LIDAR multiple scattering from clouds

Multiple-scattering LIDAR return calculations obtained by seven different models for the same specified numerical experiment are compared. This work results from an international joint effort stimulated by the workshop group called MUSCLE for MUltiple SCattering Lidar Experiments. The models include approximations to the radiative-transfer theory, Monte-Carlo calculations, a stochastic model of the process of multiple scattering, and an extension of Mie theory for particles illuminated by direct and scattered light. The model solutions are similar in form but differ by up to a factor of 5 in the strength of the multiple-scattering contributions. Various reasons for the observed differences are explored and their practical significance is discussed.     

Analytical multiple scattering extension of the mie theory

Multiple scattering of light in aerosol is described in a simple picture within the framework of the Mie theory. Our approach leads to an analytical expression of the n-fold scattered electromagnetic field and then to a generalization of the optical parameters. The multiple scattering contributions are calculated avoiding the convergency and stability problems which are often encountered in standard numerical approaches. These problems occur due to the large number of events that have to be taken into account when large optical depths and/or a low signal to noise level exists. Such conditions are frequently encountered in atmospheric measurements.     

Radar-radiometric determination of water content of rain clouds with allowance for multiple scattering

We performed combined radiometric and radar measurements of the integral water content of a small-drop fraction of rain cloud systems with allowance for the multiple scattering phenomena. The contribution of rain to emission of the “cloud-rain” system was calculated on the basis of the vector equation of radiation transfer, which enabled us to allow for all orders of multiple scattering by spherical rain drops within the framework of the model of statistically independent particles. It was found that the maximum of the integral water content of overcooled water in clouds does not correspond to the maximum of precipitation intensity. The characteristic values of the integral and specific water contents of a small-drop water fraction in cloud systems with precipitation are measured. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 6, pp. 528–534, June 1999.     

Collision cascade evolution in media with energy independent scattering: spatial,energy, and angular distribution

The evolution of an ion induced collision cascade in a solid medium is studied by means of a DPl-approximation to the linear transport equation. Infinite medium and half space geometries are considered. Special attention is given to the effect of the anisotropy of the energy independent scattering cross section. We present results on the spatial distribution of particles moving at different energies, and the energy and angle distribution at the target surface. The spatial distributions are found to obey simple scaling laws; the energy and angular distributions are independent of the form of the scattering cross section, unless it is very strongly forward peaked.     

A method based on iterative morphological filtering and multiple scattering for detecting layer boundaries and extinction coefficients with LIDAR

Layer boundaries detection with LIDAR is of great significance for the meteorological and environmental research. Apart from the background noise, multiple scattering can also seriously affect the detection results in LIDAR signal processing. To alleviate these issues, a novel approach was proposed based upon morphological filtering and multiple scattering correction with multiple iterations, which essentially acts as a weighted algorithm with multiple scattering factors in different filtering scales, and applies integral extinction coefficients as media to perform correction. Simulations on artificial signals and real LIDAR signals support this approach.     

Light collection optics for diagnostic systems detecting light from a large depth of field with application to LIDAR scattering systems

Many optical diagnostic systems collect light from an extended region. This paper presents a technique for reducing the etendue to be accepted from a region of significant longitudinal depth. The needs of LIDAR are highlighted, however the principle is also valid for other systems such as collection of light from a line of sight into a fibre.     

An analytical solution for electromagnetic wave scattering by multiple wedges

In this work an analytical solution to the problem of electromagnetic wave diffraction by multiple coplanar wedges is found by means of an infinite-order discrete superposition of non-integer cylindrical waves, i.e. products of a non-integer order Bessel function times an exponential factor. The evaluation of the expansion coefficients is accomplished by imposing the boundary conditions on every side of the geometry; the corresponding equations are solved in a ‘weak form’, i.e. by representing the dependence of the boundary fields with respect to the radial abscissa in terms of an expansion over a set of Laguerre orthogonal polynomials. A detailed study is carried out for estimating accuracy performances relevant to the finite-order numerical implementation of the method.     

A generalized Milne solution for the correlation effects of multiple light scattering with polarization

The Wiener-Hopf method is used to obtain a generalized Milne solution for scalar and electromagnetic fields with single-scattering anisotropy. For the scalar field, the solution found for the time correlation function and the interference component of backscattering is in good agreement with available experimental data. A solution of the Milne problem is constructed for the electromagnetic field. Given anisotropy, the generalized Milne equation is solved in the P₁ approximation for the quantity that describes the degree of depolarization of the scattered light. It is shown that the depolarization of the scattered light can change sign at large anisotropies.     

气泡线性振动时近海面气泡群的声散射

海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。     

Taking advantage of multiple scattering to communicate with time-reversal antennas

We present an experimental demonstration showing that, contrary to first intuition, the more scattering a mesoscopic medium is, the more information can be conveyed through it. We used a multiple input-multiple output configuration: a multichannel ultrasonic time-reversal antenna is used to transmit random series of bits simultaneously to different receivers which were only a few wavelengths apart. Whereas the transmission is free of error when multiple scattering occurs in the propagation medium, the error rate is huge in a homogeneous medium.     

Analysis of random laser scattering pulse signals with lognormal distribution

The statistical distribution of natural phenomena is of great significance in studying the laws of nature. In order to study the statistical characteristics of a random pulse signal, a random process model is proposed theoretically for better studying of the random law of measured results. Moreover, a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noise. Both normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison. In addition, the statistical laws of three typical objects and the relations between them are discussed in detail. The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups.     

Analysis of multiple scattering from two-dimensional dielectric sea surface with iterative Kirchhoff approximation

<正>An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface.The multiple interaction of the scattering field is characterized with the corrected electromagnetic currents of the wind-driven sea surface.The actual surface currents are approximated with the iterative solution of the corrected currents.A newly developed sea spectrum,Elfouhaily spectrum,is utilized to build the sea surface model.The shadowing correction is improved by the Depth-Buffer algorithm.The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.     

非均匀随机散射介质层的多次散射和热辐射的分层迭代解

为纳入矢量辐射传输方程的多次散射，将非均匀平行分层分布的随机散射介质划分成多个薄 层，利用各薄层的低阶Mueller矩阵解推导出整层的高阶散射迭代解.用这一方法计算了具有 占空比、粒子大小和温度廓线非均匀分布的平行分层随机密集球形粒子积雪层的极化热辐射 .数值结果与一层均匀随机散射层的离散坐标-特征值方法作了比较，讨论了多次散射和热辐 射与散射层各特征参数的关系，与积雪层微波遥感数据进行了对比. 关键词： VRT方程 平行分层 高阶散射解 迭代解     

Analytical solution and semi-analytical solution for anisotropic functionally graded beam subject to arbitrary loading

Analytical and semi-analytical solutions are presented for anisotropic functionally graded beams subject to an arbitrary load, which can be expanded in terms of sinusoidal series. For plane stress problems, the stress function is assumed to consist of two parts, one being a product of a trigonometric function of the longitudinal coordinate (x) and an undetermined function of the thickness coordinate (y), and the other a linear polynomial of x with unknown coefficients depending on y. The governing equations satisfied by these y-dependent functions are derived. The expressions for stresses, resultant forces and displacements are then deduced, with integral constants determinable from the boundary conditions. While the analytical solution is derived for the beam with material coefficients varying exponentially or in a power law along the thickness, the semi-analytical solution is sought by making use of the sub-layer approximation for the beam with an arbitrary variation of material parameters along the thickness. The present analysis is applicable to beams with various boundary conditions at the two ends. Three numerical examples are presented for validation of the theory and illustration of the effects of certain parameters. Supported by the National Natural Science Foundation of China (Grant Nos. 10472102, 10432030, and 10725210)     

Measuring predictability in ultrasonic signals: An application to scattering material characterization

In this paper, we present a novel and completely different approach to the problem of scattering material characterization: measuring the degree of predictability of the time series. Measuring predictability can provide information of the signal strength of the deterministic component of the time series in relation to the whole time series acquired. This relationship can provide information about coherent reflections in material grains with respect to the rest of incoherent noises that typically appear in non-destructive testing using ultrasonics. This is a non-parametric technique commonly used in chaos theory that does not require making any kind of assumptions about attenuation profiles. In highly scattering media (low SNR), it has been shown theoretically that the degree of predictability allows material characterization. The experimental results obtained in this work with 32 cement probes of 4 different porosities demonstrate the ability of this technique to do classification. It has also been shown that, in this particular application, the measurement of predictability can be used as an indicator of the percentages of porosity of the test samples with great accuracy.     

Polarization of multiple scattered light in planetary atmospheres from solution of the coupled linear integral equations derived for mixed rayleigh-isotropic scattering

A set of coupled integral equations describing nonconservative multiple scattering for a mixed isotropic and Rayleigh single scattering phase function in inhomogeneous, plane-parallel planetary atmospheres is derived. The equations are applicable for the frequency redistributions MRE (monochromatic radiative equilibrium), CFR (complete frequency redistribution), or PFR (partial frequency redistribution). Solution of the equations permits one to calculate the intensity and degree of polarization in an arbitrary direction outside or inside the plane-parallel scattering medium. The equations are readily adaptable to more complicated geometries. Solutions for several cases are presented to demonstrate the versatility and validity of the method. These include a calculation of MRE pure Rayleigh scattering of sunlight in an optically-thick planetary atmosphere to demonstrate agreement with the results of Coulson⁽¹⁾et al. (1960), calculations of the altitude profile of the degree of polarization of the earth's Ly-α 1216A and helium 584A dayglow, and the center to limb variation of the degree of polarization of the sunlight diffusely reflected from a distant planet such that the scattering is pure Rayleigh and conservative at the top of the planet's atmosphere, varying smoothly to conditions of nonconservative and pure isotropic scattering deep in the planet's atmosphere. Tables of functions that one might utilize (without resort to a digital computer) to obtain solutions in the escape function approximation are also given.     

Elastic scattering of atoms from surfaces covered with adsorbates: Exact solution for the Einstein-model

The problem of atom scattering from surfaces covered with adsorbates is considered within the Einstein model for the adsorbate phonons. In this case the problem can be solved exactly by the use of a numerical method developed earlier by the present authors. In particular we investigate the temperature dependence of the elastic scattering. It turns out that the deviations from conventional Debye-Waller-factor theory occurring in neutron scattering and Mößbauer effect for single oscillators also show up in atom surface scattering: At higher momentum transfers the elastic scattering probability does not decrease monotonously with temperature but exhibits a maximum at non-zero temperature.     

New technique to simulate angular patterns of polarized signals from multiply scattering media in MFOV and CCD lidars

We present a semi-analytical approach to determine angular patterns of a polarized intensity that form lidar signals from multiply scattering media registered by a monostatic multiple-field-of-view receiver or CCD camera for any polarization state of incident light and any analyzer state at a receiver. Multiply scattering media with a highly forward elongated phase functions are considered. The model of lidar signal formation includes the single near-backscattering and small-angle multiple scattering of light. The developed approach allows computation and analysis of polarized images, including the Mueller matrix images, formed by the laser light backscattered by multiply scattering media, for example, from atmospheric clouds, ocean waters, tissue, etc.