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Abstract Objective Flow cytometry (FC) is probably the most important technique for single-cell analysis. It’s precisely, rapid, and suitable for multidimensional single-cell analysis. The commonly used side scatter (SSC) intensity determined by FC is often interpreted as a measure of the internal cellular complexity of cells. In simple terms, the more structured a cell is, the higher the SSC intensity quantified by FC. Nevertheless, most of the studies that support this interpretation are based on data derived from animal or human cell lines and while it is assumed that the results can also be transferred to plant or algal cell lines, the details remain unclear. The objective of the recent work is to clarify the interpretation of the SSC signal from algal cells. Results Algal lipid droplets and their starch play an inherent role to shape the popular SSC signal derived from FC. This was shown by a theoretical approach based on Lorenz–Mie theory. These results were supported by experiments with different model cultures of Chlamydomonas reinhardtii in which a high linear correlation was observed between the SSC signal and the ‘physical’ starch quantity.

In situ aircraft measurements of the sizes and concentrations of liquid cloud droplets and ice crystals with maximum dimensions (Dmax) less than ~50 μm have been measured mainly using forward scattering probes over the past half century. The operating principle of forward scattering probes is that the measured intensity of light scattered by a cloud particle at specific forward scattering angles can be related to the size of that particle assuming the shape and thermodynamic phase of the target are known. Current forward-scattering probes assume spherical liquid cloud droplets and use the Lorenz–Mie theory to convert the scattered light to particle size. Uncertainties in sizing ice crystals using forward scattering probes are unavoidable since the single-scattering properties of ice crystals differ from those of spherical liquid cloud droplets and because their shapes can vary. In this study, directional scattering intensities of four different aspect ratios (ARs = 0.25, 0.50, 1.00, and 2.00) of hexagonal ice crystals with random orientations and of spherical liquid cloud droplets were calculated using the discrete dipole approximation (i.e., ADDA) and Lorenz–Mie code, respectively, to quantify the errors in sizing small ice crystals and cloud droplets using current forward scattering probes and to determine the ranges of optimal scattering angles that would be used in future forward scattering probes. The calculations showed that current forward scattering probes have average 5.0% and 17.4% errors in sizing liquid cloud droplets in the forward (4–12°) and backward (168–176°) direction, respectively. For measurements of hexagonal ice crystals, average sizing errors were 42.1% (23.9%) in the forward (backward) direction and depended on the ARs of hexagonal ice crystals, which are larger than those for liquid cloud droplets. A newly developed size conversion table based on the calculated single-scattering properties of hexagonal ice crystals using the ADDA reduced the sizing errors for the hexagonal ice crystals down to 14.2% (21.9%) in the forward (backward) direction. This study is a purely theoretical examination of the operating principle of forward scattering probes and there are several limitations, such as assumed hexagonal ice crystals with smooth surfaces and random orientations. [ABSTRACT FROM AUTHOR]

The norm for analyzing radiative transfer in randomly dispersed particulate medium is to use the independent scattering assumption, where the radiative characteristics of the system are derived from the superposition of the individual particles' radiative characteristics. This assumption is valid when the particles are sparsely distributed. There are established regime maps that are used to identify if the independent scattering assumption is valid. However, these maps which are based on experimental data have been recently questioned and updates are proposed by studies relying on direct solution of Maxwell's equations, in which scattering coefficients, cross-sections and/or efficiencies of particle ensembles are considered to identify presence of dependent scattering effects. Notably, both directionality of the scattering phenomenon and the presence of coherent scattering occurring on the free-space - particle cloud boundary are overlooked while identifying transition between independent and dependent scattering regimes. This study provides a critical overview of recent numerical approaches and shows that a regime map cannot be drawn relying solely on scattering cross section estimated by electromagnetic field solvers. The dependent scattering effects for dielectric particulate medium can be well represented using static structure factor including the directionality of scattering. Transport scattering coefficient that accounts for both magnitude and directionality of the scattering can be used to represent the radiative behavior adequately. Therefore, it can be used as the single intrinsic characteristic for identifying the transition between dependent and independent scattering, rather than the scattering coefficient and the asymmetry parameter alone. [Display omitted] • SSF estimates scattering coefficient and asymmetry parameter for dielectric particulate medium. • Transport scattering coefficient is the proper metric for representing scattering regime. • Solution of Maxwell's equations is possible for finite sized particulate media. • Coherent scattering leads to overestimation of scattering coefficient. • Calculated asymmetry parameter depends on considered ensemble size. [ABSTRACT FROM AUTHOR]

In situ aircraft measurements of the sizes and concentrations of liquid cloud droplets and ice crystals with maximum dimensions (Dmax) less than ~50 μm have been measured mainly using forward scattering probes over the past half century. The operating principle of forward scattering probes is that the measured intensity of light scattered by a cloud particle at specific forward scattering angles can be related to the size of that particle assuming the shape and thermodynamic phase of the target are known. Current forward-scattering probes assume spherical liquid cloud droplets and use the Lorenz–Mie theory to convert the scattered light to particle size. Uncertainties in sizing ice crystals using forward scattering probes are unavoidable since the single-scattering properties of ice crystals differ from those of spherical liquid cloud droplets and because their shapes can vary. In this study, directional scattering intensities of four different aspect ratios (ARs = 0.25, 0.50, 1.00, and 2.00) of hexagonal ice crystals with random orientations and of spherical liquid cloud droplets were calculated using the discrete dipole approximation (i.e., ADDA) and Lorenz–Mie code, respectively, to quantify the errors in sizing small ice crystals and cloud droplets using current forward scattering probes and to determine the ranges of optimal scattering angles that would be used in future forward scattering probes. The calculations showed that current forward scattering probes have average 5.0% and 17.4% errors in sizing liquid cloud droplets in the forward (4–12°) and backward (168–176°) direction, respectively. For measurements of hexagonal ice crystals, average sizing errors were 42.1% (23.9%) in the forward (backward) direction and depended on the ARs of hexagonal ice crystals, which are larger than those for liquid cloud droplets. A newly developed size conversion table based on the calculated single-scattering properties of hexagonal ice crystals using the ADDA reduced the sizing errors for the hexagonal ice crystals down to 14.2% (21.9%) in the forward (backward) direction. This study is a purely theoretical examination of the operating principle of forward scattering probes and there are several limitations, such as assumed hexagonal ice crystals with smooth surfaces and random orientations.

Global rainbow refractometry (GRR) is an important technique for temperature measurements of droplets and has been applied to a wide field of technical sprays. In this work, the application of GRR to sprays with droplets as small as 1 − 30 μ m in diameter is investigated by means of Lorenz–Mie theory to evaluate the influence of varying droplet size distributions (DSD) and varying refractive indexes on the global rainbow. DSDs were found by fitting a Rosin–Rammler–Sperling–Bennett distribution to experimental data. Different DSDs, that are typical for flame spray pyrolysis applications were evaluated systematically with varying widths and mean diameters. A study of the angular rainbow maxima position with varying widths of DSDs shows a strong non-linearity. It is concluded that GRR experiments in polydisperse applications should be accompanied with an accurate sizing technique. Furthermore, possible droplet size-dependent distributions of refractive indexes within the samples may influence the results. [ABSTRACT FROM AUTHOR]

Light scattering by non-spherical particles is an important factor influencing atmospheric radiative transfer. To accurately simulate the scattering properties of non-spherical particles, the Invariant Imbedded T-matrix method (IIM T-Matrix) is developed by combining the Lorenz–Mie theory and invariant imbedding technique. In this model, the non-spherical particle is regarded as an inhomogeneous sphere and discretized into multiple spherical layers in the spherical coordinate system. The T-matrix of the inscribed sphere is firstly calculated by the Lorenz–Mie theory, and then taking it as the initial value, the T-matrix is updated layer by layer by using the invariant imbedding technique. To improve the computational efficiency, the model is further parallelized by the OpenMP technique. To verify the simulation accuracy of the IIM T-Matrix method, the results of the model are compared with those of the EBCM (Extended Boundary Condition Method) T-Matrix method, DDA (Discrete Dipole Approximation) and MRTD (Multi-Resolution Time Domain). The results show that the scattering phase matrix simulated by the IIM T-Matrix method closely agrees with that of the well-tested models, indicating that the IIM T-Matrix method is a powerful tool for the light scattering simulation of non-spherical particles. Since the IIM T-Matrix method is derived from the volume integral equation, compared to the T-Matrix method which is based on surface integral principles (i.e., "EBCM" or the "null field method"), it can be applied to the scattering calculations of particle with arbitrary shapes and inhomogeneous compositions, which can greatly expand the application scope of the T-Matrix method. [ABSTRACT FROM AUTHOR]

• Radiative transfer problems for three different cases of refractive indexes for spherical particles embedded in an absorbing medium are systematically investigated. • The errors of the directional-hemispherical reflectance and transmittance caused by neglecting the effect of host medium absorption on particle scattering are analyzed. • Neglecting the effect of host medium absorption on particle scattering will underestimate the directional-hemispherical reflectance and transmittance to some extent. • For the case of monodisperse particles embedded in an absorbing thin layer considered in this paper, the relative error of hemispherical reflectances increases approximate linearly from 5.9% to 59.4% with the particle size parameter increases from 1.0 to 40. For many practical radiative transfer problems in dispersed media, the host medium surrounding the particles is absorbing rather than lossless, therefore it may lead to inaccurate results when the effect of host medium absorption on particle scattering is neglected. This paper presents a systematical investigation on the radiative transfer problems for three different cases of refractive indexes for spherical particles embedded in an absorbing medium. The single-scattering properties of the particles are calculated using the recently developed public-domain Lorenz-Mie program for the case of an absorbing host medium. The directional-hemispherical reflectance and transmittance for a plane-parallel layer of spherical particles are obtained by using the Monte Carlo method. The effects of host medium absorption, particle size parameter and size distribution on the radiative transfer characteristics are discussed. The results show that neglecting the effect of host medium absorption on particle scattering will underestimate the directional-hemispherical reflectance and transmittance to some extent. Meanwhile, the errors caused by using the conventional Lorenz–Mie theory increase obviously with increase of host medium absorption index and particle size parameter. For the case of monodisperse particles embedded in an absorbing thin layer (i.e., with layer thickness of 0.05 mm and host medium absorption index of 0.01), the relative error of hemispherical reflectances increases approximate linearly from 5.9% to 59.4% with the particle size parameter increases from 1.0 to 40. [ABSTRACT FROM AUTHOR]

To study the optical properties of background atmospheric aerosols in East China, we carried out observations of the physical, chemical and optical properties of atmospheric aerosols at the summit of Mount Tai (Mt. Tai, 1533.7 m above sea level) from 13 May to 25 June 2017. The results show that the average scattering coefficient ( σ sca , 550 ) at 550 nm of the aerosols at the summit of Mt. Tai is 40.3 Mm−1, and the average absorption coefficient ( σ abs , 550 ) at 550 nm is 16.0 Mm−1. The complex refractive index of aerosols is a key parameter for aerosol retrieval and modeling. There are few studies on the equivalent complex refractive index of aerosol in the Taishan area. We calculated the aerosol equivalent complex refractive index using the observed aerosol scattering coefficients, absorption coefficients and particle size distribution data, providing more data support for future modeling in this region. The real part (n) of the complex refractive index at 550 nm of aerosol ranges from 1.31 to 1.98 (mostly under 1.50), with an average value of 1.38, while the imaginary part (k) ranges from 0.014 to 0.251 (less than 0.10 for over 95% samples), with an average value of 0.040. The analysis of the n and k of the aerosol average complex refractive index shows that the scattering properties of the aerosols at the summit of Mt. Tai are relatively weak and the absorption properties are relatively strong when compared with those of other kinds of aerosols. The k of the aerosol complex refractive index at the summit of Mt. Tai has strong correlations with the wind speed, temperature, as revealed by the correlation analysis.

Ηighlights • Electromagnetic torque on spheres in circularly polarized illumination reviewed. • Humblet-decomposition applied to spin and orbital angular momentum of scattered radiation. • Spin angular momentum of scattered radiation related to Stokes parameters. • Numerical examples from Lorenz-Mie theory for metallic spheres using the Hagen–Rubens approximation. • Orbital angular momentum of scattered radiation can exceed spin angular momentum in Mie theory. • Development of Hagen–Rubens approximation for the complex refractive index of metals reviewed. Abstract When a circularly polarized electromagnetic wave is scattered by an isotropic sphere, Humblet's decomposition from 1943 is helpful for understanding why the axial projection of the spin-angular momentum gives incomplete information concerning the total radiated angular momentum. Humblet asserted that some field angular momentum is orbital angular momentum (OAM). This distinction, applied here to Mie scattering, gives insight into why classical electromagnetic radiation torque is proportional to absorbed power for isotropic spheres. It also reveals the direct measurability (from Stokes parameters) of spin contributions to the radiated angular momentum. This approach is applied to metallic spheres in circularly polarized illumination modeled with Lorenz–Mie theory using the Hagen–Rubens approximation (1903) in which the real and imaginary components of the sphere's refractive index are equal in magnitude. That approximation is often useful for terahertz and lower frequencies. It was helpful to compare a spin efficiency factor Q spin with the canonical scattering efficiency factor Q sca for varying sphere sizes at a fixed frequency. A small-size limiting case Q sca /Q spin = 2 is recovered associated with a common interpretation of electric dipole-related torque. For larger sizes, the OAM contribution increases giving Q sca /Q spin > 2. Van de Hulst's scattering calculations for metal spheres are also reproduced. Dedicated in memory of Seattle Pacific University Professor James H. Crichton (1937–1999). [ABSTRACT FROM AUTHOR]

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz–Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html . [ABSTRACT FROM AUTHOR]

Abstract: Ludvig Lorenz was Denmark's first theoretical physicist of international recognition. Despite his important contributions to a broad range of experimental and theoretical physics, he generally appears as a somewhat peripheral figure in histories of late‐nineteenth‐century physics and is completely overshadowed by his near‐namesake H. A. Lorentz. Herein, a selected number of Lorenz's works is introduced with an eye on those which are still of relevance to modern physics and today eponymously associated with his name. These contributions are known as the Lorenz number, the Lorenz gauge, the Lorenz–Lorentz law or formula, and the Lorenz–Mie scattering theory. [ABSTRACT FROM AUTHOR]

Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum. [ABSTRACT FROM AUTHOR]

Avogadro constant determines the number of particles in one mole of a substance, thus relating the molar mass of the substance to the mass of this substance. Avogadro constant is related to Système Internationale base units by defining the very concept of chemical quantity. Revisions of the base units created a need to redefine the Avogadro constant, where a collaborative work called the Avogadro Project is established to employ optical interferometry to measure the diameter of high quality 100 mm silicon spheres. We propose far-infrared spectroscopy for determining the Avogadro constant by using elastic scattering from the 100 mm Avogadro Project silicon spheres. Similar spectroscopic methods are already in use in the near-infrared, relating whispering gallery modes of the 1 mm silicon spheres to the diameter of the spheres. We present numerical simulations in the far-infrared and the near-infrared, as well as spatially scaled down elastic scattering measurements in the near-infrared. These numerical and experimental results show that, the diameter measurements of 100 mm single crystal silicon spheres with elastic scattering in the far-infrared can be considered as an alternative to optical interferometry. [ABSTRACT FROM AUTHOR]

Light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, is here considered. In this short review, some of the basic features of its resonant scattering behavior are covered. First, a general physical picture is described by a full electrodynamic perspective, the Lorenz–Mie theory. The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization enhancement: the plasmonic and the dielectric resonances. The corresponding electrostatic (Rayleigh) picture is analyzed and the polarizability of a homogeneous spherical inclusion is extracted. This description facilitates the identification of the first type of resonance, i.e., the localized surface plasmon (plasmonic) resonance, as a function of the permittivity. Moreover, the electrostatic picture is linked with the plasmon hybridization model through the case of a step-inhomogeneous structure, i.e., a core–shell sphere. The connections between the electrostatic and electrodynamic models are reviewed in the small size limit and details on size-induced aspects, such as the dynamic depolarization and the radiation reaction on a small sphere are exposed through the newly introduced Mie–Padé approximative perspective. The applicability of this approximation is further expanded including the second type of resonances, i.e., the dielectric resonances. For this type of resonances, the Mie–Padé approximation reveals the main character of the two different cases of resonances of either magnetic or electric origin. A unified picture is therefore described encompassing both plasmonic and dielectric resonances, and the resonant conditions of all three different types are extracted as functions of the permittivity and the size of the sphere. Lastly, the directional scattering behavior of the first two dielectric resonances is exposed in a simple manner, namely the Kerker conditions for maximum forward and backscattering between the first magnetic and electric dipole contributions of a dielectric sphere. The presented results address several prominent functional features, aiming at readers with either theoretical or applied interest for the scattering aspects of a resonant sphere. [ABSTRACT FROM AUTHOR]

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz–Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html , and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations. [ABSTRACT FROM AUTHOR]

Light scattering by non-spherical particles is an important factor influencing atmospheric radiative transfer. To accurately simulate the scattering properties of non-spherical particles, the Invariant Imbedded T-matrix method (IIM T-Matrix) is developed by combining the Lorenz−Mie theory and invariant imbedding technique. In this model, the non-spherical particle is regarded as an inhomogeneous sphere and discretized into multiple spherical layers in the spherical coordinate system. The T-matrix of the inscribed sphere is firstly calculated by the Lorenz−Mie theory, and then taking it as the initial value, the T-matrix is updated layer by layer by using the invariant imbedding technique. To improve the computational efficiency, the model is further parallelized by the OpenMP technique. To verify the simulation accuracy of the IIM T-Matrix method, the results of the model are compared with those of the EBCM (Extended Boundary Condition Method) T-Matrix method, DDA (Discrete Dipole Approximation) and MRTD (Multi-Resolution Time Domain). The results show that the scattering phase matrix simulated by the IIM T-Matrix method closely agrees with that of the well-tested models, indicating that the IIM T-Matrix method is a powerful tool for the light scattering simulation of non-spherical particles. Since the IIM T-Matrix method is derived from the volume integral equation, compared to the T-Matrix method which is based on surface integral principles (i.e., “EBCM” or the “null field method”), it can be applied to the scattering calculations of particle with arbitrary shapes and inhomogeneous compositions, which can greatly expand the application scope of the T-Matrix method.

A statistical approach in defining particle morphology in terms of an ensemble of hexahedra of distorted shapes is employed for modeling the Inherent Optical Properties (IOPs) of aquatic particles. The approach is inspired by the rich variability in shapes of real aquatic particles that cannot be represented by one particular shape. Two methods, the Invariant Imbedding T-matrix (II-TM) and Physical Geometric Optics Hybrid (PGOH) method, are combined to simulate the IOPs for aquatic particles of sizes ranging from the Rayleigh scattering to geometric optics regimes. Nonspherical effects on the IOPs are examined by comparing the results with predictions based on the Lorenz-Mie theory to explore the limitations of assuming the particles to be spherical. We pay special attention to backscattering-related and polarimetric scattering properties, particularly the backscattering ratio, Gordon parameter, backscattering volume scattering function and the degree of linear polarization. The simulated IOPs are compared with the in-situ measurements to assess the feasibility of using a hexahedral ensemble in modeling the IOPs of the aquatic particles. [ABSTRACT FROM AUTHOR]

Light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, is here considered. In this short review, some of the basic features of its resonant scattering behavior are covered. First, a general physical picture is described by a full electrodynamic perspective, the Lorenz–Mie theory. The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization enhancement: the plasmonic and the dielectric resonances. The corresponding electrostatic (Rayleigh) picture is analyzed and the polarizability of a homogeneous spherical inclusion is extracted. This description facilitates the identification of the first type of resonance, i.e., the localized surface plasmon (plasmonic) resonance, as a function of the permittivity. Moreover, the electrostatic picture is linked with the plasmon hybridization model through the case of a step-inhomogeneous structure, i.e., a core–shell sphere. The connections between the electrostatic and electrodynamic models are reviewed in the small size limit and details on size-induced aspects, such as the dynamic depolarization and the radiation reaction on a small sphere are exposed through the newly introduced Mie–Padé approximative perspective. The applicability of this approximation is further expanded including the second type of resonances, i.e., the dielectric resonances. For this type of resonances, the Mie–Padé approximation reveals the main character of the two different cases of resonances of either magnetic or electric origin. A unified picture is therefore described encompassing both plasmonic and dielectric resonances, and the resonant conditions of all three different types are extracted as functions of the permittivity and the size of the sphere. Lastly, the directional scattering behavior of the first two dielectric resonances is exposed in a simple manner, namely the Kerker conditions for maximum forward and backscattering between the first magnetic and electric dipole contributions of a dielectric sphere. The presented results address several prominent functional features, aiming at readers with either theoretical or applied interest for the scattering aspects of a resonant sphere.

In this paper we present a theoretical analysis of the generalized Lorenz–Mie theory for negative refractive index (NRI) media and spherical scatterers, extending the well-known concepts and definitions found in the literature involving dielectric or positive refractive index (PRI) particles. The consequences of a negative phase velocity and an anti-parallelism of the wave vector with respect to the Poynting vector are investigated and interpreted in this framework and, together with the symmetries found for the beam-shape coefficients when compared to the conventional PRI case, it is shown that the description of plane waves, Gaussian beams and, more generally, on-axis azimuthally symmetric waves along a NRI medium, their fields and all physical properties can be conveniently correlated with that of dielectric media once the electromagnetic response functions are replaced by their corresponding dielectric counterparts. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some new developments in particle characterization. More precisely, the paper will be focused on the description of some progresses in the characterization of particles by interferometric methods which are generally considered as the most accurate ones. Three standard configurations will be presented and discussed: i) Interference between scattered light from a particle and a single reference beam (holography), ii) Interference between different kinds of light scattered by a single particle (ILIDS), iii) Interference between the light scattered from different particles. A special attention will be devoted to the possibility to obtain 3D information on the particle location. [ABSTRACT FROM AUTHOR]

In the field of combustion, the characterization of particles (such as 3D-location, particle shape, particle size, particle component and temperature) is a challenge. Newly developed technique, Fourier Interferometric Imaging (FII), have been proposed for characterizing a field of spherical particles. Based on the analysis of the interference field recorded on 2D detectors, information on the size, shape, temperature and relative position of the particles can be extracted. This article is devoted to the numerical and experimental validation of the FII approach on a line of monodispersed droplets. A simple model is introduced for efficient and fast computations of Fourier interferometric images. The predictions issue from that model are compared to Lorenz–Mie computations and experimental images. Good agreement between both the numerical and experimental behavior is obtained. [ABSTRACT FROM AUTHOR]

Abstract: We develop an orders-of-scattering approximation, termed the “screened cylindrical void/core” (SCV) approximation, for a composite cylinder. The composite cylinder consists of a large host cylinder that contains a small, eccentrically embedded, core cylinder. The SCV approximation is developed via separation of variables in conjunction with addition theorems for cylindrical functions. We show that the SCV approximation is in good agreement with the numerically exact solution. A simple physical interpretation of the SCV approximation is also presented. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a monochromatic plane wave scattering from an infinite homogeneous cylindrical annulus. In particular, we study the effect that the inner part of the cylindrical annulus (cylindrical void, if you will) has on the scattered field. This is done by isolating the cylindrical void's contribution to the scattered field. We show that if the cylindrical void is small, then its contribution to the scattered field may be approximated by the “screened cylindrical void” (SCV) approximation. We first develop the SCV approximation in a physically intuitive manner, and then show that it could also be obtained in a more mathematically rigorous manner. Numerical results comparing the SCV approximation to the exact solution are also presented. [Copyright &y& Elsevier]

Abstract: In liquid combustion, the evaporation process is one of the key parameters which controls combustion efficiency. To understand the combustion process, and to be able to develop an efficient combustor which produces less pollutant, it is necessary to be able to measure evaporation properties. Several techniques exist to measure the physical properties of fuel droplets, but very few exist to measure the thermo-chemical properties. The global rainbow technique (GRT) has been proposed and successfully used to measure the average temperature and the size distribution of sprays under the assumption that all the droplets are at the same temperature. This paper explores the applicability of GRT to sprays where the refractive index is a function of the particle size. A first result proves that the refractive index measured by GRT is weighted by the droplet diameter to the power of 7/3. This result permits accurate and fast comparisons between the numerical simulations and the experiments. A second result is the measurement of the refractive index by the size class by coupling GRT and Phase Doppler Anemometry (PDA) measurements (or another measurement technique with a low sensitivity to the refractive index such as holography, diffractometry, etc). [Copyright &y& Elsevier]

In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops. [ABSTRACT FROM AUTHOR]

Abstract: We report on the results of theoretical investigation of the parameters of photonic nanojets formed near the shadow surface of micron-sized dielectric spheres irradiated by a laser radiation. The longitudinal and transversal dimensions of the photonic nanojet and its peak intensity also are calculated as the functions of particle size, index of absorption, and optical contrast of the particulate material. The photonic nano-flux was simulated numerically in composite particles made of a core and a shell with different refractive indices and variable shell thickness. Some practical conclusions are drawn concerning the possible ways to gain the control over the nanojet parameters in micron-sized spherical particles. [ABSTRACT FROM AUTHOR]

This paper introduces a theoretical model for computing the scattering properties of participating media and translucent materials. The model takes as input a description of the components of a medium and computes all the parameters necessary to render it. These parameters are the extinction and scattering coefficients, the phase function, and the index of refraction. Our theory is based on a robust generalization of the Lorenz-Mie theory. Previous models using Lorenz-Mie theory have been limited to non-absorbing media with spherical particles such as paints and clouds. Our generalized theory is capable of handling both absorbing host media and non-spherical particles, which significantly extends the classes of media and materials that can be modeled. We use the theory to compute optical properties for different types of ice and ocean water, and we derive a novel appearance model for milk parameterized by the fat and protein contents. Our results show that we are able to match measured scattering properties in cases where the classical Lorenz-Mie theory breaks down, and we can compute properties for media that cannot be measured using existing techniques in computer graphics. [ABSTRACT FROM AUTHOR]

Abstract: The paper is devoted to the study of the intensity distributions and the angular spectra of the second and fifth rainbows of homogeneous and inhomogeneous spherical particles predicted by Lorenz–Mie theory. The results show that the distribution around the second rainbow angle for a homogeneous sphere of refractive index between 1.32 and 1.33 is due to the interference of the light after two or five internal reflections. The structure of the scattering diagram and the angular spectrum for homogeneous and radially inhomogeneous spheres are studied. For a homogeneous sphere we show that the second and fifth rainbows can be independently reconstructed by filtering the calculated spectrum. Since each order of rainbow penetrates the particle to different depths, such methods could be used to provide information about the refractive index profile or the temperature gradient of an inhomogeneous sphere. The Airy-like peaks of the second and fifth rainbows are closely connected with the refractive index profile, which is beneficial to the measurement of its refractive index profile or temperature gradient. [Copyright &y& Elsevier]

Abstract: Simulations of the transmission of a short light pulse (50fs) through a strongly scattering medium constituted by water droplets (50–150μm diameter) are presented. Temporal emerging signals are computed using a Monte Carlo technique. In case of large particles with respect to the pulse duration, the time delay related to the interaction between light and individual particles has to be taken into account, in addition to the time delay related to the travel of light between particles. After careful comparisons with temporal Lorenz–Mie theory, it has been chosen to pre-calculate scattering characteristics of individual droplets using Debye series. Transmitted signals in forward direction and in a small temporal window (0–400fs) are presented, showing that temporal information on particle size are still observable facing strongly scattering media. [Copyright &y& Elsevier]

A simple and robust method for the inversion of the laser diffraction diagrams of small transparent fibres is introduced. Based on Lorenz-Mie theory (LMT) calculations and the definition of a correlation estimator, it allows the particle diameter to be determined without the classical size ambiguity problem due to morphological-dependent resonances (MDRs). Experimentally, when sizing single reinforcement glass fibres during their forming process, the typical resolution obtained is about σ≈0.02 μm for the size range D=7–42 μm. This inversion method is thought to be also applicable for the diagnosis of other highly symmetrical and transparent particles as well as other particle characteristics. [Copyright &y& Elsevier]

This paper is devoted to the research on the characteristics of angular spectra of the intensity distributions near rainbow angles of a homogeneous cylinder where different orders of rainbow appear. The geometric optics predicts that two or more different orders of rainbow can appear at the same angle for certain refractive index. In the point of view of physical optics, the rays undergone different paths (corresponding to different orders of rainbow) interfere. By using the FFT and inverse FFT to the intensity distributions simulated by Lorenz–Mie theory and the Debye series, we can recognize the contributions of each order. This means that we can extract the information of different orders of rainbow from the signal collected by only one detector. Since the rays of different orders of rainbow pass through different paths and provide information of different parts in the particle, we can measure the parameters such as diameter, (gradient of) refractive index and non-circularity/non-sphericity of the particle from the unique signal. The results are also validated by experiments for a cylinder of diameter d=125 μm and refractive index m=1.4571. [Copyright &y& Elsevier]

We propose using the circle polynomials to describe a particle’s transmission function in a digital holography setup. This allows both opaque and phase particles to be determined. By means of this description, we demonstrate that it is possible to estimate the digital in-line hologram produced by a spherical particle. The experimental intensity distribution due to an opaque micro-inclusion is compared to the theoretical one obtained by our new model. Moreover, the simulated hologram and reconstructed image of the particle by an optimal fractional Fourier transformation under the opaque disk, quadratic phase, and quasi-spherical phase approximation are compared with the results obtained by simulating holograms by the Lorenz–Mie Theory (LMT). The Zernike coefficients corresponding to the considered particles are evaluated using the double exponential (DE) method which is optimal in various respects.

To study the optical properties of background atmospheric aerosols in East China, we carried out observations of the physical, chemical and optical properties of atmospheric aerosols at the summit of Mount Tai (Mt. Tai, 1533.7 m above sea level) from 13 May to 25 June 2017. The results show that the average scattering coefficient ( σ sca , 550 ) at 550 nm of the aerosols at the summit of Mt. Tai is 40.3 Mm−1, and the average absorption coefficient ( σ abs , 550 ) at 550 nm is 16.0 Mm−1. The complex refractive index of aerosols is a key parameter for aerosol retrieval and modeling. There are few studies on the equivalent complex refractive index of aerosol in the Taishan area. We calculated the aerosol equivalent complex refractive index using the observed aerosol scattering coefficients, absorption coefficients and particle size distribution data, providing more data support for future modeling in this region. The real part (n) of the complex refractive index at 550 nm of aerosol ranges from 1.31 to 1.98 (mostly under 1.50), with an average value of 1.38, while the imaginary part (k) ranges from 0.014 to 0.251 (less than 0.10 for over 95% samples), with an average value of 0.040. The analysis of the n and k of the aerosol average complex refractive index shows that the scattering properties of the aerosols at the summit of Mt. Tai are relatively weak and the absorption properties are relatively strong when compared with those of other kinds of aerosols. The k of the aerosol complex refractive index at the summit of Mt. Tai has strong correlations with the wind speed, temperature, as revealed by the correlation analysis. [ABSTRACT FROM AUTHOR]

• Scattering by non-absorbing bispheres and particle suspensions and aggregates was studied systematically. • A wide range of size parameter, refractive index, and interparticle distance-to-wavelength ratio was explored. • New transition criteria between independent/dependent scattering regimes were established. • The scattering cross-section and asymmetry factor feature different transition criteria. • Criteria for bispheres cannot be extended to suspensions and aggregates of small particles. Independent scattering refers to situations when particles are sufficiently distant that some of the radiation characteristics of particle systems can be determined by adding the contributions of each particle. When particles are in close proximity, however, dependent scattering prevails and is affected by near-field interactions and far-field interferences among scattered waves from nearby particles. The dimensionless parameters governing the scattering cross-section and asymmetry factor of non-absorbing bispheres, disordered and ordered suspensions and aggregates with up to 8 spherical particles were found to be the particle size parameter χ s , the relative index of refraction m , the interparticle distance-to-wavelength ratio d *, and the number of particles. Here, χ s ranged from 0.031 to 8.05, m varied from 0.667 to 2.6, and d * reached up to 30. Dependent effects were observed in aggregates with particles of all sizes and were strongly affected by the relative index of refraction in particle systems with χ s ≥ 2 due to large phase shifts across the particles. Moreover, new criteria for the transition between the dependent and independent scattering regimes for the scattering cross-section and the asymmetry factor were derived. For the scattering cross-section of structures with a narrow interparticle distance distribution, the independent scattering regime prevailed when the average interparticle distance-to-wavelength ratio d ¯ * exceeded (i) 2 for particles with χ s ≤ 2 and (ii) 5 for particles with χ s > 2. For the asymmetry factor, the transition from the dependent to the independent regimes for particles with χ s ≤ 2 was achieved for d ¯ * as high as 25. These transition criteria could be extended to particle systems with a broad interparticle distance distribution when based on the minimum interparticle distance-to-wavelength ratio. Finally, the relative index of refraction m did not affect these transition criteria. [ABSTRACT FROM AUTHOR]