Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates

The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including x(p) = 0.01-1.0, ‖m - 1‖ = 0.1-2.0, N = 16-256, and D(f) = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the ‖m - 1‖x(p) domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D(f) ≈ 1.0) to compact clusters (D(f) ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m - 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x(p) ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.     

Modeling light scattering from Diesel soot particles

The Mie model is widely used to analyze light scattering from particulate aerosols. The Diesel particle scatterometer, for example, determines the size and optical properties of Diesel exhaust particles that are characterized by the measurement of three angle-dependent elements of the Mueller scattering matrix. These elements are then fitted by Mie calculations with a Levenburg-Marquardt optimization program. This approach has achieved good fits for most experimental data. However, in many cases, the predicted complex index of refraction was smaller than that for solid carbon. To understand this result and explain the experimental data, we present an assessment of the Mie model by use of a light-scattering model based on the coupled-dipole approximation. The results indicate that the Mie calculation can be used to determine the largest dimension of irregularly shaped particles at sizes characteristic of Diesel soot and, for particles of known refractive index, tables can be constructed to determine the average porosity of the particles from the predicted index of refraction.     

Radiative-conductive heat transfer in a semitransparent composite with microspherical particles

A mathematical model for calculating the temperature field in a semitransparent composite material that includes a polymethyl methacrylate matrix and quartz microspheres is suggested. In calculating the optical properties of the composite material, use was made of the optical properties of the matrix and of the interacting quartz microspheres at different filling factors which characterize the volume concentration of particles in the matrix. Allowance for the interaction between the composite components is made following the Maxwell–Garnett approximation. Data on the complex refractive index of the composite were used for calculating the coefficients of absorption, scattering, and attenuation of packed particles by the Mie theory. The temperature fields in a layer of the material are found from solving the boundary-value problem for the energy equation and a system of radiation transfer equations with the use of these coefficients.     

Mean-field approximation of Mie scattering by fractal aggregates of identical spheres

We apply the recent exact theory of multiple electromagnetic scattering by sphere aggregates to statistically isotropic finite fractal clusters of identical spheres. In the mean-field approximation the usual Mie expansion of the scattered wave is shown to be still valid, with renormalized Mie coefficients as the multipolar terms. We give an efficient method of computing these coefficients, and we compare this mean-field approach with exact results for silica aggregates of fractal dimension 2.     

Optical sizing of aggregated combustion particles: computational development of a two-angle laser scattering technique

To simplify the experimental efforts involved in the nonintrusive optical characterization of typical combustion-generated particulates, an inverse analysis of scattering measurements at only two angles is developed and evaluated based on the exact scattering computations on simulated fractallike aggregates. Two optimum angles are suggested by combination of theoretical (sensitivity analysis) and practical (spatial resolution) considerations that have led to the interpretation of spherule diameter from the ratio of large-angle scattering and absorption coefficients and the aggregate gyration radius from the ratio of scattering dissymmetry. The inferred spherule and aggregate sizes are found to be generally in good agreement with the initially prescribed values for the range of physical and optical particulate properties considered here. These computational results under precise simulation conditions demonstrate the accuracy of the proposed particulate-sizing technique by avoiding the common experimental uncertainties that prevent a definitive performance assessment of any experimental method.     

Local optical parameters of spherical polydispersions: simple approximations

New analytical solutions for the local optical characteristics (extinction and absorption coefficients, asymmetry parameters of phase functions) of spherical polydispersions composed of comparatively large particles are derived. The geometric optics (GO) approximation is used to solve the problem. For the accuracy of the GO approximation to be improved, the edge effects were taken into account. A comparison with the data obtained by the use of the Mie theory shows a satisfactory accuracy of our analytical formulas. The simple formulas for the cloud local optical characteristics are derived.     

Estimation of optical constants from multiple-scattered light using approximations for single particle scattering characteristics

The inversion of multiple-scattered light measurements to extract the optical constant (complex refractive index) is computationally intensive. A significant portion of this time is due to the effort required for computing the single particle characteristics (absorption and scattering cross sections, anisotropy factor, and the phase function). We investigate approximations for computing these characteristics so as to significantly speed up the calculations without introducing large inaccuracies. Two suspensions of spherical particles viz., polystyrene and poly(methyl methacrylate) were used for this investigation. It was found that using the exact Mie theory to compute the absorption and scattering cross sections and the anisotropy factor with the phase function computed using the Henyey-Greenstein approximation yielded the best results. Analysis suggests that errors in the phase functions and thus in the estimated optical constants depend mainly on how closely the approximations match the Mie phase function at small scattering angles.     

Validating the assumption to the interference approximation by use of measurements of absorption efficiency and hindered scattering in dense suspensions

Frequency domain photon migration (FDPM) measurements were employed to accurately quantify optical properties of both the suspending fluid and particles within dense polystyrene suspensions of 143- or 226-nm mean diameter at varying concentrations (5-30% by volume). The measured absorption coefficients varied linearly with particle volume fraction whereas the isotropic scattering coefficients varied nonlinearly in agreement with the prediction that utilizes the hard-sphere structure factor model. These results validate the interference approximation of light scattering to describe light propagation accurately within dense suspensions. Furthermore, owing to the accuracy of FDPM absorption measurements, the imaginary refractive indices for both particles and their suspending fluid were determined and were found to compare favorably with literature values.     

Effective medium theories for irregular fluffy structures: aggregation of small particles

The extinction efficiencies as well as the scattering properties of particles of different porosity are studied. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from 1.20+0.00i to 1.75+0.58i were selected. They correspond to biological particles, dirty ice, silicate, and amorphous carbon and soot in the visual part of the spectrum. We attempt to describe the optical properties of such particles using Lorenz-Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in the extinction factor do not exceed approximately 5% for particle porosity P = 0 - 0.9 and size parameters x(porous) = 2 pi r(s,porous)/lambda < or approximately = 25. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and the asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus the effective models of spherical and nonspherical particles can be used to significantly simplify the computations of the optical properties of aggregates containing only Rayleigh inclusions.     

Electromagnetic scattering by an aggregate of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.     

Semiconductor laser insert with uniform illumination for use in photodynamic therapy

A low-cost semiconductor red laser light delivery system for esophagus cancer treatment is presented. The system is small enough for insertion into the patient's body. Scattering elements with nanoscale particles are used to achieve uniform illumination. The scattering element optimization calculations, with Mie theory, provide scattering and absorption efficiency factors for scattering particles composed of various materials. The possibility of using randomly deformed spheres and composite particles instead of perfect spheres is analyzed using an extension to Mie theory. The measured radiation pattern from a prototype light delivery system fabricated using these design criteria shows reasonable agreement with the theoretically predicted pattern.     

Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles

An analysis of radiative absorption and scattering by clusters of spheres in the Rayleigh limit is developed with an electrostatics analysis. This approach assumes that the largest dimension of the cluster is significantly smaller than the wavelength of the radiation. The electric field that is incident upon and scattered by the cluster can then be represented by the gradient of a potential that in turn satisfies Laplace's equation. An analytical solution for the potential that exactly satisfies the boundary conditions at the surfaces of the spheres is obtained with a coupled spherical harmonics method. The components of the polarizability tensor and the absorption, scattering, and depolarization factors are obtained from the solution. Calculations are performed on fractallike clusters of spheres, with refractive-index values that are characteristic of carbonaceous soot in the visible and the IR wavelengths. Results indicate that the absorption cross sections of fractal soot clusters can be significantly larger in the mid-IR wavelengths than what is predicted for Rayleigh-limit spheres that have the same total volume. The absorption cross section (relative to a sphere of the same volume) is dependent on the number of spheres in the aggregate for aggregates with up to approximately 100 primary spheres, and for larger aggregates the relative absorption becomes constant. The predicted spectral variation of soot absorption in the visible and the mid-IR wavelengths is shown to agree well with experimental measurements.     

扩散火焰中初始形成碳核的光学测量

根据米氏散射理论 ,推导出碳核的散射属于瑞利散射。介绍一种实验方法 ,该方法利用在入射光为偏振激光时碳核的瑞利散射光与碳核原始化合物 PAH辐射的荧光的差异 ,测量扩散火焰中形成的碳核     

Ultraviolet-visible bulk optical properties of randomly distributed soot

The presence of soot in the lower stratosphere was recently established by in situ measurements. To isolate their contribution to optical measurements from that of background aerosol, the soot's bulk optical properties must be determined. Laboratory measurements of extinction and polarization of randomly distributed soot were conducted. For all soot, measurements show a slight reddening extinction between 400 and 700 nm and exhibit a maximum of 100% polarization at a scattering angle of 75 +/- 5 degrees. Such results cannot be reproduced by use of Mie theory assumptions. The different optical properties of soot and background stratospheric aerosol could allow isolation of soot in future analyses of stratospheric measurements.     

Ice-crystal absorption: a comparison between theory and implications for remote sensing

The problem of the disagreement between cirrus crystal sizes determined remotely and by in situ measurements is shown to be due to inappropriate application of Mie theory. We retrieved the absorption optical depth at 8.3 and 11.1 mum from 11 tropical anvil cirrus clouds, using data from the High Resolution Infrared Radiation Sounder (HIRS). We related the absorption optical depth ratio between the two wavelengths to crystal size (the size was defined in terms of the crystal median mass dimension) by assuming Mie theory applied to ice spheres and anomalous diffraction theory (ADT) applied to hexagonal columns, hexagonal plates, bullet rosettes, and aggregates (polycrystals). The application of Mie theory to retrievals yielded crystal sizes approximately one third those obtained with ADT. The retrievals of crystal size by use of HIRS data are compared with measurements of habit and crystal size obtained from in situ measurements of tropical anvil cirrus particles. The results of the comparison show that ADT provides the more realistic retrieval. Moreover, we demonstrate that at infrared wavelengths retrieval of crystal size depends on assumed habit. The reason why Mie theory predicts smaller sizes than ADT is shown to result from particle geometry and enhanced absorption owing to the capture of photons from above the edge of the particle (tunneling). The contribution of particle geometry to absorption is three times greater than from tunneling, but this process enhances absorption by a further 35%. The complex angular momentum and T-matrix methods are used to show that the contribution to absorption by tunneling is diminished as the asphericity of spheroidal particles is increased. At an aspect ratio of 6 the contribution to the absorption that is due to tunneling is substantially reduced for oblate particles, whereas for prolate particles the tunneling contribution is reduced by 50% relative to the sphere.     

Soot formation characteristics in a pulverized coal flame formed in a swirling flow

To understand the soot formation characteristics in a pulverized coal flame with a swirling flow, simultaneous imaging of Mie scattering of coal particles and laser induced incandescence (LII) of soot were performed in this study. The pulverized coal flame was stabilized by a hydrogen diffusion pilot flame. The characteristic structures of soot formation in the pulverized coal flame with a swirling flow were analyzed based on a comparison of the experimental results and two-dimensional numerical simulation in the mixing region of coal particles and the oxidizer. The interactions between coal particle clouds and soot formation are discussed in detail. The results clearly show that the averaged radial dispersions of scattering signals from coal particles and of the LII signals from soot are overlapped. The overlapping region appeared nearby the nozzle exit due to the turbulent mixing and the high temperature region formed by swirl-induced recirculation flow. This overlapping region radially expands with increasing the height from the burner. Additionally, the characteristic areas of soot formation were observed in the results of simultaneous imaging of Mie scattering and LII. These areas are 1) streaky soot formation areas around the particle clouds, 2) soot formation areas inside of the particle clouds and 3) soot formation areas around the large coal particles.     

Changes in spectral shape of tissue optical properties in conjunction with laser-induced thermotherapy

We measured the optical properties on samples of rat liver tissue before and after laser-induced thermotherapy performed in vivo with Nd:YAG laser irradiation. This made it possible to monitor not only the influence of coagulation on the scattering properties but also the influence of damages to vessels and heat-induced damage to blood on the absorption properties. An experimental integrating-sphere arrangement was modified to allow the determination of the g factor and the absorption and scattering coefficients versus the wavelength in the 600-1050-nm spectral region, with the use of a spectrometer and a CCD camera. The results show a relative decrease in the g factor of on average 21 ? 7% over the entire spectral range following thermotherapy, and a corresponding relative increase in the scattering and absorption coefficients of 23 ? 8% and 200 ? 100%, respectively. An increase of on average 200 ? 80% was consequently found for the reduced scattering coefficient. The cause of these changes in terms of the Mie-equivalent average radius of tissue scatterers as well as of the distribution and biochemistry of tissue absorbers was analyzed, utilizing the information yielded by the g factor and the spectral shapes of the reduced scattering and absorption coefficients. These results were correlated with the alterations in the ultrastructure found in the histological evaluation. The average radius of tissue scattering centers, determined by using either the g factors calculated on the basis of Mie theory or the spectral shape of reduced scattering coefficients calculated on the Mie theory, was estimated to be 21-32% lower in treated than in untreated liver samples. The Mie-equivalent average radii of scattering centers in untreated liver tissue deduced by the two methods corresponded well and were found to be 0.31 and 0.29 mum, respectively, yielding particle sizes in the same range as the size of a mitochondrion.     

人造水雾粒度测试及红外消光因子计算分析

在大型半密闭空间内发生具有不同粒度分布的水雾体系,用喷雾激光粒度仪测试粒度分布规律并采用Van Der Hulst公式计算不同大小水雾粒子对红外辐射的散射效率因子、吸收效率因子和消光效率因子。结果表明:试验条件下水雾粒子的平均直径在5~65μm范围内。计算结果显示:水雾粒子对3～5、8～14μm红外辐射的消光作用主要取决于散射效应而非吸收效应。当水雾粒子的直径大于等于红外辐射的波长时,水雾体系对该波长红外辐射能够产生较强的消光效果。综合分析水雾体系的稳定性和消光特性,直径在3~30μm之间的水雾粒子对3～5、8～14μm红外辐射的衰减效果更为明显。     

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.     

Simulation of the optical properties of plate aggregates for application to the remote sensing of cirrus clouds

In regions of deep tropical convection, ice particles often undergo aggregation and form complex chains. To investigate the effect of the representation of aggregates on electromagnetic scattering calculations, we developed an algorithm to efficiently specify the geometries of aggregates and to compute some of their geometric parameters, such as the projected area. Based on in situ observations, ice aggregates are defined as clusters of hexagonal plates with a chainlike overall shape, which may have smooth or roughened surfaces. An aggregate representation is developed with 10 ensemble members, each consisting of between 4-12 hexagonal plates. The scattering properties of an individual aggregate ice particle are computed using either the discrete dipole approximation or an improved geometric optics method, depending upon the size parameters. Subsequently, the aggregate properties are averaged over all geometries. The scattering properties of the aggregate representation closely agree with those computed from 1000 different aggregate geometries. As a result, the aggregate representation provides an accurate and computationally efficient way to represent all aggregates occurring within ice clouds. Furthermore, the aggregate representation can be used to study the influence of these complex ice particles on the satellite-based remote sensing of ice clouds. The computed cloud reflectances for aggregates are different from those associated with randomly oriented individual hexagonal plates. When aggregates are neglected, simulated cloud reflectances are generally lower at visible and shortwave-infrared wavelengths, resulting in smaller effective particle sizes but larger optical thicknesses.