Fast and accurate radiance calculations using truncation approximation for anisotropic scattering phase functions

The phase function for solar light scattering by large particles such as cloud droplets is strongly anisotropic due to very strong peaking in the forward direction. This creates numerical difficulties when attempting to calculate accurate reflected and transmitted radiances, which are important for remote sensing of atmospheric and surface properties. A popular approach uses the delta function to approximate the forward-scattering peak in a fraction of energy and a limited number of polynomial terms or a geometrically truncated function for the remaining fraction (so-called truncation approximations). This article compares and discusses several methods for fast and accurate calculations using truncation approximations. When using a single truncation approximation for all scattering orders, large biases appear in directions near the solar and anti-solar points. As shown here, high accuracy can be obtained using different truncation approximations depending on the order of scattering. Of particular importance is the use of phase functions close to the exact phase functions for the first few orders of scattering. Applying the method in combination with the Monte Carlo (MC) method, in which the truncation fraction for a scattering order depends on the scattering angle at the previous scattering event, obtains accurate radiance calculations under almost all geometrical and optical conditions, including in directions near the solar point. Because the method also reduces computational noise due to the MC sampling of radiance, it is useful for fast and accurate radiance calculations for cloudy atmospheres.     

T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

Energy scan photoelectron diffraction: An integrated method for adsorbate structure determinations

In order to determine the structure of adsorbates on surfaces an integrated multi-step approach has been developed for the analysis of energy scan photoelectron diffraction data. The first step of the method gives an approximate three-dimensional image of the dominant nearest neighbour scatterers surrounding an emitter atom. In a second step this approximate structure is further refined using multiple scattering cluster calculations. Finally, a very recently developed procedure is employed in which the dynamics/displacements of the emitter atom are examined utilising the Maximum Entropy Method. The application of this integrated method is illustrated with examples of molecular adsorbates.     

复杂形状封闭薄壳内部存在散射体时的内部散射声场计算

基于覆盖域的思想和方法,本文给出了复杂形状封闭薄壳在内部存在散射体时的内部散射声场计算表达式.研究结果表明,该内部散射声场可表示为封闭薄壳的内部散射声场和这些散射体的外部散射声场之和的形式.最后用数值分析验证了该结论的正确性.     

Modified T-matrix formulation for multiple scattering of acoustic waves

In studying the multiple scattering of acoustic waves by distributed discrete scatterers, the 'two-exterior' T-matrix or the modified T-matrix is needed. In this paper, the modified T-matrix formulae for a scatterer of arbitrary shape are derived, based on Huygen's principle and the method of optimal truncation (MOOT), respectively. Analytical expressions are given for the modified T-matrix elements of a spheroid in the low-frequency limit. The agreement with the existing results is shown to be exact to the given order of ka. It is also shown that the results based on Huygen's principle are merely the special cases of those based on MOOT.     

Electromagnetic Modelling of Fine Features in Photonic Applications

Straightforward application of numerical modelling approaches to Photonic Band-Gap structures demands the use of fine meshes, notably finer that the size of a single scattering element, in order that high accuracy is achieved. However simulations employing sufficiently fine meshing to correctly represent the geometry of the scatterers lead to very long computational run-times and huge memory consumption. Such direct numerical approaches to PBG characterisation are only suited to the analysis of single unit cells or for benchmarking. In practice, the computational overheads significantly increase when one deals with an array of cells or when modelling the global behaviour of a large number of devices integrated on a single substrate. Therefore in order to model the macroscopic response of PBG structures the possibility of employing meshes of much larger size than the individual scattering elements has been explored. A suitable approach, initially developed for Electromagnetic Compatibility predictions, has been modified to permit modelling of Photonic Crystal Waveguides. The method provides second order accuracy and leaves a designer with the flexibility to discretise the entire problem space with an arbitrary number of scatterers per mesh cell. Results are first presented for small clusters of scatterers and subsequently for complete photonic structures.     

Multiple scattering in a reflecting cavity: application to fish counting in a tank.

Classical fisheries acoustics techniques are useless in the presence of multiple scattering or reflecting boundaries. A general technique is developed that provides the number and the scattering strength of scatterers in motion placed inside a highly reflecting cavity. This approach is based on multiple scattering theory. The idea is to measure the average effect of the scatterers on the acoustic echoes of the cavity interfaces. This leads to the measure of the scattering mean free path, a typical length that characterizes the scattering strength of the cloud of scatterers. Numerical results are shown to agree with a simple theoretical analysis. Experiments are performed with fish in a tank at two different scales: ultrasonic frequency (400 kHz) in a 1.4-l beaker with 1-cm-long fish as well as fisheries acoustics frequency (12.8 kHz) in a 30-m3 tank with 35-cm-long fish. These results have interesting applications to fish target strength measurement and fish counting in aquaculture.     

Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement

The present paper gives a more complete treatment of the scattering from a two-dimensional random surface than previous works. Reciprocal theorems for the stochastic wave field and the incoherent scattering distribution (bistatic cross section) are derived and the presence of backscattering enhancement in the case of a slightly random Neumann surface is demonstrated. A physical interpretation of the backscattering enhancement associated with the presence of anomalous scattering on a slightly random Neumann surface is given. Some numerical calculations are performed to show the incoherent scattering distribution and the backscattering enhancement.     

Similarity of radiative transfer equation: Error analysis of phase function truncation techniques

Accurate radiance computations with highly peaked phase functions is a challenging problem. The developed truncation methods replace the peak of phase function using different approximations in the cone of forward scattering. The main goal of this paper is to employ a new integral form of similarity conditions to the error analysis of truncation techniques. This analysis emphasizes two main error sources of these methods from (1) truncation of Legendre series, and (2) truncation of the forward cone for peaked phase functions. The first error has an oscillating pattern and is effectively suppressed by the single scattering correction. The second, often overlooked, error manifests itself as a bias which weakly depends on the number of Legendre terms used in the solution unless it becomes comparable to the total order of Legendre expansion series. This paper presents a comparative theoretical and numerical error analysis of the Delta function method [15], Delta-fit method [7], and Delta-M method [21]. The Delta-M method, combined with the single scattering correction, is shown to provide the best overall accuracy for the intensity computations.     

中红外散射的基质折射率效应研究

本文利用Mie散射理论对中红外波段三种不同类型散射体的散射和消光进行了研究,发现基质在三种不同类型散射体的散射和消光中所起作用完全不同。对于无吸收的高折射率散射体,基质折射率越大面积散射比(或面积消光比)越低;对于反常色散散射体,基质折射率越大面积散射比和面积肖光比越高;而对于金属散射体,基质折射率的大小对于散射和消光影响极小。     

Effects of interaction between two bubble scatterers

The backscattering of sound from two regularly arranged bubbles is studied theoretically and experimentally. In well-controlled laboratory experiments a bistatic acoustic system is used to interrogate the scatterers, which are placed on a very fine thread at the same distance d from the combined beam axis of the set of transmitting and receiving transducers. The radius of each bubble is 585 microm. The frequency range is 80-140 kHz, and d is varied so that the variable kd spans the range 0.2-21, where k is the acoustic wave number. Scattering calculations are carried out using an exact, closed-form solution derived from the multiple scattering series. Several experiments are performed, and the results are in close agreement with the calculations. It is verified that multiple scattering induces an oscillatory behavior about the exact coherent scattering level, with decreasing amplitude for increasing kd. For interbubble distance 2d approximately lambda/2 the backscattered radiation is maximized, while for 2d相似文献   

Electronic states in liquid metals

An approximation scheme has been developed for calculating the density of states and autocorrelation of independent electrons in a dense array of weak stationary scatterers. This method, which avoids the customary perturbation expansions in powers of the scattering potential, requires a knowledge only of the autocorrelation of the potential. Results are presented of calculations for liquid Na at various temperatures. Comparison is made with the experimentally observed resistivity and angular correlation in positron annihilation experiments.     

群聚球形粒子极化散射的T矩阵数值模拟

对于不小于波长或可与波长相比的大粒子集合性的相干散射,要求严格求解多次散射的Maxwel方程。作者利用多个粒子多次散射的严格的T矩阵公式,发展了数值模似算法,求出非均匀群聚分布的球形粒子相干极化散射在全方位上的数值结果,研究了群聚粒子相干极化散射的特征表现,并与双球粒子散射的实验结果作了很好的比较。     

A Hybrid Technique Combining FDTD and Series Solution for Near-to-Far-Field Transformation

A new near-to-far-field transformation that combines the FDTD and the series solution is presented. In this method, near-field data is calculated by FDTD and far-field data is also expressed by series solution. The boundary condition is applied to a virtual surface, which encloses arbitrarily shaped scatterers. In order to verify this method, scattering patterns from this transformation are compared with scattering patterns from exact solution. Numerical results show that errors in the far-field data from this method is less than surface equivalence theorem. Thus, this method is valid for obtaining the far-field data.     

光通过纳米颗粒随机散射体透射光强的计算及分析

光通过随机散射体后透射光强的估算,对于提取散射体内部无法直接测量或者无法直接观察的信息至关重要。在分析平行光束通过纳米圆形颗粒随机散射体出射面上光强组成的基础上推导了透射光强的计算公式,并指出多重散射理论、一阶多重散射理论和朗伯-比尔定律在一定近似程度上可以相对精确地估算透射光强。这三种方法的估算结果之间会出现四种相对关系。根据这些相对关系,分析了光在散射体内部传输时散射过程的特征以及各种散射过程对出射面光强的贡献大小。     

Distortion operator approach and [N, 1] Padé sequence in nonrelativistic scattering theory

A brief account of the scattering theory using the so called distortion operator is given. The Neumann series for a matrix element of the distortion operator is proved to imply the [N, 1] Padé sequence for the transition matrix element. As a consequence a region of convergence of the [N, 1] Padé sequence is found.     

On acoustic scattering by a shell-covered seafloor

Acoustic scattering by the seafloor is sometimes influenced, if not dominated, by the presence of discrete volumetric objects such as shells. A series of measurements of target strength of a type of benthic shelled animal and associated scattering modeling have recently been completed (Stanton et al., "Acoustic scattering by benthic and planktonic shelled animals," J. Acoust. Soc. Am., this issue). The results of that study are used herein to estimate the scattering by the seafloor with a covering of shells at high acoustic frequencies. A simple formulation is derived that expresses the area scattering strength of the seafloor in terms of the average reduced target strength or material properties of the discrete scatterers and their packing factor (where the reduced target strength is the target strength normalized by the geometric cross section of the scatterers and the averaging is done over orientation and/or a narrow range of size or frequency). The formula shows that, to first order, the backscattering at high acoustic frequencies by a layer of shells (or other discrete bodies such as rocks) depends principally upon material properties of the objects and packing factor and is independent of size and acoustic frequency. Estimates of area scattering strength using this formula and measured values of the target strength of shelled bodies from Stanton et al. (this issue) are close to or consistent with observed area scattering strengths due to shell-covered seafloors published in other papers.     

A unified optical theorem for scalar and vectorial wave fields

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.