作为对散乱点集的工程近似化并重构曲面样本点的内在拓扑关系,实现曲面密集三维散乱点数据的自组织压缩。按六角形阵列侧抑制邻区训练调整网络神经元权重矢量,使网络输出层结点呈六角形阵列分布,可实现测量点集压缩后的Delaunay三角逼近剖分。计算机仿真实验表明,所建神经网络模型可以实现期望规模和精度的三角网格剖分并有效保持原数据点集的拓扑特征。     

Scattering of the Lowest Lamb Wave Modes by a Corrosion Pit

Scattering of time-harmonic Lamb wave modes by a partial spherical corrosion pit in a plate is investigated. By using superposition, the total field consists of the incident and scattered fields, where the latter is generated by tractions on the surface of the cavity. In the approximation advanced in this article these tractions are represented by time-harmonic body forces on a trace of the cavity in the interior of the plate. The acoustic radiation from the resultants of these body forces applied to the surface of the plate approximates the scattered field. The resultant forces are decomposed in symmetric and anti-symmetric systems, which generate symmetric and anti-symmetric radiating modes. The time-harmonic elastodynamic form of the reciprocity theorem is employed to obtain an analytical solution to the scattered field amplitudes. We obtain the ratio of scattered to incident Lamb mode amplitudes, which in a closed generalized form include material properties, geometry of the pit and layer, and angular frequency of the incident wave. Results of this study yield graphical representations for the amplitude ratios with respect to pit geometry and has the potential to lead to a unique solution of the inverse problem under some conditions.