Analysis of particle sizes, concentration, and refractive index in measurement of light transmittance in the forward-scattering-angle range

A simple method for determining the mean size, the concentration, and the refractive index of the monodispersion and the polydispersion of particles has been presented. The method is based on the empirical inversion of measurements of forward-angle light-scattering transmittance. The effects of particle size distribution and optical constants on forward-angle-scattering transmittance have been considered by using Mie theory. The proposed method has been used successfully for single latex spheres in water and polydispersed weakly absorbing particles of Al(2) O(3) and SiO(2) in the flow of the propane-air flame combustion products.     

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.     

Mass-specific scattering coefficient for natural minerogenic particle populations: particle size distribution effect and closure analyses

The relationship between the particulate scattering coefficient (b(p)) and the concentration of suspended particulate matter (SPM), as represented by the mass-specific scattering coefficient of particulates (b(p)*=b(p)/SPM), depends on particle size distribution (PSD). This dependence is quantified for minerogenic particle populations in this paper through calculations of b(p)* for common minerals as idealized populations (monodispersed spheres); contemporaneous measurements of b(p), SPM, and light-scattering attributes of mineral particles with scanning electron microscopy interfaced with automated image and x-ray analyses (SAX), for a connected stream-reservoir system where minerogenic particles dominate b(p); and estimates of b(p) and its size dependency (through SAX results-driven Mie theory calculations), particle volume concentration, and b(p)*. Modest changes in minerogenic PSDs are shown to result in substantial variations in b(p)*. Good closure of the SAX-based estimates of b(p) and particle volume concentration with bulk measurements is demonstrated. Converging relationships between b(p)* and particle size, developed from three approaches, were well described by power law expressions.     

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.     

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.     

Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment

This study compares the optical coefficients of size-selected soot particles measured at a wavelength of 870 nm with those predicted by three theories, namely, Rayleigh-Debye-Gans (RDG) approximation, volume-equivalent Mie theory, and integral equation formulation for scattering (IEFS). Soot particles, produced by a premixed ethene flame, were size-selected using two differential mobility analyzers in series, and their scattering and absorption coefficients were measured with nephelometry and photoacoustic spectroscopy. Scanning electron microscopy and image processing techniques were used for the parameterization of the structural properties of the fractal-like soot aggregates. The aggregate structural parameters were used to evaluate the predictions of the optical coefficients based on the three light-scattering and absorption theories. Our results show that the RDG approximation agrees within 10% with the experimental results and the exact electromagnetic calculations of the IEFS theory. Volume-equivalent Mie theory overpredicts the experimental scattering coefficient by a factor of approximately 3.2. The optical coefficients predicted by the RDG approximation showed pronounced sensitivity to changes in monomer mean diameter, the count median diameter of the aggregates, and the geometric standard deviation of the aggregate number size distribution.     

Absolute real-time measurement of particle size distribution with the flying light-scattering indicatrix method

The flying light-scattering indicatrix (FLSI, angular dependency of the intensity of light scattered by a moving individual particle) method, based on a scanning flow cytometer (SFC) that permits measurement of individual particle characteristics from light-scattering data, has been used for the determination of size distribution of the following particles: polystyrene latex, milk fat, and spores (Penicillium levitum, Aspergillus pseudoglaucus). The optical system of the SPC and empirical equations provided absolute sizing at the rate of 50 particles/s. Size distributions obtained with the FLSI method and a best-fit procedure using Mie scattering theory have been compared.     

Discrete-dipole-approximation-based light-scattering calculations for particles with a real refractive index smaller than unity

To assess the efficiency and accuracy of light-scattering calculations based on the discrete dipole approximation (DDA) for particles with a real relative refractive index smaller than unity, differential scattering cross sections and scattering efficiency factors were calculated for spherical particles. We performed the calculations for oxide particles and voids embedded in glass and silicon, using the exact scattering theory (Mie scattering) and the DDA. A comparison of the results shows that the DDA is applicable in the above refractive-index regime, and the conditions under which DDA-based calculations can provide scattering data with good accuracy are discussed.     

Color effects of uniform colloidal particles of different morphologies packed into films

The experimentally determined chromaticities and reflectance spectra of films consisting of uniform ellipsoidal or spherical colloidal hematite particles are compared with calculated values and are found to be in good agreement. The theoretical treatment of the light-scattering problem involves the Mie theory for the spheres and the T-matrix method for the ellipsoids. The reflectance spectra for the pigment films are calculated through the use of the Kubelka-Munk analysis.     

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.     

颗粒层状结构对散射特性及激光粒度测量的影响

根据Aden-Kerker理论,对双层颗粒前向散射特性进行了研究。在此基础上,分别用衍射理论、Mie理论和Aden-Kerker理论计算了散射系数矩阵并采用非独立模式算法进行反演。数值计算结果表明,双层颗粒的散射光强由颗粒折射率和内外径决定,在实际的激光前向散射粒度测量中,如果沿用Fraunhofer衍射理论或Mie理论计算系数矩阵,在测量双层颗粒时,反演结果会有一定的误差。相比于Mie理论,衍射理论的反演误差更大。     

Application of dynamic light scattering to the study of small marine particles

Small particles ranging from approximately 0.1 μm to several micrometers in size, which include detrital material, bacteria, and other planktonic microorganisms, make a significant contribution to light scattering in the upper ocean. The scattering properties of these particles are strongly dependent on their size, which is difficult to measure in the submicrometer range with commonly used electronic resistive counters and microscopic techniques. We examined the size of small marine particles by application of the dynamic light scattering (DLS) method. In this method the time-dependent autocorrelation function of scattered intensity by particles undergoing Brownian motion provides information about the size of particles. The samples were collected in clear oceanic waters off the coast of Southern California. The mean hydrodynamic diameter of particles, determined from the DLS measurements at a scattering angle of 45°, was 0.54μ m. This indicates that the major contribution to scattering at this angle comes rom submicrometer particles. We also described an inverse method for estimating the general slope of the size distribution of small marine particles from the mean hydrodynamic diameter. This method is based on calculations of the size distribution weighted by distribution from Mie theory and assumes that a power-law approximation represents the actual particle scattered intensity. These calculations suggested that particulate assemblage in our seawater samples was best characterized by a differential size distribution with a slope of -4.35. This estimation was supported by independent measurements of particle size distribution and the spectral beam attenuation coefficient taken from the same samples as those used for the DLS measurements. We also demonstrated that multiangle DLS measurements may be used to determine the representative value of the refractive index of particles.     

Use of equivalent spheres to model the relation between radar reflectivity and optical extinction of ice cloud particles

The effect of ice crystal size and shape on the relation between radar reflectivity and optical extinction is examined. Discrete-dipole approximation calculations of 95-GHz radar reflectivity and ray-tracing calculations are applied to ice crystals of various habits and sizes. Ray tracing was used primarily to calculate optical extinction and to provide approximate information on the lidar backscatter cross section. The results of the combined calculations are compared with Mie calculations applied to collections of different types of equivalent spheres. Various equivalent sphere formulations are considered, including equivalent radar-lidar spheres; equivalent maximum dimension spheres; equivalent area spheres, and equivalent volume and equivalent effective radius spheres. Marked differences are found with respect to the accuracy of different formulations, and certain types of equivalent spheres can be used for useful prediction of both the radar reflectivity at 95 GHz and the optical extinction (but not lidar backscatter cross section) over a wide range of particle sizes. The implications of these results on combined lidar-radar ice cloud remote sensing are discussed.     

A STUDY OF THE ACCURACY OF OPTICAL FRAUNHOFER DIFFRACTION SIZE ANALYZER

In this paper the discrepance of scattered light between Mie theory and Fraunhofer diffraction is showed at different refractive indexes and sizes of particle. The accuracy of the Malvern particle size analyzer is discussed when it is used to measure small particles and some advice is proposed for its use.     

Light scattering by dust particles in microgravity: polarization and brightness imaging with the new version of the PROGRA2 instrument

A new version of the PROGRA2 instrument, dedicated to measuring the polarization phase function of various kinds of solid particles, allows obtaining maps of polarization and brightness with a spatial resolution of a few tens of micrometers. The measurements are conducted in microgravity during parabolic flights to ensure random distribution and orientation of the particles. The results of the first two sessions are presented. Comparison between measurements and Mie theory modeling for glass spheres shows that the instrument works well and that accurate results can be obtained even at small phase angles. Results for irregularly shaped particles are also presented.     

Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results

A general method is developed to formulate extinction and absorption efficiency for nonspherical particles at arbitrary and random orientations by use of anomalous diffraction theory (ADT). An ADT for finite circular cylinders is evaluated as an example. Existing ADT's for infinite cylinders at arbitrary orientations and for finite cylinders at the normal incidence are shown to be special cases of the new formulation. ADT solutions for finite cylinders are shown to approach the rigorous T-matrix results when the refractive indices approach unity. The importance of some physical processes that are neglected in the ADT approximation are evaluated by comparisons between ADT and rigorous calculations for different particle geometries. For spheres, van de Hulst's ADT and Mie theory are used, whereas the ADT that we present and T-matrix calculations are used for cylinders of different diameter-to-length ratios. The results show that the differences in extinction between ADT and exact solutions generally decrease with nonsphericity. A similar decrease occurs for absorption at wavelengths of relatively strong absorption. The influence of complex refractive index is evaluated. Our results suggest that ADT may provide a useful approximation in parameterization and remote sensing of cirrus clouds in the Christiansen bands where the real part of the refractive index approaches unity and/or where relative absorption is strong.     

A STUDY OF THE ACCURACY OF OPTICAL FRAUNHOFER DIFFRACTION SIZE ANALYZER

ABSTRACT

In this paper the discrepance of scattered light between Mie theory and Fraunhofer diffraction is showed at different refractive indexes and sizes of particle. The accuracy of the Malvern particle size analyzer is discussed when it is used to measure small particles and some advice is proposed for its use.     

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.     

Modeling radiation characteristics of semitransparent media containing bubbles or particles

Modeling of radiation characteristics of semitransparent media containing particles or bubbles in the independent scattering limit is examined. The existing radiative properties models of a single particle in an absorbing medium using the approaches based on (1) the classical Mie theory neglecting absorption by the matrix, (2) the far field approximation, and (3) the near field approximation are reviewed. Comparison between models and experimental measurements are carried out not only for the radiation characteristics but also for hemispherical transmittance and reflectance of porous fused quartz. Large differences are found among the three models predicting the bubble radiative properties when the matrix is strongly absorbing and/or the bubbles are optically large. However, these disagreements are masked by the matrix absorption during calculation of radiation characteristics of the participating medium. It is shown that all three approaches can be used for radiative transfer calculations in an absorbing matrix containing bubbles.     

Estimation of complex refractive index of polydisperse particulate systems from multiple-scattered ultraviolet-visible-near-infrared measurements

A method to extract the complex refractive index of spherical particles from a polydisperse suspension at concentrations where multiple light-scattering effects are significant is presented. The optical constants are estimated from total diffuse reflectance and transmittance measurements and inverting the measurements using the radiative transfer equation (RTE) and the Mie theory for scattering by polydisperse spherical particles. The method is tested by applying it to three different polydisperse polystyrene suspensions and extracting the optical constants of polystyrene particles in the wavelength range of 450-1200 nm. The effect of particle size, concentration, and polydispersity on the estimated values of the optical constants is also discussed.