Rayleigh-Gans Approximation Research Articles

Transmittance predictions for transparent alumina ceramics based on the complete grain size distribution or a single mean grain size replacing the whole distribution

A simple method, based on the equivalent composite model or the dense polycrystalline model, is proposed for predicting the in-line transmittance in ceramics with a grain size distribution of birefringent crystallites. It is shown that the transmittance predictions based on the Rayleigh-Gans approximation are indistinguishable from those based on Mie theory, so that the latter can be replaced by the former. Based on normal distributions of different position and width it is shown that size distributions with smaller mean sizes lead to higher transmittance, whereas the effect of the distribution width on the transmittance is comparatively weak (with the narrowest distribution being the most favorable for high transmittance). The key result of this paper is the fact that for the distributions investigated (normal and log-normal) the transmittance prediction based the whole grain size distribution can be replaced by a transmittance prediction based on the geometric mean of the intensity-weighted distribution.

Allometric Vegetation Modeling and SAR Image Simulation for Polarimetry and Interferometry

This paper establishes a low degrees-of-freedom allometric vegetation model based on the Biomass and allometry database (BAAD). It consists of a 5-bit species encoding scheme and a 5-parameter relationship derived from the BAAD data records. Combined with opensource fractal tree generation engine, it can produce realistic tree samples of a large variety of species. A coherent electromagnetic scattering calculation method is developed for the vegetation model where the generalized Rayleigh-Gans (GRG) approximation and the infinite cylinder approximation are used to calculate the scattering matrix of leaves and branches/trunk. Four-path multiple scattering mechanisms between vegetation and the ground are considered and attenuations through vegetation canopy are also considered. The scattering model is validated against numerical methods. In addition, an end-to-end simulation tool is developed. Optical image is used to extract individual trees with center positions and crown diameters. The rest parameters are generated using the derived allometry model. Virtual 3D scene with vegetation on digital elevation map (DEM) can be generated and SAR images can be simulated. Several case studies are carried out for both polarimetric synthetic aperture radar (SAR) interferometry (PolInSAR) and multi-temporal interferometric SAR (InSAR). One case of the Mount Fuji area is simulated and validated against ALOS-2 data and demonstrates an average scattering coefficient error of less than 3dB. Additional cases of Southwest China, Hainan Island and the Great Khingan Mountain demonstrate the feasibility of the proposed simulation scheme for various application scenarios.

SnowScatt 1.0: consistent model of microphysical and scattering properties of rimed and unrimed snowflakes based on the self-similar Rayleigh–Gans approximation

Abstract. More detailed observational capabilities in the microwave (MW) range and advancements in the details of microphysical schemes for ice and snow demand increasing complexity to be included in scattering databases. The majority of existing databases rely on the discrete dipole approximation (DDA) whose high computational costs limit either the variety of particle types or the range of parameters included, such as frequency, temperature, and particle size. The snowScatt tool is innovative in that it provides consistent microphysical and scattering properties of an ensemble of 50 000 snowflake aggregates generated with different physical particle models. Many diverse snowflake types, including rimed particles and aggregates of different monomer composition, are accounted for. The scattering formulation adopted by snowScatt is based on the self-similar Rayleigh–Gans approximation (SSRGA), which is capable of modeling the scattering properties of large ensembles of particles. Previous comparisons of SSRGA and DDA are extended in this study by including unrimed and rimed aggregates up to centimeter sizes and frequencies up to the sub-millimeter spectrum. The results generally reveal the wide applicability of the SSRGA method for active and passive MW applications. Unlike DDA databases, the set of SSRGA parameters can be used to infer scattering properties at any frequency and refractive index; snowScatt also provides tools to derive the SSRGA parameters for new sets of particle structures, which can be easily included in the library. The flexibility of the snowScatt tool with respect to applications that require continuously changing definitions of snow properties is demonstrated in a forward simulation example based on the output of the predicted particle properties (P3) scheme. The snowScatt tool provides the same level of flexibility as commonly used T-matrix solutions, while the computed scattering properties reach the level of accuracy of detailed discrete dipole approximation calculations.

An accurate and computationally cheap microwave scattering method for ice aggregates: the Independent Monomer Approximation

AbstractThe Discrete Dipole Approximation (DDA) is widely used to simulate scattering of microwaves by snowflakes, by discretising the snowflake into small ‘dipoles’ which oscillate in response to (a) the incident wave, and (b) scattered waves from all the other dipoles in the particle. It is this coupling between all dipole pairs which makes solving the DDA system computationally expensive, and that cost grows nonlinearly as the number of crystals n within an aggregate is increased. Motivated by this, many studies have ignored the dipole coupling (the Rayleigh–Gans Approximation, RGA). However, use of RGA leads to systematic underestimation of both scattering and absorption, and an inability to predict polarimetric properties. To address this, we present a new approach (the Independent Monomer Approximation, IMA) which solves the DDA system for each crystal ‘monomer’ separately, then combines them to construct the full solution. By including intra‐monomer coupling, but neglecting inter‐monomer coupling, we save a factor of n in computation time over DDA. Benchmarking IMA against DDA solutions indicates that its accuracy is greatly superior to RGA, and provides ensemble scattering cross‐sections which closely agree with their more expensive DDA counterparts, particularly at size parameters smaller than ∼ 5 . Addition of rime to the aggregates does not significantly degrade the results, despite the increased density. The use of IMA for radar remote sensing is evaluated, and we show that multi‐wavelength and multi‐polarisation parameters are successfully captured to within a few tenths of a dB for aggregates probed with frequencies between 3 and 200 GHz, in contrast to RGA where errors of up to 2.5 dB are observed. Finally, we explore the realism of the IMA solutions in greater detail by analysing internal electric fields, and discuss some broader insights that IMA provides into the physical features of aggregates that are important for microwave scattering.

Light scattering models for describing the transmittance of transparent and translucent alumina and zirconia ceramics

The original Apetz-van-Bruggen model for predicting the transmittance of dense polycrystalline ceramics with randomly oriented birefringent crystallites is shown to be incorrect. In a correct Apetz-van-Bruggen equivalent composite model (ECM) the volume fraction must be 1/3 instead of 1/2 and the factor 2/3 in front of the maximum birefringence must be abandoned. This ECM is in good agreement with the simplified version of Pecharromán’s dense polycrystalline model (DPM) and can be improved by replacing the Jobst approximation (i.e. the large-size limit of the Rayleigh-Gans approximation) by the van-de-Hulst approximation. Similarly, a new DPM is proposed that combines the van-de-Hulst approximation with Pecharromán’s texture function. However, all these models fail for small grains. Therefore two new models (infimum-supremum-based ECM and DPM) are proposed, which combine the full Rayleigh-Gans approximation (for small grains) with the van-de-Hulst approximation (for large grains) and provide (for all grain sizes) predictions almost identical to Mie theory.

PAMTRA 1.0: the Passive and Active Microwave radiative TRAnsfer tool for simulating radiometer and radar measurements of the cloudy atmosphere

Abstract. Forward models are a key tool to generate synthetic observations given knowledge of the atmospheric state. In this way, they are an integral part of inversion algorithms that aim to retrieve geophysical variables from observations or in data assimilation. Their application for the exploitation of the full information content of remote sensing observations becomes increasingly important when these are used to evaluate the performance of cloud-resolving models (CRMs). Herein, CRM profiles or fields provide the input to the forward model whose simulation results are subsequently compared to the observations. This paper introduces the freely available comprehensive microwave forward model PAMTRA (Passive and Active Microwave TRAnsfer), demonstrates its capabilities to simulate passive and active measurements across the microwave spectral region for upward- and downward-looking geometries, and illustrates how the forward simulations can be used to evaluate CRMs and to interpret measurements to improve our understanding of cloud processes. PAMTRA is unique as it treats passive and active radiative transfer (RT) in a consistent way with the passive forward model providing upwelling and downwelling polarized brightness temperatures and radiances for arbitrary observation angles. The active part is capable of simulating the full radar Doppler spectrum and its moments. PAMTRA is designed to be flexible with respect to instrument specifications and interfaces to many different formats of input and output, especially CRMs, spanning the range from bin-resolved microphysical output to one- and two-moment schemes, and to in situ measured hydrometeor properties. A specific highlight is the incorporation of the self-similar Rayleigh–Gans approximation (SSRGA) for both active and passive applications, which becomes especially important for the investigation of frozen hydrometeors.

Evaluation of differential absorption radars in the 183 GHz band for profiling water vapour in ice clouds

Abstract. Relative humidity (RH) measurements in ice clouds are essential for determining ice crystal growth processes and rates. A differential absorption radar (DAR) system with several frequency channels within the 183.3 GHz water vapour absorption band is proposed for measuring RH within ice clouds. Here, the performance of a DAR system is evaluated by applying a DAR simulator to A-Train observations in combination with co-located European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis. Observations from the CloudSat W-band radar and from the CALIPSO lidar are converted first into ice microphysical properties and then coupled with ECMWF temperature and relative humidity profiles in order to compute scattering properties at any frequency within the 183.3 GHz band. A self-similar Rayleigh–Gans approximation is used to model the ice crystal scattering properties. The radar reflectivities are computed both for a space-borne and airborne and a ground-based DAR system by using appropriate radar receiver characteristics. Sets of multi-frequency synthetic observation of attenuated reflectivities are then exploited to retrieve profiles of water vapour density by fitting the line shape at different levels. A total of 10 d of A-Train observations are used to test the measurement technique performance for different combinations of tones when sampling ice clouds globally. Results show that water vapour densities can be derived at the level that can enable ice process studies (i.e. better than 3 %), both from a ground-based system (at the minute temporal scale and with circa 100 m vertical resolution) and from a space-borne system (at 500 m vertical resolution and with circa 5 km integration lengths) with four tones in the upper wing of the absorption line. Deploying ground-based DAR system at high latitudes and high altitudes is highly recommended to test the findings of this work in the field.

Analysis of the internal electric fields of pristine ice crystals and aggregate snowflakes, and their effect on scattering

The discrete dipole approximation is used to explore the internal electric fields of plane-wave-illuminated ice particles, and analyse their differential scattering cross sections. The results are displayed for monocrystals and aggregates of size parameters x=2 and x=10. We show that the field is relatively uniform for x=2, but for monocrystals of x=10 there is a complex internal structure. For a hexagonal plate, this structure is a combination of two components: a “distorted” plane wave, with wavefronts aligned perpendicular to the incident wave close to the centre of the plate, and curved forward near the particle boundary; and a standing wave, internally reflected around the perimeter. The former is due to the transverse component of the field i.e., the component perpendicular to the incident wave, and the latter is due to the component parallel to the incident direction. Focussing of the field towards the forward side of the particle is observed. As the particle complexity is increased due to aggregation, the field becomes smoother and less focussing is seen. For complex aggregates, the individual monomers act independently of one another, suggesting simplified methods of calculating scattering from such particles. The influence of the internal fields on far-field scattering is explored. It is demonstrated that scattering in the forward and backward directions is dominated by the transverse component. The parallel component contributes to sidescattering, with its influence on total scattering decreasing with particle complexity. We propose that this is due to the inability of complex particles to maintain a standing wave, diminishing much of the sidescattering observed for monocrystals. Comparisons of the far-field scattering properties of complex aggregates using the discrete dipole and Rayleigh–Gans approximations are also presented for x=2 and x=10, along with results obtained using a soft sphere approximation.

Measuring nanoparticles in the size range to 2000\xa0nm

Measurement of light scattered from suspensions of monodisperse nanoparticles in solution (“turbidity”) long has been used to derive their size. Following some means of fractionation, the light (monochromatic) scattered by the particles into a set of distinct angles is collected and a non-linear least squares fit was made to an appropriate theory in order to extract their size. For a wide range of particle structures, where this process becomes very complex and of questionable validity, there is a far simpler interpretive means based upon measurements at extremely small, and often inaccessible, scattering angles. A method is described whereby the required small angle values are derived from measurements made over a range of larger, more readily accessible, angles. Although the basis for the analyses developed is the Rayleigh-Gans approximation, the results presented confirm that the method provides meaningful results up to a size of about 2000 nm. The larger sizes are well beyond the RG limits.

Evaluation of the Rayleigh–Gans approximation for microwave scattering by rimed snowflakes

We have evaluated the applicability of the Rayleigh–Gans approximation (RGA) and self‐similar Rayleigh–Gans approximation (SSRGA) for microwave scattering by rimed snowflakes. This study extends previous findings that showed that, for unrimed snowflakes, the RGA is in good agreement with the discrete dipole approximation (DDA), which we used as a reference method. When riming is introduced, the RGA‐derived scattering properties of individual snowflakes deviate significantly – up to 20–25 dB for the backscattering cross‐section in the W band – from the corresponding DDA results. In contrast, the average scattering properties given by RGA are in good agreement with DDA for all but the most heavily rimed snowflakes: the mean bias in the backscattering cross‐section rarely exceeds 1 dB for light and moderate riming. We also found that an adjustment that accounts for the non‐spherical shapes of ice crystals can help eliminate the small constant bias found in RGA in earlier studies. The SSRGA approximates the RGA results with good accuracy at all degrees of riming, indicating that it, too, can be used with up to moderately rimed snowflakes.

Calculating the millimetre‐wave scattering phase function of snowflakes using the self‐similar Rayleigh–Gans Approximation

Exploitation of millimetre‐wave radiometer and radar observations of ice clouds and snow requires the ability to model the scattering properties of snowflakes. This article extends the Self‐Similar Rayleigh–Gans Approximation (SSRGA) for rapid computation of the backscatter cross‐section of ice aggregates, to compute the full scattering phase function, the scattering and absorption cross‐sections and the asymmetry factor. We also show that the Rayleigh–Gans Approximation (RGA) may be improved to represent the enhanced scattering and absorption when the monomers from which the aggregate is composed are non‐spherical. The new model is shown to perform well when compared to benchmark 94 and 183 GHz Discrete Dipole Approximation (DDA) calculations of the scattering by simulated unrimed aggregates of maximum dimension up to 1 cm that have a mass–size relationship in the range observed from aircraft. For denser particles, such as would result from riming, the validity of the underlying RGA becomes questionable and both the backscatter and scattering cross‐sections can be underestimated by a factor of 2.

Lord of the Rings – Return of the King:Swift-XRT observations of dust scattering rings around V404 Cygni

On 2015 June 15, the black hole X-ray binary V404 Cygni went into outburst, exhibiting extreme X-ray variability which culminated in a final flare on June 26. Over the following days, the Swift-X-ray Telescope detected a series of bright rings, comprising five main components that expanded and faded with time, caused by X-rays scattered from the otherwise unobservable dust layers in the interstellar medium in the direction of the source. Simple geometrical modelling of the rings’ angular evolution reveals that they have a common temporal origin, coincident with the final, brightest flare seen by INTEGRAL's JEM X-1, which reached a 3–10?keV flux of ?25 Crab. The high quality of the data allows the dust properties and density distribution along the line of sight to the source to be estimated. Using the Rayleigh–Gans approximation for the dust scattering cross-section and a power-law distribution of grain sizes a, ??a?q, the average dust emission is well modelled by q=3.90+0.09?0.08 and maximum grain size of a+=0.147+0.024?0.004 ?m, though significant variations in q are seen between the rings. The recovered dust density distribution shows five peaks associated with the dense sheets responsible for the rings at distances ranging from 1.19 to 2.13?kpc, with thicknesses of ?40–80?pc and a maximum density occurring at the location of the nearest sheet. We find a dust column density of Ndust ? (2.0–2.5) × 1011?cm?2, consistent with the optical extinction to the source. Comparison of the inner rings’ azimuthal X-ray evolution with archival Wide-field Infrared Survey Explorer mid-IR data suggests that the second most distant ring follows the general IR emission trend, which increases in brightness towards the Galactic north side of the source.

The dust scattering halo of Cygnus X-3

Dust grains scatter X-ray light through small angles, producing a diffuse halo image around bright X-ray point sources situated behind a large amount of interstellar material. We present analytic solutions to the integral for the dust scattering intensity, which allow for a Bayesian analysis of the scattering halo around Cygnus X-3. Fitting the optically thin 4-6 keV halo surface brightness profile yields the dust grain size and spatial distribution. We assume a power law distribution of grain sizes ($n \propto a^{-p}$) and fit for $p$, the grain radius cut-off amax, and dust mass column. We find that a $p \approx 3.5$ dust grain size distribution with amax $\approx 0.2$ um fits the halo profile relatively well, whether the dust is distributed uniformly along the line of sight or in clumps. We find that a model consisting of two dust screens, representative of foreground spiral arms, requires the foreground Perseus arm to contain 80\% of the total dust mass. The remaining 20\% of the dust, which may be associated with the outer spiral arm of the Milky Way, is located within 1 kpc of Cyg X-3. Regardless of which model was used, we found $\tau_{\rm sca} \sim 2 \ E_{\rm keV}^{-2}$. We examine the energy resolved halos of Cyg X-3 from 1 - 6 keV and find that there is a sharp drop in scattering halo intensity when $E < 2-3$ keV, which cannot be explained with multiple scattering effects. We hypothesize that this may be caused by large dust grains or material with unique dielectric properties, causing the scattering cross-section to depart from the Rayleigh-Gans approximation that is used most often in X-ray scattering studies. The foreground Cyg OB2 association, which contains several evolved stars with large extinction values, is a likely culprit for grains of unique size or composition.

Equation for the Microwave Backscatter Cross Section of Aggregate Snowflakes Using the Self-Similar Rayleigh–Gans Approximation

Abstract In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Measurement of special nanoparticle structures by light scattering.

The characterization of nanoparticle size and structure by means of classical light scattering measurements from monodisperse suspensions is examined from both the Rayleigh-Gans (R-G) approximation as well as (for various spherical structures) the exact Lorenz-Mie theory. A means by which the traditional limits of the R-G theory may be extended and simplified is shown by a detailed discussion of the characteristic mean-square radius. This becomes particularly important for irregular particle shapes, where scattering depends on the orientation of such particles with respect to the direction of the incident illumination. A variety of particle structures are addressed, including rods, tubes, ellipsoids, rings, and superellipsoids.

SPECTRAL SOFTENING IN THE X-RAY AFTERGLOW OF GRB 130925A AS PREDICTED BY THE DUST SCATTERING MODEL

Gamma-ray bursts (GRBs) usually occurs in a dense star-forming region with massive circum-burst medium. The small-angle scattering of intense prompt X-ray emission off the surrounding dust grains will have observable consequences, and sometimes can dominate the X-ray afterglow. In most of the previous studies, only Rayleigh-Gans (RG) approximation is employed for describing the scattering process, which works accurately for the typical size of grains (with radius $a\leq 0.1\,{\rm \mu m}$) in the diffuse interstellar medium. When the size of the grains may significantly increase as in a more dense region where GRBs would occur, the RG approximation may not be valid enough for modeling detailed observational data. In order to study the temporal and spectral properties of the scattered X-ray emission more accurately with potentially larger dust grains, we provide a practical approach using the series expansions of anomalous diffraction (AD) approximation based on the complicated Mie theory. We apply our calculations to understanding the puzzling X-ray afterglow of recently observed GRB~130925A which showed a significant spectral softening. We find that the X-ray scattering scenarios with either AD or RG approximation adopted could both well reproduce the temporal and spectral profile simultaneously. Given the plateau present in early X-ray light curve, a typical distribution of smaller grains as in the interstellar medium would be suggested for GRB 130925A.

Scattering of clusters of spherical particles—Modeling and inverse problem solution in the Rayleigh–Gans approximation

In this work, an exact scattering model for a system of clusters of spherical particles, based on the Rayleigh–Gans approximation, has been parameterized in such a way that it can be solved in inverse form using Thikhonov Regularization to obtain the morphological parameters of the clusters. That is to say, the average number of particles per cluster, the size of the primary spherical units that form the cluster, and the Discrete Distance Distribution Function from which the z-average square radius of gyration of the system of clusters is obtained. The methodology is validated through a series of simulated and experimental examples of x-ray and light scattering that show that the proposed methodology works satisfactorily in unideal situations such as: presence of error in the measurements, presence of error in the model, and several types of unideallities present in the experimental cases.

Applicability of the Rayleigh‐Gans approximation for scattering by snowflakes at microwave frequencies in vertical incidence

AbstractThe applicability of the Rayleigh‐Gans approximation (RGA) for scattering by snowflakes is studied in the microwave region of the electromagnetic spectrum. Both the shapes of the single ice crystals, or monomers, and their amounts in the modeled snowflakes are varied. For reference, the discrete‐dipole approximation (DDA) is used to produce numerically accurate solutions to the single‐scattering properties, such as the backscattering and extinction cross‐sections, single‐scattering albedo, and the asymmetry parameter. We find that the single‐scattering albedo is the most accurate with only about 10% relative bias at maximum. The asymmetry parameter has about 0.12 absolute bias at maximum. The backscattering and extinction cross‐sections show about − 65% relative biases at maximum, corresponding to about − 4.6 dB difference. Overall, the RGA agrees well with the DDA computations for all the cases studied and is more accurate for the integrated quantities, such as the single‐scattering albedo and the asymmetry parameter than the cross‐sections for the same snowflakes. The accuracy of the RGA seems to improve, when the number of monomers is increased in an aggregate, and decrease, when the frequency increases. It is also more accurate for less dense monomer shapes, such as stellar dendrites. The DDA and RGA results are well correlated; the sample correlation coefficients of those are close to unity throughout the study. Therefore, the accuracy of the RGA could be improved by applying appropriate correction factors.

Membrane Bilayer Environment Influences Thermodynamics of Rhodopsin Membrane Protein-Lipid Interactions

The interaction between lipid bilayers and membrane proteins plays an important role in the functionality of GPCRs such as rhodopsin. During rhodopsin photoactivation, the photoreactive 11-cis retinylidene chromophore is isomerized to an all-trans state attaining an equilibrium between the MetaI and MetaII states. Lipid bilayer interaction with rhodopsin during its photoactivation process is explained using the flexible surface model (FSM). The FSM describes the elastic coupling of membrane lipids to integral membrane proteins through a balance of curvature and hydrophobic forces in lipid-protein interactions [1]. The FSM predicts a shift of the MetaI-MetaII equilibrium towards the activated MetaII state for unsaturated phosphatidylcholines with an increase in acyl chain length [1] or temperature. using UV-visible spectroscopy, we test the FSM by evaluating how the MetaI-MetaII equilibrium and thermodynamic parameters are influenced by a change in membrane environment. Absorption wavelength maxima at 485 nm and 380 nm correspond to the MetaI and MetaII states (inactive and active MetaII-H+), respectively. Accurate results are obtained by using the Rayleigh-Gans approximation to Mie scattering to compensate for light scattering in the UV-visible spectra. We determine effects of the type of head group, lipid to protein ratio, acyl chain length, and temperature on the MetaI-MetaII equilibrium by comparing pH titration curves for reconstituted rhodopsin in different lipid bilayers to those for native disk membranes [2,3]. The thermodynamic parameters are obtained for this equilibrium by fitting a modified phenomenological Henderson-Hasselbalch function [2] to the pH titration curves. These thermodynamic parameters illustrate how free energy drives the structural changes in rhodopsin upon photoactivation and can be used to model other GPCRs.[1] A.V. Botelho et al. (2006) BJ91, 4464-4477.[2] M. Mahalingam et al. (2008) PNAS105, 17795-17800.[3] E. Zaitseva et al. (2010) JACS132, 4815-4821.

Light scattering by optically soft large particles of arbitrary shape

Light scattering by chaotically oriented optically soft large particles of arbitrary shape is considered within the framework of the Rayleigh-Gans approximation. It has been shown that outside the forward direction, the scattering pattern has the dependence of <S>Δk⁻⁴(1+cos²θ), where <S> is an average particle surface area, Δk is the difference between scattered and initial wave vectors, θ is the scattering angle, and this pattern is independent of particle shape. A simple approximating formula is suggested, which correctly describes the scattering pattern in the entire range of scattering angles. This formula is compared to the particular case of size-distributed spherical particles and is shown to have high accuracy. Also, it is shown that the inherent optical properties, as total, transport, and backward scattering coefficients, are determined by the specific particle surface area and the effective particle size.