Multiple scattering of light by water cloud droplets with external and internal mixing of black carbon aerosols

The mixture of water cloud droplets with black carbon impurities is modeled by external and internal mixing models.The internal mixing model is modeled with a two-layered sphere（water cloud droplets containing black carbon（BC） inclusions）,and the single scattering and absorption characteristics are calculated at the visible wavelength of 0.55 μm by using the Lorenz-Mie theory.The external mixing model is developed assuming that the same amount of BC particles are mixed with the water droplets externally.The multiple scattering characteristics are computed by using the Monte Carlo method.The results show that when the size of the BC aerosol is small,the reflection intensity of the internal mixing model is bigger than that of the external mixing model.However,if the size of the BC aerosol is big,the absorption of the internal mixing model will be larger than that of the external mixing model.

Multiple scattering and modeling of laser in fog

When a laser is transmitted in fog, and the water droplets will scatter and absorb the laser, which affects the intensity of the laser transmission and the accuracy of radar detection. Therefore, it is of great significance to study the laser transmission in the fog. At present, the main method of calculating the scattering and attenuation characteristics of fog is based on the radiation transmission theory, which is realized by a large number of numerical calculations or physical simulation methods, which takes time and cannot meet the requirements for obtaining the fast and accurate results. Therefore, in this paper established are a new laser forward attenuation model and backward attenuation model in low visibility fog. It is found that in low visibility environments, the results calculated by the Monte Carlo method are more accurate than those from most of the existing forward attenuation models. For the cases of 0.86-μm, 1.06-μm, 1.315-μm, 10.6-μm typical lasers incident on different fogs with different visibilities, a backscatter model is established, the error between the fitting result and the calculation result is analyzed, the backward attenuation fitting parameters of the new model are tested, and a more accurate fitting result is obtained.

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

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 Dept-Buffer algorithm. The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.

Improve the Prediction Accuracy of Apple Tree Canopy Nitrogen Content through Multiple Scattering Correction Using Spectroscopy

Method: Use Multiple Scattering Correction to eliminate the interference of scattering on spectrum in the process of field measurement so as to improve the accuracy of prediction model of tree canopy nitrogen content. Apple trees in Qixia of Yantai City were taken as the test material. The spectral reflectivity of apple tree canopy went through the First Derivative (FD) and Multiple Scattering Correction (MSC) plus first derivative, respectively. The correlation coefficients were calculated between spectral reflectivity and nitrogen content. The Support Vector Machine (SVM) method was used to establish the prediction model. The result indicates that the MSC pre-processing can improve the correlation between spectral reflectivity and nitrogen content. The SVM model with MSC + FD pre-processing was a good way to predict the nitrogen content. The calibration R2 of the model was 0.746;the validation R2 was 0.720;and its RMSE was 0.452 g·kgˉ1. MSC can commendably eliminate scattering error to improve the prediction accuracy of prediction model.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

MULTIPLE SCATTERING THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF INHOMOGENEOUS MEDIA

The rate of hydrothermal reaction of SiO_2 and/or A1_2O_3 in the system of CaO-Al_2O_3-SiO_2-H_2O at 200℃ and the factors which influence the reactions are investigated by determining the reaction ratio.The rate of reactions depends on the reactive activities of raw materials, initial composition of mixture and relative activity of SiO_2 and A12O3. The hydrothermal reaction can be accelerated by sodium hydroxide,in the case of silica,which has low activity, this is quite obvious.

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions(HRTFs)measurement,two or more independent sound sources are usually employed in the measurement system.However,the multiple scattering between adjacent sound sources may influence the accuracy of measurement.On the other hand,the directivity of sound source could induce measurement error.Therefore,a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources.An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of±1.0 dB below a frequency of 20 kHz,provided that the sound source radius does not exceed 0.025 m,the source distance relative to head center is not less than 0.5 m,and the angular interval between two adjacent sources is not less than 20 degrees.Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method.Furthermore,the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.

Effect of multiple coulomb scattering on the beam tests of silicon pixel detectors

In the research and development of new silicon pixel detectors,a collimated monoenergetic charged-particle test beam equipped with a high-resolution pixel-beam telescope is crucial for prototype verification and performance evaluation.When the beam energy is low,the effect of multiple Coulomb scattering on the measured resolution of the Device Under Test(DUT)must be considered to accurately evaluate the performance of the pixel chips and detectors.This study aimed to investigate the effect of multiple Coulomb scattering on the measured resolution,particularly at low beam energies.Simulations were conducted using Allpix^(2) to study the effects of multiple Coulomb scattering under different beam energies,material budgets,and telescope layouts.The simulations also provided the minimum energy at which the effect of multiple Coulomb scattering could be ignored.Compared with the results of a five-layer detector system tested with an electron beam at DESY,the simulation results were consistent with the beam test results,confirming the reliability of the simulations.

A simulation method on target strength and circular SAS imaging of Xrudder UUV including multiple acoustic scattering

Target strength(TS)and circular synthetic aperture sonar(CSAS)images provide essential information for active acoustic detection and recognition of non-cooperative unmanned undersea vehicles(UUVs),which pose a significant threat to underwater preset facilities.To access them,we propose an iterative physical acoustics(IPA)-based method to simulate the multiple acoustic scattered fields on rigid surfaces in high-frequency cases.It uses the Helmholtz integral equation with an appropriate Green's function in terms of the Neumann series,and then incorporates the ideas of triangulation and iteration into a numerical implementation.Then two approximate analytic formulae with precise physical meanings are derived to predict the TS and CSAS images of concave targets,respectively.There are no restrictions on the surface's curvature and the order of multiple scattering.The method is validated against the finite element method(FEM)for acoustic scattering from a sphere segment and against an experiment involving an X-rudder UUV's stern.On this basis,we simulate and analyze the TS and CSAS images of an X-rudder UUV.In addition,the influence of the angle of adjacent rudders on the multiple scattering characteristics is discussed.Results show that this method can potentially predict accurate UUV features,especially the multiple scattered features.

Numerical calculation of multiple scattering with the layer model

The optical measurement technique based on Mie scattering has been applied to various areas, in which single scattering at low particle concentration is assumed. Nevertheless, since multiple scattering is usually unavoidable in online measurements, we present in this work a multiple scattering calculation method, in which a layer model is employed. The three-dimensional particle system is divided into a pile of layers the number of which is automatically determined, depending on the obscuration of the particle system. The calculation is found to be fast, reasonable and reliable.

Improved Monte Carlo model for multiple scattering calculations

The coupling between the Monte Carlo （MC） method and geometrical optics to improve accuracy is investigated. The results obtained show improved agreement with previous experimental data, demonstrating that the MC method, when coupled with simple geometrical optics, can simulate multiple scattering with enhanced fidelity.

Holographic particle localization under multiple scattering

We introduce a computational framework that incorporates multiple scattering for large-scale threedimensional(3-D)particle localization using single-shot in-line holography.Traditional holographic techniques rely on single-scattering models that become inaccurate under high particle densities and large refractive index contrasts.Existing multiple scattering solvers become computationally prohibitive for large-scale problems,which comprise millions of voxels within the scattering volume.Our approach overcomes the computational bottleneck by slicewise computation of multiple scattering under an efficient recursive framework.In the forward model,each recursion estimates the next higher-order multiple scattered field among the object slices.In the inverse model,each order of scattering is recursively estimated by a nonlinear optimization procedure.This nonlinear inverse model is further supplemented by a sparsity promoting procedure that is particularly effective in localizing 3-D distributed particles.We show that our multiple-scattering model leads to significant improvement in the quality of 3-D localization compared to traditional methods based on single scattering approximation.Our experiments demonstrate robust inverse multiple scattering,allowing reconstruction of 100 million voxels from a single 1-megapixel hologram with a sparsity prior.The performance bound of our approach is quantified in simulation and validated experimentally.Our work promises utilization of multiple scattering for versatile large-scale applications.

A method for determining cirrus height with multiple scattering

An approach for determining cirrus height with multiple scattering effect using data from a Mie scattering lidar is proposed. We compute the exact extinction coefficients of cirrus via altitude. The regulated height of cirrus is obtained through multiple scattering factors. Experimental result demonstrates that the proposed approach can be used to determine effectively cirrus height with multiple scattering.

Influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media

Monte Carlo algorithm and Stokes-Mueller formalism are used to simulate the propagation behavior of polarized light in turbid media. The influence of single scattering and multiple scattering on backscattered Mueller matrix in turbid media is discussed. Single and double scattering photons form the major part of backscattered polarization patterns, while multiple scattering photons present more likely as background. Further quantitative analyses show that single scattering approximation and double scattering approximation are quite accurate when discussing the polarization patterns near the incident point.

UAV remote sensing atmospheric degradation image restoration based on multiple scattering APSF estimation

Unmanned aerial vehicle(UAV) remote imaging is affected by the bad weather, and the obtained images have the disadvantages of low contrast, complex texture and blurring. In this paper, we propose a blind deconvolution model based on multiple scattering atmosphere point spread function(APSF) estimation to recovery the remote sensing image. According to Narasimhan analytical theory, a new multiple scattering restoration model is established based on the improved dichromatic model. Then using the L0 norm sparse priors of gradient and dark channel to estimate APSF blur kernel, the fast Fourier transform is used to recover the original clear image by Wiener filtering. By comparing with other state-of-the-art methods, the proposed method can correctly estimate blur kernel, effectively remove the atmospheric degradation phenomena, preserve image detail information and increase the quality evaluation indexes.

MULTIPLE-SCATTERING STUDIES OF ADSORPTION STRUCTURE OF C_2D_2/Si(111)7×7

The multiple scattering cluster (MSC) method has been employed to perform a theoretical analysis on carbon is near edge X-ray absorption fine structure of the deuteron acetylene (C2 D2) adsorbed on Si(111)7× 7 at room temperature. From the MSC study. it is confirmed that the (22D2 molecule is bonded to a pair of adjacent Si adatom and Si restatom with C-Si bond length about 0.18nm. The carbon-deuteron bond is bent away front the surface and the CCD bond angle is about 120°. The molecule plane tilt slightly away from the surface normal. Compared with C2D2 in gas phase, the C-C bond and C-D bond are elongated by about 0.03nm and 0.02nm respectively when acetylene was adsorbed on the subtrate. Keyowrds: adsorption of deuteron acetylene on Si(111)7×7. near edge X- ray absorption fine structure. multiple scattering cluster method

On acoustic performance for viscoelastic coating containing axisymmetric cavities using the multiple scattering method

A semi-analytical/numerical model based on the multiple scattering （MS） method has been established for analyzing the effect of acoustic performance on main energy attenua- tion mechanism in viscoelastic coating containing axisymmetric cavities. The basic functions of stress and displacement of the axisymmetric cavity surface are derived in the system of spheri- cal coordinates. The transition matrix between the incident wave and the scattering wave are obtained by the numerical integral of the basic functions of the cavity surface. The reflection, transmission and absorption performance of viscoelastic materials containing periodic cavities are calculated using the MS method and the wave propagating theory of the multi-layered medium. The results indicate that low frequency energy is mainly attenuated through cavity resonance. The resonant properties are found to be very sensitive to the boundary conditions. The coupling of the double-cavity is capable of extending the absorption to even lower fre- quencies. The absorption performance of the viscoelastic coating in the high frequency range is independent of the backing material. Its energy attenuation depends mainly on acoustic properties of cavity scattering and mode conversion.

ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES

Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.

Kinetics for Describing the Creaming of Protein-Stabilized O/W Emulsions by Multiple Light Scattering

In the present work, new kinetics to describe the creaming stability of oil-in-water emulsions determined by backscattering measurements （BS） is proposed. The emulsions assayed exhibited a different backscattering profiles regarding creaming destabilization hyperbolic and sigmoid one. Hyperbolic behavior can be described by a second order kinetics, where k_h could be equaled to a rate constant that describes the creaming process and its values would indicate the stability of emulsions. While for the sigmoid BS pattern, kinetics with two terms, is adequate to describe the creaming process in contrast to kinetics previously reported in the literature. The kh value has the same meaning as before, and ks indicates the delaying effect on the creaming rate.

Arbitrary direction incident Gaussian beam scattering by multispheres

Based on spherical vector wave functions and their coordinate rotation theory, the field of a Gaussian beam in terms of the spherical vector wave functions in an arbitrary unparallel Cartesian coordinate system is expanded. The beam shape coefficient and its convergence property are discussed in detail. Scattering of an arbitrary direction Gaussian beam by multiple homogeneous isotropic spheres is investigated. The effects of beam waist width, sphere separation distance, sphere number, beam centre positioning, and incident angle for a Gaussian beam with two polarization modes incident on various shaped sphere clusters are numerically studied. Moreover, the scattering characteristics of two kinds of shaped red blood cells illuminated by an arbitrary direction incident Gaussian beam with two polarization modes are investigated. Our results are expected to provide useful insights into particle sizing and the measurement of the scattering characteristics of blood corpuscle particles with laser diagnostic techniques.