不同插值算法的光场重聚焦分析

光场数据重聚焦包括空间域重聚焦和频域重聚焦两种方法,在重聚焦过程中均需要进行插值计算,重聚焦精度与插值精度密切相关,而插值算法的复杂度会影响计算效率。在实际大量图像处理中,在重聚焦效果满足精度要求的前提下选择计算效率最高的方法,其中,插值精度对频域影响远大于空间域。介绍了空间域重聚焦和频域重聚焦的原理,以及传统3种插值方法和sinc函数插值法,分别用不同的插值方法对这两种重聚焦方法进行实验,比较其重聚焦效果并计算其效率。实验结果表明,在实际应用中为了满足计算效率的需求,在满足精度要求情况下,空间域重聚焦采用线性插值法最佳,频域采用采样半径为2像素的sinc插值最佳。对同一幅影像多次重聚焦时,频域方法优于空间域方法。     

Characteristic Electromagnetic Fields in Dielectric Waveguide Array

Based on the modal solution of one dimensionally periodic structure with piecewise uniform dielectric constant distribution, characteristic solutions for two dimensionally Dielectric Waveguide Array (DWA) are rigorously formulated. By satisfying periodic boundary conditions in the interfaces inside a unit cell, semi-closed-form dispersion relation for DWA can be established. Numerical results are presented and compared with a previous method. A class of guidance and radiation problems can be solved with much more simplicity and accuracy.     

A high accuracy algorithm for 3D periodic electromagnetic scattering

We develop a highly accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. We approximate scattered fields using the Müller boundary integral formulation of Maxwell’s equations. The accuracy is achieved as singularities are isolated through the use of partitions of unity, leaving smooth, periodic integrands that can be evaluated with high accuracy using trapezoid sums. The removed singularities are resolved through a transformation to polar coordinates. The method relies on the ideas used in the free space scattering algorithm of Bruno and Kunyansky.     

1维介质光栅近场及其衍射的FDTD分析

 应用FDTD方法计算了单色平面波斜入射时1维介质光栅的近场，进而求出介质光栅的衍射效率。借助于周期边界条件，整个计算区域为周期结构的一个单元。考虑入射波在两种介质界面上会产生反射和透射，故在总场边界上引入入射波、反射波和透射波。给出了光栅单元截面为矩形和梯形的算例。该方法可用于斜入射情形下具有复杂结构和任意单元截面的介质栅近场及其衍射特性分析。     

Factors influencing electromagnetic scattering from the dielectric periodic surface

The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens' s principle and Floquet's theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.     

An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

弹性力学的插值型重构核粒子法

采用具有离散点插值特性的重构核粒子法形函数, 较精确地重构弹性体 变形的位移试函数, 再与弹性力学的最小势能原理相结合, 形成新的分析弹性力 学平面问题的插值型重构核粒子法. 由于插值型重构核粒子法形函数具有点插值特性和不低于核函数 的高阶光滑性, 因而既克服了多数无网格方法处理本质边界条件的困难, 也保证了较高的数值精度. 与早期的无网格方法相比, 本方法具有精度高、解题规模较小、可直接施加边界条件等优点. 通过对典型弹性力学问题数值模拟, 验证了所提方法的有效性和正确性.     

米散射激光雷达剖面数据三次样条垂直水平插值法

传统的空间数据插值方法在米散射激光雷达剖面扫描数据的距离高度显示图可视化应用方面具有一定的局限性.本文分析了米散射激光雷达剖面扫描数据以仰角为基础的空间位置关系与大气参数的空间分布特性,分别在垂直与水平位置上合理选取参考数据,给出位置相关性权重,基于三次样条函数法进行数据变化趋势的平滑性修正,完成缺失数据插值.实验结果表明,该方法能够有效提高米散射大气激光雷达扫描数据空间插值的准确性,插值数据误差小,距离高度显示图图形趋势过度平滑,符合大气参数的整体变化规律.     

Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

To deal with the staircase approximation problem in the standard finite-difference time-domain(FDTD) simulation,the two-dimensional boundary condition equations(BCE) method is proposed in this paper.In the BCE method,the standard FDTD algorithm can be used as usual,and the curved surface is treated by adding the boundary condition equations.Thus,while maintaining the simplicity and computational efficiency of the standard FDTD algorithm,the BCE method can solve the staircase approximation problem.The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders.The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors.Moreover,the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities.     

Reciprocity principle for radiative transfer models that use periodic boundary conditions

Many numerical models use periodic boundary conditions in solving the radiative transfer through heterogeneous media specified over a fixed domain. A reciprocity principle applicable to solutions from these models is derived for the common situation of a scattering and absorbing heterogeneous medium that is illuminated over the entire domain from a single direction. The derived reciprocity principle states that the domain-averaged bidirectional reflectance distribution function remains invariant when incoming and outgoing directions are interchanged, regardless of the heterogeneity of the medium and the size of the domain. This reciprocity principle provides a simple and useful benchmark test for radiative transfer models that use periodic boundary conditions.     

A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals

This paper presents an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell’s equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. We verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi-layered dielectric slab. We then apply the proposed method to scattering problems for periodic two-dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies. We also consider scattering problems for woodpile crystals, where we find a passband related to a localised mode. Through these numerical tests we conclude that the proposed method is efficient and accurate.     

Computational simulation of wave propagation problems in infinite domains

This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon.     

土壤表面与部分埋藏多目标复合散射的时域有限差分方法

采用Dobson半经验模型和电介质复介电常数表示土壤介电常数的实部和虚部,用指数型分布粗糙面和Monte Carlo方法模拟土壤表面,运用时域有限差分方法研究土壤表面与部分埋藏多个矩形截面混凝土柱复合模型的电磁散射.结果表明：复合散射系数随散射角振荡变化;土壤表面高度起伏均方根、土壤含水率、目标介电常数、入射角对复合散射系数影响较大;土壤表面相关长度、目标截面宽度、高度、间距、倾角对复合散射系数影响较小;目标埋藏深度对复合散射系数几乎没有影响.与其他数值计算方法比较,采用时域有限差分方法既可获得较高的准确性,又可减少计算时间和内存占用量.可以用来计算地、海粗糙面与附近任意多目标的复合散射.     

Implementation and validation of the curvilinear coordinate method for the scattering of electromagnetic waves from two-dimensional dielectric random rough surfaces

The curvilinear coordinate method is applied for analysing 2-D dielectric random rough surfaces. The theory is based on Maxwell's equations written in a non-orthogonal coordinate system. For each medium, this method leads to an eigenvalue system. The scattered fields within two media are expanded as linear combinations of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The coherent and incoherent intensities are estimated by averaging the scattering amplitudes over several realizations. The theory is verified by comparison with results obtained by other exact method. A discussion on the C-method and the Sparse-Matrix CAnonical Grid method is proposed in terms of accuracy and computation time.     

The use of the virtual source technique in computing scattering from periodic ocean surfaces

In this paper the virtual source technique is used to compute scattering of a plane wave from a periodic ocean surface. The virtual source technique is a method of imposing boundary conditions using virtual sources, with initially unknown complex amplitudes. These amplitudes are then determined by applying the boundary conditions. The fields due to these virtual sources are given by the environment Green's function. In principle, satisfying boundary conditions on an infinite surface requires an infinite number of sources. In this paper, the periodic nature of the surface is employed to populate a single period of the surface with virtual sources and m surface periods are added to obtain scattering from the entire surface. The use of an accelerated sum formula makes it possible to obtain a convergent sum with relatively small number of terms (～40). The accuracy of the technique is verified by comparing its results with those obtained using the integral equation technique.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

光子晶体传输特性的时域精细积分法分析

将精细积分法应用于时域有限差分法中,提出了一种求解光子晶体传输特性的时域精细积分法,并对其计算精度及稳定性进行了分析.从一阶麦克斯韦方程出发,在空间上采用Yee元胞进行差分离散,结合吸收边界条件及激励源表达式将方程整理为标准的一阶常微分方程组形式.通过时间步长的精细划分和指数矩阵的加法定理,在时间上利用精细积分法对齐次微分方程进行积分求解,并结合激励向量的特解得到空间离散的场分量,最终通过傅里叶变换求得方程的解.利用时域精细积分法对光子晶体进行了实例计算,并将其结果分别与时域有限差分法和四阶龙格库塔法在精度、稳定性等方面进行了比较,结果表明时域精细积分法具有更高的计算精度,并且克服了时域有限差分法以及四阶龙格库塔法在计算稳定性上对时间步长的限制.提出的方法具有精确、稳定的特点,为光子晶体传输特性的研究提供了一种新的有效的分析方法.     

移动边界问题的时空域正则区域迭代配点法

考虑热传导方程的移动边界问题,其定解区域随着时间而变化.构造一种时空域上的高精度数值算法求解1+1维移动边界问题.在时空域上假设一个初始移动边界位置,构成移动边界问题的不规则计算区域,选择一个适当的正则区域(矩形区域)完全覆盖所计算的不规则区域,在正则区域上利用移动边界约束条件和固定边界条件,采用时空域重心插值配点法求...