Vesicle sizing by static light scattering: a Fourier cosine transform approach

A Fourier cosine transform method, based on the Rayleigh-Gans-Debye thin-shell approximation, was developed to retrieve vesicle size distribution directly from the angular dependence of scattered light intensity. Its feasibility for real vesicles was partially tested on scattering data generated by the exact Mie solutions for isotropic vesicles. The noise tolerance of the method in recovering unimodal and biomodal distributions was studied with the simulated data. Applicability of this approach to vesicles with weak anisotropy was examined using Mie theory for anisotropic hollow spheres. Aprimitive theory about the first four moments of the radius distribution about the origin, excluding the mean radius, was obtained as an alternative to the direct retrieval of size distributions.     

Measured infrared optical cross sections for a variety of chemical and biological aerosol simulants

We conducted a series of spectral extinction measurements on a variety of aerosolized chemical and biological simulants over the spectral range 3-13 microm using conventional Fourier-transform IR (FTIR) aerosol spectroscopy. Samples consist of both aerosolized particulates and atomized liquids. Materials considered include Bacillus subtilis endospores, lyophilized ovalbumin, polyethylene glycol, dimethicone (SF-96), and three common background materials: kaolin clay (hydrated aluminum silicate), Arizona road dust (primarily SiO2), and diesel soot. Aerosol size distributions and mass density were measured simultaneously with the FTIR spectra. As a result, all optical parameters presented here are mass normalized, i.e., in square meters per gram. In an effort to establish the utility of using Mie theory to predict such parameters, we conducted a series of calculations. For materials in which the complex indices of refraction are known, e.g., silicone oil (SF-96) and kaolin, measured size distributions were convolved with Mie theory and the resultant spectral extinction calculated. Where there was good agreement between measured and calculated extinction spectra, absorption, total scattering, and backscatter were also calculated.     

Extinction-to-backscatter ratio of Asian dust observed with high-spectral-resolution lidar and Raman lidar

Extinction-to-backscatter ratio or lidar ratio is a key parameter in the issue of backscatter-lidar inversions. The lidar ratio of Asian dust was observed with a high-spectral-resolution lidar and a combined Raman elastic-backscatter lidar during the springs of 1998 and 1999. The measured values range from 42 to55 sr in most cases, with a mean of 51 sr. These values are significantly larger than those predicted by the Mie computations that incorporate measured Asian dust size distributions and a range of refractive index with a typical value of 1.55-0.005i. The enhancement of lidar ratio is mostly due to the nonsphericity of dust particles, as indicated by the T-matrix calculations for spheroid particles and a number of other theoretical studies. In addition, possible contamination of urban aerosols may also contribute somewhat in optically thin cases. Mie theory, although it can well describe spherical particle scattering, will not be sufficient to represent the scattering characteristics of irregular particles such as Asian dust, especially in directions larger than approximately 90 degrees when the size parameter is large.     

Initial phase of laser-induced air optical breakdown: a new picture

Optical breakdown has been generated by focusing YAG laser radiation in the air. The laser radiation itself was scattered due to laser-induced air optical breakdown. Angular distributions of scattered radiation at 1064, 532, and 355 nm were measured. Analysis of the distributions has been performed in terms of Mie scattering. It has been assumed that scattering of laser radiation is due mainly to highly ionized plasma balls in the initial phase of air optical breakdown. The wavelength-dependent angular distribution has been analyzed with two parameters. The mean radius and the plasma frequency of the plasma balls have been determined by a least-squares fit procedure. Observed wavelength-dependent angular distributions are in good agreement with ones calculated by Mie theory.     

Atmospheric glories: simulations and observations

Mie theory can be used to provide full-color simulations of atmospheric glories. Comparison of such simulations with images of real glories suggests that most glories are caused by spherical water droplets with radii between 4 and 25 microm. This paper also examines the appearance of glories taking into account the size of the droplets and the width of the droplet size distributions. Simulations of glories viewed through a linear polarizer compare well with the few available pictures, but they show some features that need corroboration by more observations.     

Measured Infrared Spectral Extinction for Aerosolized Bacillus subtilis var. niger Endospores from 3 to 13 mum

We measured spectral extinction in situ for aerosolized Bacillus subtilis var. niger endospores using Fourier-transform infrared spectroscopy from 3.0 to 13.0 mum. Corresponding aerosol size distributions were measured with a commercially available elastic light-scattering probe and verified by direct particle capture and subsequent counting by video microscopy. Aerosol mass density was monitored simultaneously with conventional dosimetry and was used to mass normalize the measured spectral extinction. Mie theory calculations based on measured distributions and available complex indices of refraction agreed well. We also present resultant Mie calculations for the absorption, total scattering, and backscatter. For comparison, measured spectral extinction for three common environmental aerosols is also presented, i.e., for water fog, diesel soot, and Arizona road dust.     

经典Mie散射的数值计算方法改进

在光散射颗粒测量技术中,Mie散射理论的计算非常重要。本文介绍一种改进的Mie散射数值计算方法,通过对Mie散射系数进行重新构造,找到参量来控制Mie计算的收敛和计算精度。对各有关参量选用合适、稳定的递推关系进行计算。数值计算结果表明该方法具有快速、稳定的优点,可以在极大的颗粒粒径和折射率范围内得到合理结果。     

Radiative Properties of Silica Nanoporous Matrices

Superinsulating materials are currently of much interest because of the price of energy on the one hand and CO₂ emissions attributed to offices and houses cooling and heating on the other hand. In this work, we aim at understanding and modeling the radiative transfer within silica nanoporous matrices that are the principal components of nanoporous superinsulating materials. We first elaborate samples of various thicknesses from a pyrogenic silica powder. These samples are characterized using two spectrophotometers on the whole wavelength range [250 nm; 20 μm]. Using a parameter identification technique, we compute the radiative properties of the various samples. Then, our samples being made of packed quasi-spherical particles, we use the Mie theory to model the radiative properties of these materials. Due to the observed discrepancies between the experimental radiative properties and those computed from the Mie theory with a uniform value of 10 nm for the scatterer diameter (value derived from TEM images), we determine an effective scatterer diameter that allows a good agreement between the experimental radiative properties and the Mie results. Nevertheless, in the short wavelength range, the Mie theory gives results that significantly differ from the experimental radiative properties. This behavior is attributed to structure effects as the wavelength is of the same order of magnitude as the diameter of the scatterer that is now regarded as an aggregate of nanoparticles. Hence, to take into account these effects, we use the discrete dipole approximation (DDA). The DDA extinction coefficient spectra appear to be much closer to the experimental results than the Mie spectra, and these first results are quite encouraging.     

基于米氏散射及夫朗和费衍射的FAM激光测粒仪

提出了综合运用夫朗和费衍射和米氏散射，即在大粒径范围内采用夫朗和费衍射理论，而在小粒径范围内采用米氏散射理论，来改善小粒径范围内的测量精度，保证激光测粒仪在整个粒径范围内的测量精度。     

Mie理论在静态光散射粒度测量的应用下限研究

测量下限是光散射颗粒测试技术的关键问题。本文通过理论分析、比较归一化散射光强的分布图和构造方差函数F(d)对颗粒散射光的光强分布进行了定性和定量的讨论,对Mie散射向Rayleigh散射趋近的情况进行了分析,讨论了散射光光强大小的分布,分析了测量不同粒径的颗粒的可行性,最终得到在入射光源是波长为0.6328μm的He-Ne激光器的情况下,当粒径d取200nm以上时,不同粒径颗粒的M ie散射光强分布有较大差别,适合用静态光散射的方法来判断颗粒粒径。     

Numerical study of particle-size distributions retrieved from angular light-scattering data using an evolution strategy with the Fraunhofer approximation

An algorithm is presented based on an evolution strategy to retrieve a particle size distribution from angular light-scattering data. The analyzed intensity patterns are generated using the Mie theory, and the algorithm retrieves a series of known normal, gamma, and lognormal distributions by using the Fraunhofer approximation. The distributions scan the interval of modal size parameters 100 < or = alpha < or = 150. The numerical results show that the evolution strategy can be successfully applied to solve this kind of inverse problem, obtaining a more accurate solution than, for example, the Chin-Shifrin inversion method, and avoiding the use of a priori information concerning the domain of the distribution, commonly necessary for reconstructing the particle size distribution when this analytical inversion method is used.     

Size distribution of mineral aerosol: using light-scattering models in laser particle sizing

The size distribution of semitransparent irregularly shaped mineral dust aerosol samples is determined using a commonly used laser particle-sizing technique. The size distribution is derived from intensity measurements of singly scattered light at various scattering angles close to the forward-scattering direction at a wavelength of 632.8 nm. We analyze the results based on various light-scattering models including diffraction theory, Mie calculations for spheres with various refractive indices, and T-matrix calculations for spheroidal particles. We identify systematic errors of the retrieved size distribution when the semitransparent and nonspherical properties of the particles are neglected. Synthetic light-scattering data for a variety of parameterized size distributions of spheres and spheroids are used to investigate the effect of simplifying assumptions made when the diffraction model or Mie theory is applied in the retrieval.     

Visible and near-infrared backscattering spectroscopy for sizing spherical microparticles

Scattering is a useful tool for the determination of particle size in solution. In particular, spectroscopic analysis of backscattering renders the possibility of a simplified experimental setup and direct data processing using Mie theory. We show that a simple technique based on near-infrared (NIR) backscattering spectroscopy together with the development of the corresponding algorithm based on Fourier transform (FT) and Mie theory are a powerful tool for sizing microparticles in the range from 8 to 60 microm diameter. There are three wavelength intervals in the NIR, within which different diameter ranges were analyzed. In each one, the FT yields a coarse diameter value with an uncertainty dependent on the wavelength range. A more accurate value is obtained by further applying cross correlation between experimental and theoretical spectra. This latter step reduces the uncertainty in diameter determination between 30% and 40%, depending on wavelength interval and particle diameter. These results extend previous information on visible backscattering spectroscopy applied to sizing microparticles in the range between 1 and 24 mum diameter. This technique could be the basis for the construction of a portable and practical instrument.     

Mie light-scattering granulometer with adaptive numerical filtering. I. Theory

A search procedure based on a least-squares method including a regularization scheme constructed from numerical filtering is presented. This method, with the addition of a nephelometer, can be used to determine the particle-size distributions of various scattering media (aerosols, fogs, rocket exhausts, motor plumes) from angular static light-scattering measurements. For retrieval of the distribution function, the experimental data are matched with theoretical patterns derived from Mie theory. The method is numerically investigated with simulated data, and the performance of the inverse procedure is evaluated. The results show that the retrieved distribution function is quite reliable, even for strong levels of noise.     

Generalized eikonal approximation for fast retrieval of particle size distribution in spectral extinction technique

In retrieving particle size distribution from spectral extinction data, a critical issue is the calculation of extinction efficiency, which affects the accuracy and rapidity of the whole retrieval. The generalized eikonal approximation (GEA) method, used as an alternative to the rigorous Mie theory, is introduced for retrieval of the unparameterized shape-independent particle size distribution (PSD). To compute the extinction efficiency more efficiently, the combination of GEA method and Mie theory is adopted in this paper, which not only extends the applicable range of the approximation method but also improves the speed of the whole retrieval. Within the framework of the combined approximation method, the accuracy and limitations of the retrieval are investigated. Moreover, the retrieval time and memory requirement are also discussed. Both simulations and experimental results show that the combined approximation method can be successfully applied to retrieval of PSD when the refractive index is within the validity range. The retrieval results we present demonstrate the high reliability and stability of the method. By using this method, we find the complexity and computation time of the retrieval are significantly reduced and the memory resources can also be saved effectively, thus making this method more suitable for online particle sizing.     

Monte Carlo modeling of optical coherence tomography imaging through turbid media

We combine a Monte Carlo technique with Mie theory to develop a method for simulating optical coherence tomography (OCT) imaging through homogeneous turbid media. In our model the propagating light is represented by a plane wavelet; its line propagation direction and path length in the turbid medium are determined by the Monte Carlo technique, and the process of scattering by small particles is computed according to Mie theory. Incorporated into the model is the numerical phase function obtained with Mie theory. The effect of phase function on simulation is also illustrated. Based on this improved Monte Carlo technique, OCT imaging is directly simulated and phase information is recorded. Speckles, resolution, and coherence gating are discussed. The simulation results show that axial and transversal resolutions decrease as probing depth increases. Adapting a light source with a low coherence improves the resolution. The selection of an appropriate coherence length involves a trade-off between intensity and resolution.     

Simulation of rainbows,coronas, and glories by use of Mie theory

Mie theory offers an exact solution to the problem of scattering of sunlight by spherical drops of water. Until recently, most applications of Mie theory to scattering of light were restricted to a single wavelength. Mie theory can now be used on modern personal computers to produce full-color simulations of atmospheric optical effects, such as rainbows, coronas, and glories. Comparison of such simulations with observations of natural glories and cloudbows is encouraging.     

Particulate-matter distribution and its flow from power plants using infrared spectrometry and thermodynamics for in situ continuous emissions monitoring

Spectroscopy measurements made through a continuum having suspended particulate matter are addressed. The applications presented permit correction of spectral transmissions as effected by particulate-producing fossil-fuel combustion. The research is especially applicable to large effluent flows from coal-fired power plants, whose effluents are studied with in situ (smokestack) radiometers. Methods involving fast calculation procedures based on measured irradiances in unabsorbed regions of the IR spectrum are presented. The methodology is based on wavelength-dependent extinction of radiation by small particles, considering both elastic scattering and absorbing effects. This extinction leads to an observed skeweness (or shift) of the blackbody spectral shape. Based on such skeweness, the particulate number distribution is determined with Mie theory. In order to simplify, and to speed up the routine for real-time application, a two-step procedure is presented. During preinstallation calibration with Mie theory, sets of integral tables are computed for all possible solution values and stored in computer memory. Based on instantaneous spectral measurements, the appropriate integral tables are retrieved, then used as inputs in a process leading to particulate number distribution. Because all time-consuming calculations associated with Mie theory are performed during preinstallation calibration, the technique is capable of monitoring particulate emission in real time. Furthermore, given resolution of the number distribution in combination with thermodynamic analysis of the system, determination of particulate apparent density and particulate mass flow rate is made. These values have importance for environmental reporting. Comparisons of calculated particulate distributions with in situ measurements are also presented. Confirmatory testing programs conducted at several power plants are discussed.     

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.     

Single scattering by red blood cells

A highly diluted suspension of red blood cells (hematocrit 0.01) was illuminated with an Ar or a dye laser in the wavelength range of 458-660 nm. The extinction and the angle-resolved intensity of scattered light were measured and compared with the predictions of Mie theory, the Rayleigh-Gans approximation, and the anomalous diffraction approximation. Furthermore, empirical phase functions were fitted to the measurements. The measurements were in satisfactory agreement with the predictions of Mie theory. However, better agreement was found with the anomalous diffraction model. In the Rayleigh-Gans approximation, only small-angle scattering is described appropriately. The scattering phase function of erythrocytes may be represented by the Gegenbauer kernel phase function.