The influence of anisotropic scattering on the radiative intensity in a gray, plane-parallel medium calculated by the DRESOR method

Even though there have been many ways to treat complex anisotropic scattering problems, in most of the cases only the radiation flux or its dimensionless data were provided, and radiative intensity with high directional resolution could merely be seen. In this paper, a comprehensive formulation for the DRESOR method was proposed to deal with the anisotropic scattering, emitting, absorbing, plane-parallel media with different boundary conditions. The method was validated by the data from literature and the integral formulation of RTE. The DRESOR value plays an important role in the DRESOR method, and how it is determined by the anisotropic scattering was demonstrated by some typical results. The intensities with high directional resolution at any point can be given by the present method. It was found that the scattering phase function has little effect on the intensity for thin optical thickness, for example, 0.1. And there is the largest boundary intensity for the medium with the largest forward scattering capability, and the smallest one with the largest backward scattering capability. An attractive phenomenon was observed that the scattering of the medium makes the intensity at boundary can not reach the blackbody emission capability with the same temperature, even if the optical thickness tends to very large. It was also revealed that the scattering of the medium does not mean it cannot alter the magnitude of the energy; actually, stronger scattering causes the energy to have more chance to be absorbed by the medium, and indirectly changes the energy magnitude in the medium. Finally, it is easy to deduce all the associated quantities such as the radiation flux, the incident radiation and the heat source from the intensity, just as done in literature.     

Two-dimensional radiative transfer in a finite scattering planar medium

The source function, radiative flux, and intensity at the boundaries are calculated for a two-dimensional, scattering, finite medium subjected to collimated radiation. The scattering phase function is composed of a spike in the forward direction super-imposed on an isotropic background. Exact radiative transfer theory is used to formulate the problem and Ambarzumian's method is used to obtain results. Using the principle of superposition, the results for any step variation in incident radiation are expressed in terms of universal functions for the semi-infinite step case. Two-dimensional effects are most pronounced at large optical thicknesses and albedos.     

A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam

Monte Carlo approaches to compute multiple scattering of polarized light are examined. A Backward Monte Carlo (BMC) method is developed to solve the Stokes vector of the multiple scattered light for an inhomogeneous scattering medium with boundaries. A generalized form of the BMC method in vector notation is proposed. This method can determine the scattered light with sufficient accuracy in both intensity and polarization compared to the same calculation using the doubling-adding method for a plane parallel medium.For application to a narrow incident beam and an inhomogeneous medium, a modified BMC method is developed, borrowing a concept from the Forward Monte Carlo (FMC) method for the first scattering events. Furthermore, a modification of the total scattering matrix, i.e., the combination of the derived scattering matrix with its time inverse, is discussed. This BMC method can be used successfully for model calculations of lidar and other laser measurements of polarized light.     

The Iterative-DRESOR method to solve radiative transfer in a plane-parallel, anisotropic scattering medium with specular-diffuse boundaries

Using the intensity with high directional resolution obtained by the Basic-DRESOR method as an initial guess, which is substituted into the integrated radiative transfer equation (IRTE), an iterative algorithm is proposed, called the Iterative-DRESOR method. This method can reduce the error levels of the intensity from several percent using the Basic-DRESOR method to a level of less than 1.0×10⁻⁶ with acceptable computation costs. The method is also validated against the exact heat flux in literature in some cases. It further clarifies some uncertain results for the reflectance in a pure, linearly anisotropic scattering medium with specular-diffuse boundaries. The directional distributions of intensity are obviously influenced by the reflecting modes of the boundary, especially in the zone near the boundary. The reflecting mode of an emitting boundary has little effect on the transmittance or reflectance. The reflecting mode of a non-emitting boundary also has little effect on the transmittance, but it obviously influences the reflectance. The difference between the reflectance for specular and diffuse boundaries increases at first, and then decreases, as the optical thickness of the medium increases. The difference will decrease as the scattering albedo of the medium increases, and it is negligible when the medium is pure scattering. The effect of the scattering phase function of the medium on the difference can also not be ignored. The Iterative-DRESOR method is expected to strengthen the capability of the Monte Carlo method to produce accurate results and to validate the results of other methods to solve RTE.     

Radiative heat transfer in a planar medium with anisotropic scattering and directional boundaries

Radiation heat transfer in an absorbing, emitting and scattering medium has been the subject of many previous investigations. Most solutions are numerically complex and the existing analytical solutions are restricted in application by the simplifying assumptions involved. A plane-parallel medium is considered which scatters anisotropically. The boundaries are considered to be specular reflectors, as predicted by Fresnel's relations, while the diffusely incident radiation is refracted according to Snell's law. The emission is restricted to a medium with a uniform temperature distribution. Approximate closed-form solutions for the radiative heat flux and incident intensity are presented for dielectric layers and linear anisotropic scattering. Numerical results are also presented and show that the effects of directional boundaries, anisotropic scattering, scattering albedo and optical depth are accurately predicted by the approximate solution.     

DRESOR法对平行入射辐射问题的研究

本采用一种基于蒙特卡洛法(Monte Carlo Method,MCM)求解辐射传递方程(Radiative Transfer Equation, RTE)的快捷、有效的方法-DRESOR法(Distributions of Ratios of Energy Scattered Or Reflected)在一维充满吸收、各向同性散射介质平行平板中,外部有平行入射条件下,求解计算空间点的辐射强度沿空间方向角的分布,而不需要辐射平衡和在空间位置坐标和方向角度坐标上同时离散辐射传递方程进行迭代求解。     

The use of the galerkin method for radiation transfer in an anisotropically scattering slab with reflecting boundaries

Radiation transfer in an absorbing, emitting, anisotropically scattering, plane-parallel medium with diffusely reflecting boundaries is solved by application of the Galerkin method. With this approach, the radiation heat flux, angular distribution of radiation intensity, and the divergence of the radiation heat flux anywhere in the medium can be determined highly accurately. For optical thicknesses up to about 10, exact results are also readily obtainable if sufficient number of terms are considered in the expansion. Numerical results are presented for representative cases.     

DRESOR法对瞬态辐射传递问题的研究

用基于蒙特卡洛法(Monte Carlo Method,MCM)的DRESOR法(Distributions of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface)求解入射辐射经过介质散射、壁面反射传递后辐射强度随时间变化的瞬态辐射传递方程(Transient RadiativeTransfer Equation,TRTE)问题。通过在系统内计算一单位瞬态入射辐射对介质的DRESOR数分布,就能计算任意时间内入射辐射在系统内时间响应特性,这样有效提高数值方法处理瞬态辐射问题的通用性。并且能够获得高方向分辨率的辐射强度随时间变化的结果,这是目前大多数数值处理方法比较难做到的,显示出了DRESOR法处理瞬态入射辐射问题的能力．     

任意入射辐射条件下介质特性对瞬态辐射传递的影响

用基于Monte Carlo法的DRESOR法在平行平板系统内具有吸收、无发射介质中研究不同波形入射、壁面反射、介质散射率、光学厚度、各向异性散射等条件对瞬态辐射传递的影响.任意连续波形入射辐射是目前大多数数值方法很难处理的瞬态辐射问题,而DRESOR法通过在系统内计算一单位入射辐射能对介质的DRESOR数分布,就能计算任意连续波形入射辐射条件下高方向分辨率的瞬态辐射强度结果.DRESOR法和Monte Carlo法计算的结果进行了比较验证,两者吻合较好,证明了DRESOR法处理瞬态入射辐射问题的正确性和有效性.     

The DRESOR method for radiative heat transfer in a one-dimensional medium with variable refractive index

This paper extends the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to radiative transfer in a variable refractive index medium. In this method, the intensity is obtained from the source term along the curved integration paths determined only by the variable refractive index, and the DRESOR values are calculated by the Monte Carlo method in which the propagation of the energy bundles are affected by Snell's law. With given temperatures on the black boundaries of a one-dimensional medium, the temperature distribution inside the medium with a variable scattering property is calculated under the condition of radiative equilibrium. It is shown that the DRESOR method has a good accuracy in the cases studied. For an isotropic-scattering medium with the same optical thickness, the scattering albedo has no effect on the temperature distribution, which can be obtained from the general equations and can be seen as an extension of what exists for a constant refractive index; however, the different refractive index causes obvious changes in the temperatures inside the medium. The effect of anisotropic scattering on the temperature distribution cannot be ignored, although it is still weaker than the effect caused by variation in the refractive index.     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.     

Reconstruction evaluation of intensity ratio distribution for extraction of absorber information in homogeneous scattering medium

To extract effectively the absorber information embedded in a homogeneous scattering medium in the transmission geometry, a method of taking the ratio of the output intensity in a measured medium to that in a reference medium is evaluated. The reference medium is a virtual one with the same scattering coefficient distribution as that of the measured medium, but with a uniform absorption coefficient distribution. Numerical results show that the proposed method can enhance the output signal by extracting the ballistic-like component. We also apply a backprojection method to reconstruct the single absorber using many pairs of input and output intensity ratio distributions. The reconstruction position error and the quantitative measurement of absorption coefficient are discussed.     

Two-dimensional isotropic scattering in a finite thick cylindrical medium exposed to a laser beam

Graphical and tabular results are presented for the back-scattered intensity from a finite two-dimensional cylindrical medium exposed to a Gaussian beam of radiation. Also, results for the source function and flux at the boundaries are presented. The influence of optical thickness and albedo are most pronounced at large optical radii. The semi-infinite results can be used to approximate the finite case for small optical radii. Ranges for single, double, and multiple scattering are discussed. For locations far from the incident beam, the results can be expressed in terms of universal functions independent of beam size. A method is presented for extending the isotropic results to the anisotropic case where the phase function is made up of a spike superimposed on an otherwise isotropic phase function.     

Ultrasonic fields radiated through matching layers with nonparallel boundaries

In the case of ultrasonic measurements in aggressive media piezoelectric elements of ultrasonic transducers are separated from a medium by thick protective layers, which may posses nonparallel front and back surfaces. This enables to reduce significantly the amplitude of multiple reflections, but the structure of the ultrasonic field radiated through a layer with nonparallel boundaries becomes complicated. The main objective of this paper is to present a method suitable for simulation of ultrasonic fields radiated through a layer with nonparallel boundaries in a transient mode. The proposed simulation method is based on the transformation of a multilayered medium into a virtual one without internal boundaries, equivalent to the actual medium from the point of a view of the relative times of arrival of direct and edge waves. The simulated ultrasonic fields in water are compared with the measurement results and a good correspondence between calculated and measured fields is obtained.     

基于赝热光照明的单发光学散斑成像

散射介质对光的散射是当前限制光学成像深度或距离的一个严重的问题.本文首先数值模拟比较了光透过随机散射介质成像研究中常用的基于光学记忆效应(memory effect, ME)和自相关(autocorrelation, AC)方法的HIOER算法和乒乓(Ping-Pang, PP)算法的优缺点.通过对HIOER算法和PP算法的恢复效果和迭代次数进行比较,发现PP算法在保持较高恢复效果的前提下拥有更快的运行速度.实验中,利用连续HeNe激光器和旋转毛玻璃产生赝热光源,通过物镜对随机散射介质后数毫米距离内的不同形状物体进行了单帧成像,并采用PP算法成功地恢复出微米量级物体的实际图像.这一研究结果将进一步促进ME和AC方法在深层生物组织医学成像研究上的应用.最后,实验研究了不同的物镜和散射介质的间距对成像恢复的放大率、分辨率和图像强度的影响特性,并进行了详细研究.     

Heat transfer in a spherical turbid medium with conduction and radiation

The heat transfer through a spherical media with conduction and radiation is considered. The medium is considered to be turbid and anisotropically scattering with diffusely reflecting boundaries of constant temperatures. The radiative transfer problem is solved using the Galerkin method. An iterative method is used to solve the nonlinear relation between the radiative transfer equation and the conductive energy equation. Calculations are carried out and compared for a homogeneous, isotropically scattering medium with isothermal, transparent boundaries. The results show good agreement with previous work. Calculations are carried out for inhomogeneous media with isotropic, and forward and backward anisotropic scattering. The boundaries of the media are considered to be isothermal and may be transparent or diffusely reflecting boundaries. The calculations are used to study the effects of the single scattering albedo, the anisotropic scattering parameter, the conduction-radiation parameter and the heat source.     

透过散射介质对直线运动目标的全光成像及追踪技术

光散射是限制光传输以及降低和破坏光学成像性能的主要因素,透过复杂散射介质对运动目标的全光成像是光学领域极具挑战性的技术之一.本文提出一种利用散斑差值自相关透过散射介质对运动目标进行实时追踪的方法.采用赝热光照明,基于光学记忆效应理论,通过对运动目标采集的两帧散斑做差值,然后做自相关运算,计算目标移动的距离,实现对目标的实时追踪,并且利用相位恢复算法进行简单处理就可以重建隐藏目标.对该方法进行了实验验证,成功地对隐藏的运动目标实现了成像与追踪.这种透过散射介质对运动目标的全光成像及实时追踪技术,在生物医学等领域具有重要应用潜力.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Composition of propagated,reflected and transmitted waves in arbitrary and continuously stratified environments

First, a solution is presented for a canonical problem in wave propagation. Second, illustrations and applications of the results are carried out to study cases which are relevant to the propagation problem in the ocean and atmosphere.The canonical problem consists of a plane wave incident on an arbitrary and continuously stratified region with planar boundaries. The explicit composition of the reflected, transmitted and propagated waves are derived. The solution is systematic and allows for (i) discontinuities in the acoustic properties at boundaries and arbitrary variation within, (ii) attenuation, (iii) all angles of incidence. The general expressions are obtained by using an alternate procedure to one recently devised [1]. The present approach is straightforward and plainly amenable to physical interpretation of its auxiliary mathematical constants. The discontinuities at the boundaries are satisfied at the outset. The reflected and transmitted waves are directly and explicitly specified. Comparison to widely used techniques in both analytical and numerical works is made to demonstrate the viability of the present approach.A series of cases relevant to the problem at hand are considered. These cases illustrate the mechanics involved in use of the method, and expand its application to problems that appear to be at variance with the formulation of the canonical problem. The illustrations include attenuation in the medium, effect on the solution of different acoustic discontinuities at the boundaries, and use of an inhomogeneous background profile with known independent solutions. The expanded applications treat formally three types of problems: (i) the exact solution for plane waves in continuously stratified media where the well-used ray theory or W-K-B approximation serves only as a first approximation in a correct iterative solution; (ii) the scattering of a plane wave by non-planar boundaries, i.e., spherical or cylindrical acoustic lens with the stratification along the radial direction; (iii) the field due to a point source in a continuously stratified wave guide, like the ocean or atmosphere.     

Locally conformal method for acoustic finite-difference time-domain modeling of rigid surfaces

The finite-difference time-domain method is a simple but powerful numerical method for simulating full-wave acoustic propagation and scattering. However, the method can demand a large amount of computational resources. Traditionally, continuously curved boundaries are represented in a stair-step fashion and thus accurately modeling scattering from a boundary will require a finer discretization than would otherwise be necessary for modeling propagation in a homogeneous medium. However, a fine discretization might not be practical due to limited computational resources. A locally conformal technique is presented here for modeling acoustic scattering from continuously curved rigid boundaries. This technique is low cost, simple to implement, and gives better results for the same grid discretization than the traditional stair-step representation. These improvements can be traded for a coarser discretization which reduces the computational burden. The improved accuracy of this technique is demonstrated for a spherical scatterer.