Superposition T-matrix Method Research Articles

Dependent scattering and plasmon coupling in concentrated suspensions of optically hard nanoparticles

This study establishes the accuracy and efficacy of the recently developed radiative transfer with reciprocal transactions (R2T2) method for quickly simulating radiation transfer through concentrated thick suspensions of optically hard nanoparticles featuring a large mismatch in refractive and/or absorption indices compared with their surrounding medium. Concentrated suspensions of optically hard nanoparticles exhibit strong light scattering and dependent scattering effects including both near-field interactions among particles and interferences of scattered waves in the far-field. Concentrated suspensions of metallic nanoparticles also exhibit plasmon coupling effect that leads to widening of absorption peak and red-shift in the peak surface plasmon resonance wavelength. However, predicting these complex interactions between EM waves and particles in thick and concentrated suspensions by explicitly solving Maxwell's equations is computationally intensive, if not impossible. Conventional solutions like Lorenz–Mie theory combined with independent scattering approximation do not account for dependent scattering and plasmon coupling. Furthermore, the dense medium radiative transfer theory is a far-field approximation that does not account for near-field effects, leading to significant errors in predictions, as illustrated in this study. By contrast, the R2T2 method's predictions showed excellent agreement with the solutions of Maxwell's equations obtained using the superposition T-matrix method for thin films containing optically hard particles. The method also rigorously accounted for multiple scattering as well as plasmon coupling in thick concentrated suspensions. These results could facilitate the design of plasmonic suspensions used in various energy and environmental applications.

Effects of Aluminum/Carbon and Morphology on Optical Characteristics and Radiative Forcing of Alumina Clusters Emitted by Solid Rockets in the Stratosphere

Alumina (Al2O3) particles, the primary combustion products of solid rockets, can accumulate in the stratosphere, changing the global radiative balance. These Al2O3 particles were usually treated as homogeneous spheres. However, they contain impurities and may form clusters during the combustion process. Models representing Al-containing and C-containing Al2O3 clusters were developed, denoted as Al2O3 shell model (ASM) and Al2O3 core model (ACM), respectively. The superposition T-matrix method (STMM) was applied to examine their optical characteristics. Subsequently, a method to obtain the top-of-atmosphere flux was proposed by integrating the models with the moderate resolution atmospheric transmission code (MODTRAN). With the addition of Al/C, the absorption cross-section enhances by several orders of magnitude at 0.55 μm and increases slightly at 10 μm. The equivalent sphere models will weaken their scattering ability. A 4Tg mass burden of Al2O3 produces radiative forcing of −0.439 Wm−2. However, the addition of Al and C reduces the forcing by up to 15% and 12%, respectively. In summary, the optical characteristics and radiative forcing of Al2O3 clusters are sensitive to Al/C and morphology models. While our findings are impacted by various uncertainties, they contribute valuable insights into the radiative forcing of Al2O3 particles, potential climatic changes by space activities.

Effects of Aluminum/Carbon and Morphology on Optical Characteristics and Radiative Forcing of Alumina Clusters Emitted by Solid Rockets in the Stratosphere

Alumina (Al2O3) particles, the primary combustion products of solid rockets, can accumulate in the stratosphere, changing the global radiative balance. These Al2O3 particles were usually treated as homogeneous spheres. However, they contain impurities and may form clusters during the combustion process. Models representing Al-containing and C-containing Al2O3 clusters were developed, denoted as Al2O3 shell model (ASM) and Al2O3 core model (ACM), respectively. The superposition T-matrix method (STMM) was applied to examine their optical characteristics. Subsequently, a method to obtain the top-of-atmosphere flux was proposed by integrating the models with the moderate resolution atmospheric transmission code (MODTRAN). With the addition of Al/C, the absorption cross-section enhances by several orders of magnitude at 0.55 μm and increases slightly at 10 μm. The equivalent sphere models will weaken their scattering ability. A 4Tg mass burden of Al2O3 produces radiative forcing of −0.439 Wm−2. However, the addition of Al and C reduces the forcing by up to 15% and 12%, respectively. In summary, the optical characteristics and radiative forcing of Al2O3 clusters are sensitive to Al/C and morphology models. While our findings are impacted by various uncertainties, they contribute valuable insights into the radiative forcing of Al2O3 particles, potential climatic changes by space activities.

Optical properties of particle dispersed coatings with gradient distribution.

Particle dispersed coatings with gradient distributions, resulting from either gravity or artificial control, are frequently encountered in practical applications. However, most current studies investigating the optical properties of coatings use the uniform model (uniform single layer assumption), overlooking the gradient distribution effects. Given the pervasiveness of gradient distributions and the widespread use of the uniform model, it is imperative to evaluate applicability conditions of the uniform model in practical applications. In this work, we comprehensively investigate the quantitative performance of the uniform model in predicting the infrared optical properties of coatings with gradient distributions of particle volume fraction using the superposition T-matrix method. The results show that the gradient distribution of particle volume fraction has a limited impact on the emissivity properties of T i O 2-PDMS coatings in the midwavelength-infrared (MWIR) and long-wavelength-infrared (LWIR) bands, which validates the uniform model for the gradient coatings with weakly scattering dielectric particles. However, the uniform model can yield significant inaccuracies in estimating the emissivity properties of Al-PDMS coatings with gradient distributions in the MWIR and LWIR bands. To accurately estimate the emissivity of such gradient coatings with the scattering metallic particles, meticulous modeling of the particle volume fraction distribution is essential.

Light absorption by Volvocaceae colonies consisting of equidistant optically soft photosynthetic cells in a transparent spherical extracellular matrix

This study aims to develop a methodology to predict the absorption cross-section of colonial microalgae such as those of the Volvocaceae family including Eudorina, Pleodorina, and Volvox consisting of an ordered assembly of large and optically soft absorbing cells embedded within a non-absorbing spherical extracellular matrix (ECM). The absorption cross-section of spherical colonies, such as Eudorina, containing 16, 32, and 64 equidistant photosynthetic cells distributed on the surface of a sphere within a concentric spherical ECM was predicted by the superposition T-matrix method for ECM size parameters as large as 500 and by the Monte Carlo ray-tracing (MCRT) method for ECM size parameters as large as 900. The predicted absorption cross-sections given by the two methods were in excellent agreement despite the fact that the conditions for geometric optics were not rigorously satisfied. The absorption cross-section of the microalgae colonies considered was found to increase with increasing cell radius, absorption index or cell pigment concentration, and/or number of cells. Shading among cells decreased the mass absorption cross-section and was increasingly important for colonies with strongly absorbing cells, large cell radius, and/or large number of cells. These results demonstrate that accounting for shading effects is necessary to accurately predict the absorption cross-section of microalgae colonies. Furthermore, the study demonstrated that the MCRT method is an accurate and efficient method for modeling light absorption by an ensemble of many large, ordered, and optically soft particles. Finally, the impact of colony formation as well as pigment and biomass concentrations on the local (LRPA) and mean (MRPA) rates of photon absorption within a microalgae culture was also assessed. At low biomass concentrations, the LRPA and MRPA decreased in the presence of colonies. This effect was more pronounced at higher pigment concentrations.

Generalised coupled-dipole model for core-satellite nanostructures.

Plasmonic core-satellite nanostructures have recently attracted interest in photocatalytic applications. The core plasmonic nanoparticle acts like an antenna, funnelling incident light into the near-field region, where it excites the smaller satellite nanoparticles with resonantly enhanced absorption. Computer simulations of the optical absorption by such structures can prove challenging, even with state-of-the-art numerical methods, due to the large difference in size between core and satellite particles. We present a generalised coupled-dipole model that enables efficient computations of light absorption in such nanostructures, including those with many satellites. The method accurately predicts the local absorption in each satellite despite being two orders of magnitude weaker than the absorption in the core particle. We assess the range of applicability of this model by comparing the results against the superposition T-matrix method, a rigorous solution of Maxwell's equations that is much more resource-intensive and becomes impractical as the number of satellite particles increases.

Dependent Scattering in Thick and Concentrated Colloidal Suspensions

This study demonstrates numerically and experimentally that dependent scattering occurs in colloidal suspensions and can, counterintuitively, cause their transmittance to increase with increasing particle volume fraction. Radiation transfer through colloidal suspensions has been modeled with the radiative transfer equation (RTE) assuming independent scattering. Then, the effective absorption and scattering coefficients of the disperse medium are predicted as the sum of the cross sections of all particles divided by the volume of suspension. However, this approach is not valid when the average interparticle distance is on the same order of magnitude as the wavelength, corresponding to large particle concentrations. The latter situation is referred to as dependent scattering. Rigorously accounting for dependent scattering requires solving Maxwell’s equations, but is limited to relatively thin suspensions. Here, we extend the Radiative Transfer with Reciprocal Transactions (R2T2) method to predict the normal-hemispherical transmittance of thick and concentrated plane-parallel slabs of nonabsorbing nanoparticle suspensions and to rigorously account for dependent scattering effects. The radiation characteristics of a large number of particle ensembles were estimated using the superposition T-matrix method and the RTE was solved using Monte Carlo method combined with strategies for sampling the previously computed radiation characteristics. A wide range of particle size parameter, volume fraction, and optical properties as well as colloidal suspension thickness were investigated. Dependent scattering effects were found to prevail for particle volume fractions as low as 1% depending on the particle size and refractive index. Evidences of dependent scattering were also observed experimentally in the visible normal-hemispherical transmittance of 10 mm thick colloidal suspensions of silica nanoparticles with diameter between 16 and 30 nm and particle volume fraction ranging from 2% to 15%. Moreover, good agreement was found between experimental measurements and numerical predictions from the R2T2 method. By contrast, assuming independent scattering underestimated systematically the normal-hemispherical transmittance, especially for large particle volume fraction. As such, this paper presents, for the first time, experimental validation of the R2T2 method and its ability to account for dependent scattering.

The SSSS scheme: a method for calculating multiple scattering of electromagnetic radiation by a collection of sparsely spaced spherical scatterers of Mie-scattering size based on first principles.

We present a method for calculating multiple scattering of electromagnetic radiation by a collection of sparsely spaced spherical scatterers (SSSS) of Mie-scattering size based on first principles rather than radiative transfer theory. In this respect, our methodology is conceptually similar to the superposition T-matrix method. However, our implementation, which we call the SSSS scheme, differs in a number of respects. Overall, the SSSS scheme is simpler, it is better suited numerically to sparse spacing, and the computer memory required is only linearly dependent on the total number of scatterers. We suggest that the SSSS scheme would be particularly useful for examining the effects of different spatial configurations of drops within water clouds in Earth's atmosphere and would also be useful in other fields of research in which the exact configuration of a collection of sparsely spaced Mie-sized scatterers is important.

Orientation-averaged light scattering by nanoparticle clusters: Far-field and near-field benchmarks of numerical cubature methods

The optical properties of nanoparticles can be substantially affected by their assembly in compact aggregates. This is a common situation notably for nanoparticles synthesised and self-assembled into rigid clusters in colloidal form, where they may be further characterised or used in spectroscopic applications. The theoretical description of such experiments generally requires averaging the optical response over all possible cluster orientations, as they randomly orient themselves over the course of a measurement. This averaging is often done numerically by simulating the optical response for several directions of incidence, using a spherical cubature method. The simulation time increases with the number of directions and can become prohibitive, yet few studies have examined the trade-off between averaging accuracy and computational cost. We benchmark seven commonly-used spherical cubature methods for both far-field and near-field optical responses for a few paradigmatic cluster geometries: dimers of nanospheres and of nanorods, and a helix. The relative error is rigorously evaluated in comparison to analytical results obtained with the superposition T-matrix method. Accurate orientation averaging is especially important for quantities relating to optical activity, the differential response to left and right circularly polarised light, and our example calculations include in particular far-field circular dichroism and near-field local degree of optical chirality.

Multiple scattering of light in nanoparticle assemblies: User guide for the terms program

We introduce terms, an open-source Fortran program to simulate near-field and far-field optical properties of clusters of particles. The program solves rigorously the Maxwell equations via the superposition T-matrix method, where incident and scattered fields are decomposed into series of vector spherical waves.terms implements several algorithms to solve the coupled system of multiple scattering equations that describes the electromagnetic interaction between neighbouring scatterers. From this formal solution, the program can compute a number of physically-relevant optical properties, such as far-field cross-sections for extinction, absorption, scattering and their corresponding circular dichroism, as well as local field intensities and degree of optical chirality. By describing the incident and scattered fields in a basis of spherical waves the T-matrix framework lends itself to analytical formulas for orientation-averaged quantities, corresponding to systems of particles in random orientation; terms offers such computations for both far-field and near-field quantities of interest. This user guide introduces the program, summarises the relevant theory, and is supplemented by a comprehensive suite of stand-alone examples in the website accompanying the code.

Direct comparison between single-scattering properties of ordered and disordered aggregates of nano-sized scattering centers.

In this study, we examine the single-scattering properties of aggregates of nano-sized spherical scattering centers (spherules) of different sizes and refractive indices, with an emphasis on contrasting the single-scattering properties of ordered and disordered aggregates, holding all other parameters constant. The ordered aggregates are constructed by arranging the spherules in a simple cubic configuration, while the disordered aggregates are constructed using an ideal amorphous solid algorithm. The single-scattering properties of both kinds of aggregates are computed using the superposition T-matrix method. We find that, in most cases, the scattering and absorption and hence extinction of radiation by ordered aggregates is stronger than for disordered aggregates: for the cases we examine, the average percent difference in scattering efficiency is 14%, and the maximum percent difference in scattering efficiency is 44%; the average percent difference in absorption efficiency is 5.3%, and the maximum percent difference in absorption efficiency is 18%; the average percent difference in extinction efficiency is 12%, and the maximum percent difference in extinction efficiency is 40%. These differences have implications regarding radiative transfer in systems of amorphous particles in general.

(UV, VIS) Laboratory evaluation of the lidar depolarization ratio of freshly emitted soot aggregates from pool fire in ambient air at exact backscattering angle

In this paper, a controlled-laboratory experiment is carried out to evaluate the lidar depolarization ratio of freshly emitted soot aggregates in the exact backward scattering direction at 180.0°. The experiment is performed at two wavelengths simultaneously, namely 355 and 532 nm, often used in polarimetric lidar remote sensing. The soot aggregates are generated from a kerosene JET A-1 pool fire in laboratory ambient air and microscopic images confirm the fractal morphology of generated soot aggregates. Then, the Superposition T-Matrix (STM) method is applied to numerically simulate the soot aggregates backscattering properties for different soot particles refractive indices, monomer radii and monomer numbers. The range of these parameters which ensures the lowest discrepancy between the laboratory measurement and the STM-computations is discussed within experimental and numerical error bars. We find that the polydisperse monomers model gives an overall better evaluation of the ratio F22(π)/F11(π). In the polydisperse case, our numerical and laboratory experimental findings agree at both wavelengths for a refractive index m = 2.65 + i1.32 and monomer number Nm > 40 at a mean monomer radius of rp = 30 nm (Nm > 160 at rp = 27.5 nm). We believe this work may be useful for the light scattering and remote sensing communities and may also help future studies aimed at better understanding the impact of soot particle aggregates on the Earth's climate, which still needs to be precisely quantified.

Effects of primary particle size on light absorption enhancement of black carbon aerosols using the superposition T-matrix method

Light absorption enhancement (Eabs) of black carbon (BC) aerosol following atmospheric aging is one of the most challenging issues in the assessment of aerosol radiative forcing. BC Eabs is constrained by complex particle morphologies; however, large uncertainties continue to occur due to certain morphological parameters, including primary particle size. The values of Eabs during BC aging is quantified with diverse primary particle sizes using the superposition T-matrix method (STM). The results show that the uncertainty of absorption enhancement due to the primary particle size of fully aged BC particles ranges from ~10% to 20%, while the uncertainties arising from varied BC volume-equivalent size and fractal dimension are ~20–30% and ~8–12%, respectively. The optical properties of BC particles with volume-equivalent radii ranging from 50 to 70 nm were largely influenced (up to ~50%) by inappropriate assumptions regarding primary particle size. The specific assumptions of primary particle size in optical modeling plays an important role in constraining BC Eabs.

Effects of phase transformation on the ultraviolet optical properties of alumina clusters in aircraft plumes.

Alumina particles experience phase transition as an undercooling process along the plume, during which the liquid alumina clusters transform into multiphase, and then into α phase. The phase transformation model was built by an improved diffusion limited aggregation (DLA) algorithm with monomers of stratified structure. The effects of phase transformation on the ultraviolet optical characteristics of alumina clusters were studied using the superposition T-matrix method (STMM). We found that the alumina clusters in phase transition had completely different optical properties compared with the fixed phase ones. Forward scattering, absorption efficiency and asymmetry parameter gradually decreased, whereas backward scattering, scattering efficiency, and single-scattering albedo gradually increased during the phase transformation process. Besides, multiphase alumina clusters were compared with the other two equivalent models, including the sphere model approximated by equivalent volume sphere (EVS) and the equivalent surface sphere (ESS) approaches and single-phase cluster model approximated by Maxwell-Garnett (MG) and Bruggeman (BR) approaches. Generally speaking, the optical properties of the single-phase cluster approximated by MG and BR approaches were relatively close to those of the real multiphase alumina cluster. Whereas the spheres approximated by EVS and ESS had great deviations, especially when the number of monomers in the cluster was 20, the relative error of scattering efficiency calculated by ESS was up to 52%. Therefore, approximate approaches for multiphase clusters should be chosen cautiously. Our results give further the understanding of the optical properties of alumina clusters. As the phase states are usually closely related to the plume radiation and burning process, these kinds of researches will be helpful to aircraft detection, identification, and other related fields.

Radiative properties of soot fractal superaggregates including backscattering and depolarization

The modeling of radiative properties of soot particles can be addressed by a number of methods. Among them, the canonical Rayleigh-Debye-Gans (RDG) theory and the Superposition T-Matrix Method (STMM) are particularly well adapted to the task. Here, both RDG and STMM are used to model the radiative properties of two types of fractal aggregates indicative of soot relevant to lidar sensing. One type, a canonical aggregate with a chain-like morphology, corresponds to low-sooting flames and is well characterized by a single fractal dimension. The other type, a superaggregate, exhibits multiple fractal dimensions and is seen in heavily sooting flames. Radiative properties such as the differential scattering cross-section, total scattering cross-sections, backscattering cross-sections, and linear depolarization-ratio (LDR) are calculated for a range of wavelengths from 300−1100 nm while including the wavelength dependence of the soot refractive index. Of particular interest is that depolarization by a superaggregate is found to be approximately ten times larger than the depolarization by a canonical chain-like aggregate and both exhibit a power-law with wavelength. Results for specific wavelengths of interest to lidar (355, 532, and 1064 nm) are tabulated for lidar applications. Additionally, RDG theory yields fairly accurate results for modeling the radiative properties, including lidar relevant parameters such as backscattering cross-sections, only for canonical soot fractal aggregates.

Isosbestic light absorption by metallic dimers: effect of interparticle electromagnetic coupling.

Isosbestic plasmonic nanostructures, which feature an invariance of optical absorption and heat generation upon varying the incident light polarization, have broad application in many fields such as nanochemistry, optical nanoantennas, and microbubble formation. In this study, we focus on the isosbestic optical absorption by metallic dimers and systematically investigate the coupling between two interacting particles by using both the superposition T-matrix method and dipole approximation model. We observe that the interparticle coupling effects on particle absorption can be both positive and negative, compared to an isolated particle. Meanwhile, the optical absorption properties of spheres with small size parameters can realize more flexible control through changing the sphere size, interparticle distance, and incident light wavelength. For illuminations with incident light propagating perpendicularly to the line joining the centers of the two spheres, isosbestic conditions will be satisfied as long as the absorption efficiencies for transverse and longitudinal illuminations are equal. For transverse illuminations along the dimer axis, the ratio of absorption efficiency of the two metallic spheres presents the fluctuation change with the interparticle distance. Owing to the strong interparticle coupling effects, it even leads to the absorption efficiency of the far sphere being higher than that of the near sphere. Our results are aimed at expanding our understanding of the interparticle electromagnetic coupling effects on isosbestic light absorption in plasmonic nanoparticle systems.

Mind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids.

The T-matrix framework offers accurate and efficient modelling of electromagnetic scattering by nonspherical particles in a wide variety of applications ranging from nano-optics to atmospheric science. Its analytical setting, in contrast to purely numerical methods, also provides a fertile ground for further theoretical developments. Perhaps the main purported limitation of the method, when extended to systems of multiple particles, is the often-stated requirement that the smallest circumscribed spheres of neighbouring scatterers not overlap. We consider here such a scenario with two adjacent spheroids whose aspect ratio we vary to control the overlap of the smallest circumscribed spheres, and compute far-field cross-sections and near-field intensities using the superposition T-matrix method. The results correctly converge far beyond the no-overlap condition, and although numerical instabilities appear for the most extreme cases of overlap, requiring high multipole orders, convergence can still be obtained by switching to quadruple precision. Local fields converge wherever the Rayleigh hypothesis is valid for each single scatterer and, remarkably, even in parts of the overlap region. Our results are validated against finite-element calculations, and the agreement demonstrates that the superposition T-matrix method is more robust and broadly applicable than generally assumed.

Lidar-relevant radiative properties of soot fractal aggregate ensembles

This study presents the averaged lidar-relevant radiative properties of numerically generated soot fractal aggregate ensembles. The radiative properties of these aggregates have been computed using the Superposition T-Matrix Method, with emphasis put on those that are most relevant to lidar application; the backscattering and extinction cross-sections, the Lidar Ratio and the Linear Depolarization Ratio. These lidar-relevant radiative properties have been computed over a broad spectrum, going from the ultraviolet to the near infrared, in order to address lidar instrument need for a priori knowledge in signal inversion procedures and measurement analysis. By averaging the computed radiative properties according to each set of morphological parameters, we obtain statistically representative results and we study the impacts of morphological changes on these lidar-relevant radiative properties. Our results show a strong impact of the primary particle radius on all considered radiative properties, while the number of primary particles induce significant variations on the cross-sections only. The fractal dimension, although being an essential morphological parameter, has a weak influences on the lidar-relevant radiative properties.

Optical properties of chain-like soot with water coatings

In a moist atmosphere, the ageing process of aerosol can make the agglomerated soot particles compact, and cause them to be covered by a water coating. Based on the cluster‒cluster aggregation (CCA) algorithm, the models of chain-like soot with water coatings (Models A to E) were generated in this study. The superposition T-matrix method was employed to calculate their optical properties at 337, 550, 860, and 1060 nm wavelengths, with a focus on the impact of the soot inclusion morphology and water coating. Our results indicate that for particles with a looser soot-inclusion structure, there is a larger difference in the scattering phase function between them and the corresponding particles with a spherical soot core. The largest relative difference reached 51.8% at 337 nm. Impacted by the size parameter, the extinction cross section (Cext), absorption cross section (Cabs), scattering cross section (Csca), and single scattering albedo (SSA) increased as the water coating radius (Rwater) increased and incidence wavelength decreased. The traditional assumption of a spherical soot core can cause the Cext, Cabs, and Csca to be overestimated, and cause the SSA to be underestimated when the incident wavelength is 337 nm. At 1060 nm, the assumption can cause the Cext, Cabs, and Csca to be underestimated, and lead the SSA to be overestimated. When the fractal dimension (Df) of chain-like soot inclusion increased from 1.8 to 2.6, the SSA of the particles with a Rwater of 0.20 μm significantly decreased from 0.784 to 0.764 at 1060 nm. Moreover, the thickness of the water coating had a stronger effect on the particles with chain-like soot inclusion at 337 nm than that at 1060 nm. For the 337 nm wavelength, the difference between the Cext and Csca in Model B when Rwater = 0.30 and 0.20 μm was 0.588 and 0.587 μm2, respectively. The differences were only 0.096 and 0.095 μm2, respectively, for the 1060 nm wavelength. Based on the results calculated by the superposition T-matrix method, the ratios of P22(Θ)/P11(Θ) for chain-like soot with water coatings are not absolutely equal to 100%. When the Df value of aggregated soot inclusion is a constant, P22(Θ)/P11(Θ) decreased as the volume ratio of soot inclusion to the water droplet increased. Therefore, the ratio of P22(Θ)/P11(Θ) can be potentially used as an optical indicator to describe the morphology of non-spherical and/or inhomogeneous particles (or inclusion) for internal aerosol, fog, or cloud particles. Generally, although the thickness of the water coating, to a large extent, dominates the optical properties of the internal mixtures, the morphology of aggregated soot inclusion is a key factor for causing uncertainties in optical parameters. This is especially so when the volume ratio of the soot inclusion and water droplet is large, and the structure of the soot inclusion is loose.

Scattering And Absorption of Light in Planetary Regoliths

Theoretical, numerical, and experimental methods are presented for multiple scattering of light in macroscopic discrete random media of densely-packed microscopic particles. The theoretical and numerical methods constitute a framework of Radiative Transfer with Reciprocal Transactions (R2T2). The R2T2 framework entails Monte Carlo order-of-scattering tracing of interactions in the frequency space, assuming that the fundamental scatterers and absorbers are wavelength-scale volume elements composed of large numbers of randomly distributed particles. The discrete random media are fully packed with the volume elements. For spherical and nonspherical particles, the interactions within the volume elements are computed exactly using the Superposition T-Matrix Method (STMM) and the Volume Integral Equation Method (VIEM), respectively. For both particle types, the interactions between different volume elements are computed exactly using the STMM. As the tracing takes place within the discrete random media, incoherent electromagnetic fields are utilized, that is, the coherent field of the volume elements is removed from the interactions. The experimental methods are based on acoustic levitation of the samples for non-contact, non-destructive scattering measurements. The levitation entails full ultrasonic control of the sample position and orientation, that is, six degrees of freedom. The light source is a laser-driven white-light source with a monochromator and polarizer. The detector is a mini-photomultiplier tube on a rotating wheel, equipped with polarizers. The R2T2 is validated using measurements for a mm-scale spherical sample of densely-packed spherical silica particles. After validation, the methods are applied to interpret astronomical observations for asteroid (4) Vesta and comet 67P/Churyumov-Gerasimenko (Figure 1) recently visited by the NASA Dawn mission and the ESA Rosetta mission, respectively.