水下光场的迭代求解

水体对光线的散射是水下图像质量劣化的重要因素,为了定量分析在特定光源照射下水体散射的影响,建立了光线水下传输的散射模型,以此为基础推导出求解水下光场分布的Fredholm积分方程.在水中光线能量随距离的增大呈指数规律衰减,基于此,在水体体散射函数为常数的情况下,给出了有边界条件时该积分方程的数值迭代求解方法,得到高精度...     

两个相邻目标对平面波、高斯波束的光散射

基于等效原理和互易性定理研究了两个靠近目标对平面波、高斯波束的光散射问题,给出了这一复合光散射模型的二阶散射结果。通常一阶散射结果容易求解,但由于耦合效应的复杂性,很难给出二阶散射结果的解析形式。为了解决这一问题,应用互易性定理给出了求解任意相邻介质目标二阶散射场的公式,同时借助等效原理将求解散射场公式中的体积分简化为面积分的形式,从而降低了求解难度。求解了两相邻球形粒子的复合散射场,并将求解结果与应用时域积分方程法求得的结果进行了比较。同时,还讨论了束腰半径、目标位置对散射截面及偏振度的影响。     

Modeling the light scattering by nanoparticles of complex shape using the generalized source method

The results of modeling the scattering of light by nanoparticles of complex shape using the generalized source method are presented. It is shown that the approach implementing direct solution of the implicit equation, which is derived by the generalized source method using the three-dimensional Green’s function, in conjunction with the fast Fourier transform significantly improves convergence of the method of volume integral equation and considerably extends the range of its applicability.     

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     

CUDA-accelerated simulation of multiple scattering using decoupling approximation

Abstract  

In this research a CUDA-accelerated simulation method of multiple scattering in dense participating media based on decoupling approximation is proposed. Simulation of multiple scattering is important, in that it visually illustrates how radiance transfers between gaseous particles. The existing radiance transfer equation has poor computational performance because of its complicated integral calculation of in-scattering in each radiance update. However, this computation can be avoided using previous cached results proposed in this paper. To construct the cached results, we first decouple the phase function in radiance transfer equation with singular value decomposition (SVD) approximation. SVD approximates the multivariate phase function as a sum of products of incident light and outgoing light of lower dimensionality. Then the incident light and outgoing light data of current radiance update are cached independently in two textures. The cached two textures are used to replace integral calculation of in-scattering in the next radiance update to improve computation performance. The proposed method is designed in a parallelized way so that the parallel computing power of CUDA can be fully exploited. The simulation results show that our method allows fast rendering of dynamic scenes while high accuracy is maintained.     

Thermal analysis for transient radiative cooling of a conducting semitransparent layer of ceramic in high-temperature applications

A method is developed for obtaining transient temperature distribution in a cooling semitransparent layer of ceramic. The layer is emitting, absorbing, isotropically scattering and heat conducting with a refractive index ranging from 1 to 2. The solution involves solving simultaneously the energy equation and the integral equation for the radiative flux gradient. The energy equation is solved using an implicit finite volume scheme and the integral equation of radiative heat transfer is solved using the singularity technique and Gaussian integration. The effects of scattering are investigated. It is shown that scattering has a significant effect on the transient temperature distribution and the transient mean temperature of the layer.     

A solution of radiative transfer in isotropic plane-parallel atmosphere by integrating Milne equation

In this paper we solve the inversion problem of the radiative transfer process in the isotropic plane-parallel atmosphere by iterative integrations of the Milne integral equation. As a result, we obtain the scattering function in the form of a cubic polynomial in optical thickness. The author has already solved the same problem by iterative integrations of Chandrasekhar's integral equation. In the Milne integral equation, both the cosines of the viewing angles and the optical thickness are integral variables, while in Chandrasekhar's integral equation the cosines of the viewing angles are variables but the optical thickness is not. We derive several series of exponential-like functions as intermediate derivations. Their convergences are evaluated by the author's previous work in the solution of Chandrasekhar's integral equation. The truncated scattering function up to the third order in optical thickness thus obtained is identical to that obtained from Chandrasekhar's integral equation, though their apparent forms are different. Chandrasekhar pointed out that the solution of Chandrasekhar's integral equation does not have a uniqueness of solution. The Milne equation, in contrast, has been proven to have a unique solution. We discuss the uniqueness of the solution by these two methods.     

Local solutions to high-frequency 2D scattering problems

We consider the solution of high-frequency scattering problems in two dimensions, modeled by an integral equation on the boundary of a smooth scattering object. We devise a numerical method to obtain solutions on only parts of the boundary with little computational effort. The method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequencies. We show that the integral equation in this approach reduces to an ordinary differential equation.     

Radiation transport and internal reflection in a two region, turbid sphere

We construct an integral equation for the flux intensity in a scattering and absorbing two-region turbid spherical medium using the integro-differential form of the radiative transfer equation. The sphere is uniformly irradiated by an external source of arbitrary angular distribution and contains a distributed volume source. Anisotropic scattering is accounted for by the transport approximation. The Fresnel boundary conditions, which incorporate reflection and refraction, are used at the outer surface and at the interface between the two regions. In this respect, some new interfacial boundary conditions are introduced. For the special case of a non-scattering medium, we obtain exact solutions for specular reflection. Some numerical examples are given which show qualitative agreement with some recent work of other authors. Of particular interest are the emergent angular distribution and the albedo of the surface as a function of the refractive index and the radii of the two regions. We also draw attention to the fact that the boundary conditions at the interface differ according to the relative values of the refractive indices in the two regions. The interfacial boundary conditions for use in diffusion theory are derived and compared with those of Aronson [Boundary conditions for diffusion of light. J opt Soc Am 1995;12:2532]. In appendix B, we show how diffusion theory may be used to include scattering into the problem in a simple way.     

A new single surface integral equation for light scattering by circular dielectric cylinders

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown function for circular dielectric-coated cylinders. In addition, numerical simulations show that even applied to elliptic scatters our equation still gives reasonably good approximate solutions in the sub-wavelength limit.     

Sound scattering from partially water-filled elastic spherical shell with an internal elastic plate

According to the equation of motion in the elastic medium and integral equation of target scattering, the sound scattering from the partially water-filled elastic spherical shells with and without an inner plate is studied using the finite element and boundary element method, and the scattering normalized form functions of the shell filled with different volume of water are computed and the mechanism of resonance scattering is analyzed. The results show that the resonance of the shell with partially water-filled and without the plate is mainly related to the volume of water, and the resonance is produced by inner water and the spherical shell. The resonance characteristics of partially water-filled elastic shell with the plate are similar to that of empty structured elastic spherical shell, and the sound field in inner water is weaker which indicates the main resonance characteristics are decided by spherical shell and the plate. In addition, the scattering characteristics of spherical shell with plate and one side full water-filled are greatly different from the partially water-filled ones.     

Scattering of Electromagnetic Radiation by Linear Small-Particle Aggregates of Finite Dielectric Cylinders

Journal of Applied Spectroscopy - A volume integral equation formalism is used for numerical simulation of the normalized functions of the angular scattering intensity distribution for dimers and...     

A new integral equation method for direct electromagnetic scattering in homogeneous media and its numerical confirmation

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied to a bounded scatterer, which can be an ohmic conductor or a dielectric, with some simplification of the continuity conditions for the fields. The new integral equation method is developed by choosing the electric field and its normal derivative as boundary unknowns, which are not the usual boundary unknowns. The new integral equation method may provide significant computational advantages over the standard Stratton-Chu method [2] because it leads to a 50% sparse, rather than 100% dense, impedance (collocation) matrix. Our theoretical development of the new integral equation method is exact.     

光在水中吸附膜层气泡上的散射特性

光在水中大尺度气泡上散射特性的研究多是基于Davis模型.该模型没有考虑到吸附膜层对光在气泡上散射的影响,而海水中的大多数气泡都有膜层附着,这些膜层会影响到气泡的光散射特性.本文从几何光学的角度出发,建立了吸附膜层气泡的体积散射函数简化公式.在此理论基础上,模拟计算了尺度远大于入射光波长的大气泡散射光强分布曲线,得出光照射下气泡上散射光强的远场特性,讨论了影响气泡散射光强分布的主要因素.并与无膜气泡光散射分布曲线比较,讨论了油膜膜厚、折射率等参量对气泡的光散射特性影响.得出结论:吸附膜层气泡的光强分布曲线与无膜气泡相似,但吸附膜层会削弱前向散射光,增强后向散射光.     

Path of Momentum Integral in the Skorniakov-Ter-Martirosian Equation

The Skorniakov-Ter-Martirosian (STM) integral equation is widely used for the quantum three-body problems of low-energy particles (e.g., ultracold atom gases). With this equation these three-body problems can be efficiently solved in the momentum space. In this approach the boundary condition for the case that all the three particles are gathered together is described by the upper limit of the momentum integral, i.e., the momentum cutoff. On the other hand, in realistic systems, the three-body recombination (TBR) process can occur when all these three particles are close to each other. In this process two particles form a deep dimer and the other particle can gain high kinetic energy and then escape from the low-energy system. In the presence of the TBR process, the momentum-cutoff in the STM equation would include a non-zero imaginary part. As a result, the momentum integral in the STM equation should be done in the complex-momentum plane. In this case the result of the integral depends on the choice of the integral path. Obviously, only one integral path can lead to the correct result. In this paper we consider how to correctly choose the integral path for the STM equation. We take the atom-dimer scattering problem in a specific ultracold atom gas as an example, and show the results given by different integral paths. Based on the result for this case we explore the reasonable integral paths for general case.     

NLIE of Dirichlet sine-Gordon model for boundary bound states

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Lüscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory.     

An equivalent roughness model for seabed backscattering at very high frequencies using a band-matrix approach

This work concerns modeling of very high frequency (>100 kHz) sonar images obtained from a sandy seabed. The seabed is divided into a discrete number of ID height profiles. For each height profile the backscattered pressure is computed by an integral equation method for interface scattering between two homogeneous media as formulated by Chan [IEEE Trans. Antennas Propag. 46, 142-149 (1998)]. However, the seabed is inhomogeneous, and volume scattering is a major contributor to backscattering. The SAX99 experiments revealed that the density in the unconsolidated sediment within the first 5 mm exhibits a high spatial variation. For that reason, additional roughness is introduced: For each surface point a stochastic realization of the density along the vertical is generated, and the sediment depth at which the density has its maximum value will constitute the new height field value. The matrix of the full integral equation is reduced to a band matrix as the interaction between the point sources on the seabed is neglected from a certain range; this allows computations on long height profiles with lengths up to approximately 25 m (at 300 kHz). The equivalent roughness approach, combined with the band-matrix approach, agrees with SAX99 data at 300 kHz.     

Scattering and absorption by a thin,finite dielectric cylinder

This work investigates and interprets the volume and surface integral equation formulations relevant to the scattering and absorption of electromagnetic waves by thin, finite and lossy dielectric cylinders. Computational data are presented, describing the effective current distributions and the scattered and absorbed power for widely varying electromagnetic and geometrical parameters.     

Far-field approximation in electromagnetic scattering

The volume integral equation formalism is used to derive and analyze specific criteria of applicability of the far-field approximation in electromagnetic scattering by a finite three-dimensional object. In the case of wavelength-sized and larger objects, this analysis leads to a natural subdivision of the entire external space into a near-field zone, a transition zone, and a far-field zone. It is demonstrated that the general criteria of far-field scattering are consistent with the theory and practice of T-matrix computations.     

水中气泡上的体散射函数的模拟与计算

基于几何光学的基本原理,推导出一种可以计算水中大尺度气泡上光散射角度与强度的关系式。推导中避免引入衰减因子G,较Davis模型更为简单。该模型可应用于光在水中单个气泡上散射的数值计算。最后,模拟计算了平行光束入射水中气泡的体散射函数曲线,发现水中气泡的前向散射远大于后向散射;当气泡半径在远大于光波波长的前提下变化时,气泡上散射光强分布规律与气泡半径无关;而介质相对折射率的增大会削弱前向散射而增强后向散射光强。