A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer

The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved.     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法.在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法,实现了对光子后向散射分布和干涉特性的快速模拟.利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解.实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本,通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布,并对其中散射和吸收系数进行了反向计算.所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系,验证了该方法的可行性.     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法. 在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法, 实现了对光子后向散射分布和干涉特性的快速模拟. 利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解. 实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本, 通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布, 并对其中散射和吸收系数进行了反向计算. 所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系, 验证了该方法的可行性.     

Radiative transfer in finite volcanic eruption clouds

Radiation transfer through a volcanic aerosol medium has been studied. The radiation transfer properties of the medium as scattering, absorption and extinction coefficients are calculated using the Mie scattering theory. Average coefficients over the size parameter and the radiation wavelength are calculated. The radiation heat fluxes for volcanic eruption ash medium are calculated using the Variational Pomraning–Eddington approximation and compared with those obtained from the Galerkin method. The comparison showed very good agreement.     

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.     

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.     

各向异性介质辐射特性参数联合反演

本文基于BP神经网络方法结合蒙特卡洛和BEER定律辐射传输模拟方法建立了联合反演各向异性散射介质的辐射特性参数模型。首先采用半球透射率结合半球反射率反演模型反演了各向同性介质的吸收系数和散射系数,在此基础上增加准直透射率,建立了联合反演各向异性介质的吸收系数、散射系数和散射不对称因子三参数联合反演模型。反演结果表明该模型能准确反演出介质辐射特性参数,具有实用意义。此外,为了检验测量误差对模型的反演准确性的影响,分别在不同程度测量误差情况下进行反演,结果显示测量误差对散射不对称因子反演值影响较大。     

Measurement of the absorption coefficient of scattering liquid media by the calorimetric method

Using the example of a number of hydrosols (gold nanorods and nanoshells, silver nanoshells, zinc phthalocyanine nanoparticles), we show that the absorption coefficient of a scattering liquid medium can be measured from its heating by a short-time laser irradiation. The degree of heating was determined from expansion of the liquid in an ampoule with a capillary (the principle of liquid thermometer). Irradiation was performed at a wavelength of 671 or 1069 nm. From the transmission of samples of hydrosols at these wave-lengths, the sum of the absorption and scattering coefficients has been determined. To measure the absorption spectra of scattering liquids by this method, a laser with a tunable radiation wavelength is required. In the case of monodisperse colloidal solutions, the method ensures the measurement of the absorption and scattering cross-section ratio of particles.     

Radiative transfer in plant leaves

A two-layer model of light scattering and absorption in plant phytoelements is considered, which takes into account absorption of light by pigments and water and light scattering by particles of two types: chloroplasts and air cavities. An elementary light scattering event is described using the Mie theory. Multiple light scattering in a leaf is described within the framework of the theory of radiative transfer. The equation of radiative transfer with a strongly anisotropic phase function is solved using the method of addition of layers and the method of reduction to a medium with effective parameters depending on the propagation direction of light. The spectral dependences of reflection and transmission coefficients are calculated in the visible range as functions of the leaf structure.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

An inverse radiative transfer problem of simultaneously estimating profiles of temperature and radiative parameters from boundary intensity and temperature measurements

A parallel-plane space filled with absorbing, emitting, isotropically scattering, gray medium is studied in this paper. The boundary intensity and boundary temperature profiles are calculated for the inverse analysis. For the simultaneous estimation of temperature, absorption and scattering coefficient profiles in the medium, the sum of residuals of boundary intensity and temperature after being weighted by a balance factor is minimized through using a Newton-type iteration algorithm and the least-squares method. To avoid over-updating for the parameters, the relative updating magnitude during the iteration process is constrained not to be >0.5. It is shown that the boundary intensity measurement alone is not enough to estimate simultaneously the temperature (source) and the radiative properties (both absorption and scattering coefficients) when the measurement data contain sensitive random errors. The boundary temperature measurement can serve as a necessary supplementation to the boundary intensity to make this kind of inverse radiative transfer problem resolvable. It was shown that a compensation relationship between absorption and scattering coefficients makes it difficult to fix them accurately. Parabolic profiles for the three parameters are used to validate the estimation method. When the optical thickness approaches 4.0, the results for the radiative properties are not acceptable, although the result for temperature profile is reasonable. This means the method needs further improvements.     

近红外光谱范围人肝癌变和热凝固导致组织吸收和散射特性的变化

研究了人肝的癌变及热凝固导致其对710,730,750,770,790,810,830,850,870和890 nm的钛宝石激光的吸收和散射特性的变化,实验采用双积分球测量系统以及反向倍增法获取肝组织的吸收和散射特性参数.结果表明:人肝的癌变导致其吸收系数发生了显著的减小,其变化的最大值在850 nm,其值为86.12%,而变化的最小值在750 nm,其值为82.65%.正常人肝组织热凝固导致其吸收系数明显变化,其吸收系数的变化的最大值在710 nm,其值为79.55%,而变化的最小值在790 nm,其值为0.72%.人肝癌组织热凝固导致其吸收系数显著地增大,其变化的最大值在810 nm,其值为78.69%,而变化的最小值在710nm,其值为38.16%.人肝的癌变导致了肝组织的散射系数发生了显著的增大,其变化的最大值在710 nm,其值为158.37%,而变化的最小值在890 nm,其值为136.03%.正常人肝组织热凝固导致其散射系数显著地增大,其变化的最大值在890 nm,其值为632.92%,而变化的最小值在710 nm,其值为587.40%.人肝癌组织热凝固导致其散射系数显著地增大,其变化的最大值在810 nm,其值为384.25%,而变化的最小值在710 nm,其值为330.86%.肝组织的吸收和散射特性的变化也随着激光波长的变化而变化.     

A two-step strategy for numerical simulation of radiative transfer with anisotropic scattering and reflection

This article presents a two-step procedure for the computation of radiative heat transfer with anisotropic scattering and reflection. It is based on a concept that the coincident processes of absorption and scattering/reflection can be separated factitiously. All medium elements and wall surfaces are supposed to be pure-absorbing when receiving incident radiation. Afterwards they emit the scattered/reflected radiations. The absorption of both the initial and the secondary radiations can be assessed by the direct exchange area. It is needed to repeat the processes for a few times until the radiations are substantially absorbed. For anisotropic scattering/reflection, a vector summation obtains the directional distribution of emissive power. The method is validated by several benchmark computations in terms of emissive power and heat transfer coefficients. It is shown that the method gives more accurate solution than the isotropic scaling for the heat transfer in anisotropically scattering media.     

Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model

Optical tomography is a novel imaging modality that is employed to reconstruct cross-sectional images of the optical properties of highly scattering media given measurements performed on the surface of the medium. Recent advances in this field have mainly been driven by biomedical applications in which near-infrared light is used for transillumination and reflectance measurements of highly scattering biological tissues. Many of the reconstruction algorithms currently utilized for optical tomography make use of model-based iterative image reconstruction (MOBIIR) schemes. The imaging problem is formulated as an optimization problem, in which an objective function is minimized. In the simplest case the objective function is a normalized-squared error between measured and predicted data. The predicted data are obtained by using a forward model that describes light propagation in the scattering medium given a certain distribution of optical properties.In part I of this two-part study, we presented a forward model that is based on the time-independent equation of radiative transfer. Using experimental data we showed that this transport-theory-based forward model can accurately predict light propagation in highly scattering media that contain void-like inclusions. In part II we focus on the details of our image reconstruction scheme (inverse model). A crucial component of this scheme involves the efficient and accurate determination of the gradient of the objective function with respect to all optical properties. This calculation is performed using an adjoint differentiation algorithm that allows for fast calculation of this gradient. Having calculated this gradient, we minimize the objective function with a gradient-based optimization method, which results in the reconstruction of the spatial distribution of scattering and absorption coefficients inside the medium. In addition to presenting the mathematical and numerical background of our code, we present reconstruction results based on experimentally obtained data from highly scattering media that contain void-like regions. These types of media play an important role in optical tomographic imaging of the human brain and joints.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.     

Retrieval of the effective constitutive parameters from metamaterial absorbers

The equivalent medium theory of metamaterials provides a way to obtain their effective constitutive parameters. However, because of its non-reciprocity, the complexity of the electromagnetic coupling, and a metallic bottom layer, it has been challenging to retrieve them from a metamaterial absorber. In this paper, we propose a method without any approximation to obtain them, in which the non-reciprocity and the strong electromagnetic coupling are included. Compared with the three methods such as symmetric metamaterial method, asymmetric metamaterial method and metasurface method, our method can reveal the metamaterial absorber's electrical and magnetic resonance and show its electromagnetic coupling coefficients. To deal with a metamaterial absorber with a metallic bottom layer, four corners of the metallic bottom layer in the unit cell are removed, making it possible to retrieve the electromagnetic parameters. Surprisingly, these results show that the metamaterial absorber with a metallic bottom layer in our example operates in a negative refraction state at the half absorption frequencies, which helps further understand the absorbing mechanism of these metamaterial absorbers.     

组织模拟液Intralipid-10%的 吸收系数和各向异性因子的测量

用加吸收体法测量了组织模拟液Intralipid-10%的吸收系数和各向异性因子。运用漫射理论研究了点光源在无限大介质中的各向异性散射,实验结果得到 μ_a/D 的多个测量值的标准偏差小于0.6%,测量值与拟合值的残差方均根值为0.1%。标准偏差和残差的值表明了测量值的准确度。     

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

In conventional Raman spectroscopic measurements of liquids or surfaces the preferred geometry for detection of the Raman signal is the backscattering (or reflection) mode. For non‐transparent layered materials, sub‐surface Raman signals have been retrieved using spatially offset Raman spectroscopy (SORS), usually with light collection in the same plane as the point of excitation. However, as a result of multiple scattering in a turbid medium, Raman photons will be emitted in all directions. In this study, Monte Carlo simulations for a three‐dimensional layered sample with finite geometry have been performed to confirm the detectability of Raman signals at all angles and at all sides of the object. We considered a non‐transparent cuboid container (high density polyethylene) with explosive material (ammonium nitrate) inside. The simulation results were validated with experimental Raman intensities. Monte Carlo simulation results reveal that the ratio of sub‐surface to surface signals improves at geometries other than backscattering. In addition, we demonstrate through simulations the effects of the absorption and scattering coefficients of the layers, and that of the diameter of the excitation beam. The advantage of collecting light from all possible 4π angles, over other collection modes, is that this technique is not geometry specific and molecular identification of layers underneath non‐transparent surfaces can be obtained with minimal interference from the surface layer. To what extent all sides of the object will contribute to the total signal will depend on the absorption and scattering coefficients and the physical dimensions. Copyright © 2015 John Wiley & Sons, Ltd.