Noninvasive determination of tissue optical properties based on radiative transfer theory

We present a feasibility study of a new method for determining the tissue optical properties, including the absorption and scattering coefficients and the scattering asymmetry factor. A state-of-the-art radiative transfer model for the coupled air/tissue system, based on rigorous radiative transfer theory, is used in our forward modeling simulations. The concept of the effective photon penetration depth is introduced and used to help determine the depth below, which information about the tissue will not be available through noninvasive imaging of a biological tissue using reflected diffuse light. Simulation results show that for accurate determination of tissue optical properties, one can use radiative transfer theory in conjunction with measurements of reflected radiances as well as other existing techniques.     

Integrating sphere study of the optical properties of aluminum nanoparticles in tetranitropentaerytrite

The dependences of the transmission coefficients and the sum of the transmission and absorption coefficients for light with a wavelength of 643 nm in compressed pentaerythritol tetranitrate (PETN) samples containing aluminum nanoinclusions (average radius of 50 nm) on the pellet thickness and the mass fraction of aluminum nanoparticles in it are studied with an integrating sphere. The light absorption and scattering in this system is simulated using the Mie theory and a radiative transfer equation. The depth profile of absorbed energy in a sample is shown to approximately obey the Bouguer-Beer law. The effective cross section of radiation absorption by aluminum nanoparticles, which takes into account both light absorption and scattering by an ensemble of nanoparticles, exceeds the geometrical cross section.     

Numerical investigation of the effect of soot aggregation on the radiative properties in the infrared region and radiative heat transfer

The effect of aggregation on soot radiative properties in the infrared region of the spectrum is numerically investigated using Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA). In order to use the RDG-FA theory for a wide range of aggregate sizes and wavelengths, the predicted phase functions, scattering and absorption coefficients are compared with a more accurate theory, the integral equation formulation for scattering—IEFS. The importance of scattering when compared with absorption is investigated, as well as the effect of aggregation on the phase function shape and on the scattering cross section. It is concluded that in the case of small aggregates formed with small primary particles the scattering coefficient is negligible compared with the absorption coefficient, and scattering and aggregation of primary particles can be ignored. Thus, the Rayleigh approximation can be used leading to isotropic scattering. In the case of large aggregates constituted by large primary particles, aggregation becomes important and the scattering cross section is of the same order of magnitude of the absorption cross section. Moreover, the phase function becomes highly peaked in the forward direction. Therefore, the Rayleigh and the equivalent volume Mie sphere approximations are not valid, and the RDG-FA method emerges as a good compromise between accuracy and simplicity of application. However, radiative transfer calculations between two infinite, parallel, black walls show that scattering may always be neglected in the calculation of total radiative heat source and heat fluxes to the walls. The minor influence of scattering on the accuracy of the predictions is explained by the shift between the spectral region where scattering is important and the region where the spectral radiative heat source is large.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

A probabilistic study of the influence of parameter uncertainty on solutions of the radiative transfer equation

The influence of uncertainty in the absorption and scattering coefficients on the solution and associated parameters of the radiative transfer equation is studied using polynomial chaos theory. The uncertainty is defined by means of uniform and log-uniform probability distributions. By expanding the radiation intensity in a series of polynomial chaos functions we may reduce the stochastic transfer equation to a set of coupled deterministic equations, analogous to those that arise in multigroup neutron transport theory, with the effective multigroup transfer scattering coefficients containing information about the uncertainty. This procedure enables existing transport theory computer codes to be used, with little modification, to solve the problem. Applications are made to a transmission problem and a constant source problem in a slab. In addition, we also study the rod model for which exact analytical solutions are readily available. In all cases, numerical results in the form of mean, variance and sensitivity are given that illustrate how absorption and scattering coefficient uncertainty influences the solution of the radiative transfer equation.     

非球形生物气溶胶对偏振光的多次散射特性研究

基于回转椭球模型和有限长圆柱模型,采用T矩阵方法研究了非球形生物气溶胶的单次散射特性,计算了鼠疫耶尔森氏杆菌、土拉热杆菌二种生物气溶胶对氦氖激光的单次相矩阵、单次散射反照率以及不对称因子。根据矢量辐射传输理论,研究了激光在生物气溶胶中传输的偏振散射特性,基于累加-倍加法(adding-doubling method)求解矢量辐射传输方程,并计算了非球形生物气溶胶对激光多次散射的斯托克斯参量。计算结果表明,生物气溶胶的尺寸和形状对光的极化更为敏感,因此在利用激光进行生物气溶胶微观特性探测和反演时,利用激光的偏振散射特性为非常有效的方法。     

Adjoint problem of radiative transfer for a pseudo-spherical atmosphere and general viewing geometries

We formulate the adjoint radiative transfer for a pseudo-spherical atmosphere and various retrieval scenarios. The single scattering radiance is computed in a spherical atmosphere by using the source integration technique, while for the multiple scattering radiance we formulate an one-dimensional adjoint radiative transfer equation in a plane-parallel atmosphere. The adjoint solution of the radiative transfer equation is obtained by employing the discrete ordinate method with matrix exponential. We provide an abbreviated derivation of our formalism as well as a discussion of the numerical implementation of the theory.     

冰水混合云对可见光的吸收和散射特性

根据Mie理论，分别计算了由纯水、纯冰和冰-水同心球形粒子构成的云层在可见光波段的单次散射特性. 根据辐射传输理论，利用叠加法数值计算了这三种不同构成的云层的反射函数，以及它们的平面反照率、透过率和吸收率. 结果表明，冰云和冰_水云的反射函数和平面反照率在大部分散射角下要略小于水云，而透过率却比水云的大. 通过具体的数值计算结果和理论分析，研究了水云的异常吸收现象. 关键词： 冰_水粒子 Mie理论 叠加法 光散射     

风驱粗糙海面背景下海雾对可见和红外光多次散射特性研究

通过测量空间辐射反演海雾气溶胶的微观特性是一种重要的遥感方法,但是海雾对辐射的反射会受到海面背景的影响。该工作研究了海雾与海面的耦合多次散射。利用Mie理论研究了海雾气溶胶的单次散射特性,利用辐射传输理论研究太阳光在无下垫面海雾中传输多次散射特性;在基尔霍夫近似下研究了风驱粗糙海面的散射特性,并考虑了海面的遮蔽效应,得到了风驱海面随风速的反射函数。根据累加法研究了海雾和海面的耦合散射,计算结果表明海雾在有粗糙海面作为背景的情况下,其整体反射有较大增强。     

Radiative properties of scattering and absorbing dense media: theory and experimental study

We investigate the validity of the radiative transfer equation to model transmission of light through an absorbing and scattering medium. Assuming that radiative transfer equation is valid, the inverse scattering problem for non-polarized radiative transfer in one-dimensional absorbing and scattering media is solved using a parameter identification method. We discuss how to identify the albedo, phase function and extinction coefficient of the medium. We present experimental data that confirm that this approach is robust and can be used to make reliable predictions of the behavior of scattering absorbing systems.     

Complete matrix solution of radiative transfer equation for PILE of horizontally homogeneous slabs

This article covers the analytical solution of the discretized radiative transfer equation in the matrix form. The equation is discretized according to the discrete ordinates method. The solution is based on the representation of the light field in a scattering medium as a superposition of an anisotropic and a smooth regular parts. The first of them is calculated analytically using the smoothness of the solution angular spectrum. The regular part is obtained from a radiative transfer equation boundary problem with the anisotropic part as a source function by discrete ordinates method with a scaling transformation and a matrix-operator method applied. There is no limitation of the scattering law in a medium.     

Some new leaf normal-angle distribution models and their influence on geometry functions and area scattering phase functions related to radiative transfer problems in vegetative canopies

This note is devoted to the study of some new analytic leaf angle distribution models by a linear combination of idealized models primarily developed to study realistic light scattering processes for radiative transfer in a vegetative canopy medium.     

Scattering of light by multiple dielectric cylinders: comparison of radiative transfer and Maxwell theory

We have compared radiative transfer theory with analytical solutions of the Maxwell equations for light scattering by multiple infinitely long parallel cylinders at perpendicular incidence. The calculated scattering cross sections for both methods show large differences, but the angle-dependent differential scattering cross-section results are very similar for small cylinder densities, except close to the forward direction. In contrast to recently published results, it is shown that the radiative transfer equation is a useful approximation for small cylinder concentrations.     

Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains

This paper deals with heat transfer in nongrey media which scatter, absorb and emit radiation. Considering a two dimensional geometry, radiative and conductive phenomena through the medium have been taken into account. The radiative part of the problem was solved using the discrete ordinate method with classical S_n quadratures. The absorption and scattering coefficients involved in the radiative transfer equation (RTE) were obtained from the Mie theory. Conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model has been achieved with several simulation of water spray curtains used as fire protection walls.     

Radiative transfer in finite participating atmospheric aerosol media

The properties of radiation transfer through a plane-parallel atmospheric aerosol medium has been studied. It has been done by employing Mie theory to calculate the radiation transfer scattering parameters of the medium in the form of extinction, scattering, and absorption efficiencies. Then, the equation of radiative transfer through a plane-parallel atmosphere of aerosol has been solved for partial heat fluxes using two different analytical techniques, namely, the Variational Pomraning -Eddington approximation and Galerkin technique. Average efficiencies over log-normal and modified gamma size distributions are calculated. Therefore, the radiative properties of Carbon, Anthracite, Bituminous, Lignite, and Fly ash have been calculated. The obtained numerical results show very good agreement with each other in addition to the previous published work.     

Transmission of radiation through an aerosol medium

The properties of radiation through an aerosol medium have been achieved. This has been done by employing Mie scattering theory to calculate the radiation transfer scattering parameters in the form of extinction, absorption and scattering efficiencies. The equation of radiative transfer for the heat flux through a plane parallel atmosphere of aerosol has been solved. The aerosol size distributions are found in practical systems. Average efficiencies over size distribution for spherical particles of complex refractive index are calculated. Therefore, the radiative properties of stratospheric aerosols have been done. The obtained results found to be in a good agreement with the previous work.     

地表双向反射对天基矢量辐射探测的影响分析

矢量辐射传输方程定量描述了辐射在地表-大气耦合介质中的传输过程,是定量遥感的基础.在处理辐射和离散介质相互作用时,如何处理多次散射、辐射偏振效应和耦合地表模型是研究的重点,直接影响定量化遥感反演的精度.文中基于逐次散射近似法求解了矢量辐射传输方程,求解过程中耦合典型地表的非偏双向反射（BRDF）模型和偏振双面反射（BPDF）模型.采用相对误差因子定量分析了地表双向反射效应和大气偏振效应对天基矢量辐射的影响.为进一步研究地表-大气耦合介质系统的偏振特性及地表大气参数的定量遥感反演提供理论支持. 关键词： 矢量辐射传输方程 逐次散射近似 定量遥感 偏振遥感     

紫外波段多分散系气溶胶散射相函数随机抽样方法研究

基于电磁散射与辐射传输中的基本理论,对紫外波段霾尺度范围内满足特定分布的多种气溶胶粒子的散射相函数进行了研究.提出了一种直接随机抽样拟合散射相函数的方法.比较了H-G相函数、改进的H-G相函数及随机抽样拟合的相函数与多分散系Mie相函数的偏离程度.数值计算了不同相函数拟合方法对应气溶胶的传输特性.计算结果表明,相函数的准确模拟计算对于蒙特卡罗方法等辐射传输问题的解决具有十分重要的意义.