Light scattering in dense particulate media

Physical characterization of planetary objects would be accelerated by the capability of simulating light scattering from an arbitrary dense multiparticle medium. Even though exact methods that solve the Maxwell equations exist, such as the superposition T-matrix method (STMM), they are too compute-intensive to be applied to large macroscale objects such as an asteroid or a planetary surface. In the thesis, radiative transfer (RT) based tools are developed, studied, and offered as an approximation to simulate light scattering from dense particulate media. The RT theory has been derived for the sparse random medium, and it fails when applied to the dense random medium. In order to extend the applicability to dense random media, we have been working with the incoherent volume-element treatment for the RT called the radiative transfer with reciprocal transactions (R²T²). Instead of using a single particle as the diffuse scatterer in the RT, the properties of the incoherent volume elements are used. These properties are computed from the incoherent electric fields extracted by subtracting the coherent part from the free-space scattered electric fields. The R²T² is validated by simulating various dense random media for which the STMM is still applicable. In the geometric optics regime, there are the generalized Snel's law and Fresnel matrices that can be used to simulate light scattering from large objects. For dense particulate media, the computation can be slow, so diffuse scattering as a tool to speed up the computation is studied. Previous studies have included surface roughness with approximate functions, but here a layer of particles is added on top of the diffusely scattering medium. We replace the classical extinction mean free path with more informative extinction distance distribution that is gathered numerically. The comparison between the RT model, our model, and the "ground truth", in which only the generalized Snel's law and Fresnel matrices are used, reveal that our model works better than the RT model. Even though the computational methods are validated against each other, the methods need to be validated experimentally against controlled samples with well-known physical properties in order to be a reliable source of information. For the validation of the R²T², we computationally simulated a well-controlled sample of which the light-scattering characteristics have been measured. Although the phase function of the simulation and measurement match well, the other scattering characteristics, seem to reveal small discrepancies between the model and the measurements. Still, the various computational validations and this experimental validation show that the R²T² works well and can be used in the near future as a characterization tool.Tiheän monipartikkelipinnan valonsirontaominaisuuksien tarkka simulointi nopeuttaisi Aurinkokunnan kappaleiden pintojen ominaisuuksien kartoittamista. Nykyiset eksaktit teoreettiset menetelmät pystyvät ratkaisemaan valonsirontaongelmat numeerisesti, mutta ne ovat laskennallisesti raskaita monipartikkelisysteemeille. Valonsironta tiheistä monipartikkelipinnoista, kuten asteroidien pinnoista, täytyy siis ratkaista käyttämällä approksimatiivisia menetelmiä, joissa valonsironnan fysiikka on yksinkertaistettu. Säteilynkuljetusteoria on johdettu Maxwellin yhtälöistä olettamalla sirottava systeemi harvaksi ja siksi menetelmä tuottaa virheellisiä tuloksia tiheillä väliaineilla. Ongelman ratkaisemiseksi kehitettiin tiheiden väliaineiden säteilynkuljetus R²T² (engl. Radiative transfer with reciprocal transactions), jossa yksittäinen sirottava partikkeli on korvattu epäkoherenteilla tilavuuselementeillä. Tässä väitöskirjassa esitellyt julkaisut näyttävät menetelmän laajentavan säteilynkuljetuksen käyttöaluetta vertailemalla R²T²:n, eksaktien menetelmien ja normaalin säteilynkuljetuksen tuloksia. Lisäksi R²T²:ta sovellettiin todellisen kappaleen valonsirontaominaisuuksien laskemiseen, millä osoitettiin, että menetelmää voidaan käyttää lähitulevaisuudessa pintojen karakterisointiin. Geometrisen optiikan alueella partikkelit ovat suuria aallonpituuteen verrattuna, ja siksi säteenseurantaa voidaan käyttää valonsirontaongelman ratkaisemiseen. Säteenseurannassa valonsäde voi jakautua jokaisen sirontaprosessin yhteydessä, mikä tekee menetelmästä laskennallisesti raskaan. Ongelman lieventämiseksi säteilynkuljetuksen käyttämistä säteenseurannan tukena tutkittiin, missä osa kappaleesta korvattiin tilastollisena väliaineena. Vertailut menetelmien välillä osoittivat, että menetelmä nopeuttaa simulaatiota ilman merkittävää tarkkuuden menettämistä

Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data

This document is the Accepted Manuscript version of the following article: Emmanuel Oluwatobi Salawu, Evelyn Hesse, Chris Stopford, Neil Davey, and Yi Sun, 'Applying machine learning methods for characterization of hexagonal prisms from their 2D scattering patterns – an investigation using modelled scattering data', Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 201, pp. 115-127, first published online 5 July 2017. Under embargo. Embargo end date: 5 July 2019. The Version of Record is available online at doi: https://doi.org/10.1016/j.jqsrt.2017.07.001. © 2017 Elsevier Ltd. All rights reserved.Better understanding and characterization of cloud particles, whose properties and distributions affect climate and weather, are essential for the understanding of present climate and climate change. Since imaging cloud probes have limitations of optical resolution, especially for small particles (with diameter < 25 μm), instruments like the Small Ice Detector (SID) probes, which capture high-resolution spatial light scattering patterns from individual particles down to 1 μm in size, have been developed. In this work, we have proposed a method using Machine Learning techniques to estimate simulated particles’ orientation-averaged projected sizes (PAD) and aspect ratio from their 2D scattering patterns. The two-dimensional light scattering patterns (2DLSP) of hexagonal prisms are computed using the Ray Tracing with Diffraction on Facets (RTDF) model. The 2DLSP cover the same angular range as the SID probes. We generated 2DLSP for 162 hexagonal prisms at 133 orientations for each. In a first step, the 2DLSP were transformed into rotation-invariant Zernike moments (ZMs), which are particularly suitable for analyses of pattern symmetry. Then we used ZMs, summed intensities, and root mean square contrast as inputs to the advanced Machine Learning methods. We created one random forests classifier for predicting prism orientation, 133 orientation-specific (OS) support vector classification models for predicting the prism aspect-ratios, 133 OS support vector regression models for estimating prism sizes, and another 133 OS Support Vector Regression (SVR) models for estimating the size PADs. We have achieved a high accuracy of 0.99 in predicting prism aspect ratios, and a low value of normalized mean square error of 0.004 for estimating the particle’s size and size PADs.Peer reviewe

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging

Radiative transfer modeling of thermal infrared emissivity spectra: applications to martian regolith observations

Satellite and rover remote sensing of planetary regolith surfaces, in the form of thermal infrared emissivity spectra taken at nadir and off-nadir angles of emergence from the surface, requires use of theoretical models for interpretation of constituent grain physical properties. However, such models have remained in stasis in recent years, with nearly a ten-year gap in significant advances. To date, no radiative transfer model (semiempirical, exact, or hybrid solution) has been able to adequately predict the nadir emissivity behavior of simple mineral assemblages. Few measurements have been attempted in the laboratory or field regarding directional emissivity effects of planetary regoliths; such measurements are necessary for modeling and interpreting directional emissivity effects that are clearly present in the Mars Global Surveyor Thermal Emission Spectrometer (MGS-TES) and Mars Exploration Rover mini-TES datasets. The research goals of this dissertation directly involve the extraction of information on two major dust microphysical properties: particle size and packing fraction. Results of a theoretical model are compared to laboratory-measured thermal infrared (wavenumber = 2000-200 cm-1) emissivities for micron-sized quartz particles. This work shows that Mie theory, a widely used but poor approximation to irregular grain shape, fails to produce the single scattering properties needed to arrive at the desired laboratory emissivity values and also illustrates shortcomings of popular dense packing correction methods. Through numerical experiments, I provide evidence that, assuming RT methods work given sufficiently well-quantified inputs, assumptions about the scatterer itself constitute the most crucial aspect of modeling nadir emissivity values. Also included in the dissertation are detailed laboratory investigations used to obtain realistic and quantifiable input parameters to the theoretical model, i.e., particle size distribution and particle shape. Nadir and directional emissivity comparison datasets obtained in the laboratory and in the field at Mars terrestrial analog sites are presented to set the stage for modeling directional emissivity. Future directions (e.g., how to incorporate nonspherical particle shapes into the model) are briefly discussed

Modelling of light scattering by cirrus ice crystals using geometric optics combined with diffraction of facets

A new 3D model of light scattering applicable to dielectric faceted objects is presented. The model combines Geometric Optics with diffraction on individual facets yet maintains the low computational expense of standard Geometric Optics. The current implementation of the model is explained and then applied to the problem of light scattering by ice crystals in cirrus clouds. Accurate modelling of the scattering properties of such crystals is crucial to better understanding of cirrus radiative properties and hence to climate modelling and weather forecasting. Calculations using the new model are compared to a separation of variables method and the Improved Geometric Optics method with encouraging results. The model shows significant improvements over standard Geometric Optics. The size applicability of the new model is discussed. The model is applied to a range of crystal geometries that have been observed in cirrus including the hexagonal column, the hollow column, the droxtal and the bullet rosette. For each geometry the phase function and degree of linear polarization are presented and discussed. Ice analogue crystals grown at the University of Hertfordshire have optical properties very close to ice but are stable at room temperature. The geometries of three ice analogue crystals are reconstructed and the single scattering properties of the reconstructions are presented. 2D scattering patterns calculated using the model are compared to laboratory photographs of scattering patterns on a screen created by an ice analogue hexagonal column. The agreement is shown to be very good. By applying the model to a range of geometries, it is shown that the results in the form of 2D scattering patterns can potentially be used to aid particle characterization. By combining the model with a Monte Carlo radiative transfer code, comparisons are made with aircraft radiance measurements of cirrus provided by the Met Office. The improvements over standard Geometric Optics are found to persist following a radiative transfer treatment

Optical Remote Sensing Of Snow On Sea Ice: Ground Measurements, Satellite Data Analysis, And Radiative Transfer Modeling

Thesis (Ph.D.) University of Alaska Fairbanks, 2002The successful launch of the Terra satellite on December 18, 1999 opened a new era of earth observation from space. This thesis is motivated by the need for validation and promotion of the use of snow and sea ice products derived from MODIS, one of the main sensors aboard the Terra and Aqua satellites. Three cruises were made in the Southern Ocean, in the Ross, Amundsen and Bellingshausen seas. Measurements of all-wave albedo, spectral albedo, BRDF, snow surface temperature, snow grain size, and snow stratification etc. were carried out on pack ice floes and landfast ice. In situ measurements were also carried out concurrently with MODIS. The effect of snow physical parameters on the radiative quantities such as all-wave albedo, spectral albedo and bidirectional reflectance are studied using statistical techniques and radiative transfer modeling, including single scattering and multiple scattering. The whole thesis consists of six major parts. The first part (chapter 1) is a review of the present research work on the optical remote sensing of snow. The second part (chapter 2) describes the instrumentation and data-collection of ground measurements of all-wave albedo, spectral albedo and bidirectional reflectance distribution function (BRDF) of snow and sea ice in the visible-near-infrared (VNIR) domain in Western Antarctica. The third part (chapter 3) contains a detailed multivariate correlation and regression analysis of the measured radiative quantities with snow physical parameters such as snow density, surface temperature, single and composite grain size and number density. The fourth part (chapter 4) describes the validation of MODIS satellite data acquired concurrently with the ground measurements. The radiances collected by the MODIS sensor are converted to ground snow surface reflectances by removing the atmospheric effect using a radiative transfer algorithm (6S). Ground measured reflectance is corrected for ice concentration at the subpixel level so that the in situ and space-borne measured reflectance data are comparable. The fifth part (chapter 5) investigates the single scattering properties (extinction optical depth, single albedo, and the phase function or asymmetry factor) of snow grains (single or composite), which were calculated using the geometrical optical method. A computer code, GOMsnow, is developed and is tested against benchmark results obtained from an exact Mie scattering code (MIE0) and a Monte Carlo code. The sixth part (chapter 6) describes radiative transfer modeling of spectral albedo using a multi-layer snow model with a multiple scattering algorithm (DISORT). The effect of snow stratification on the spectral albedo is explored. The vertical heterogeneity of the snow grain-size and snow mass density is investigated. It is found that optical remote sensing of snow physical parameters from satellite measurements should take the vertical variation of snow physical parameters into account. The albedo of near-infrared bands is more sensitive to the grain-size at the very top snow layer (<5cm), while the albedo of the visible bands is sensitive to the grain-size of a much thicker snow layer. Snow parameters (grain-size, for instance) retrieved with near-infrared channels only represent the very top snow layer (most probably 1--3 cm). Multi-band measurements from visible to near-infrared have the potential to retrieve the vertical profile of snow parameters up to a snow depth limited by the maximum penetration depth of blue light

Modelling optical properties of morphologically complex aerosols

The interpretation of remote sensing data of atmospheric aerosol particles requires a thorough understanding of the links between microphysical and optical properties. Morphologically complex aerosol models describe the particles’ morphology in detail. Based on the calculations with realistic particle models, simplified models can be devised, which incorporate essential microphysical properties for reproducing the optical properties. In this thesis, such models are developed and tested for soot aerosols, for mineral dust, and for dried and partially dissolved sea salt aerosol.A tunable model for coated soot aggregates is presented, and corresponding uncertainty estimates are performed. One of the main sources of uncertainty for thickly coated soot is the chemical composition of the coating, as represented by its refractive index. These uncertainties are so substantial, they are investigated as a potential source of information. The calculated lidar-measurable (spectral) quantities are distinct for two coating materials.The non-sphericity of a particle is identified as an essential morphological property affecting the linear depolarisation ratio. For coated soot another important property is the amount of carbon interacting with the incident wave, as it affects the absorption cross section. Combining these two insights resulted in the core grey shell dimer (CGS2) model, which is introduced in this thesis.For dry sea salt aerosol different random geometries are investigated, to simultaneously calculate linear depolarisation and extinction-to-backscatter ratio of dried sea salt aerosol particles. The results indicate that convex polyhedra are best suited to represent dried sea salt aerosol particles. Thus, the coated convex polyhedra model is proposed as the basis for modelling dissolving sea salt in a further study. For dissolving sea salt three simplified, equally well-performing models are presented, which identify the change in particle sphericity as a key morphological feature.A spheroidal model with a single refractive index and a single aspect ratio is fitted to laboratory measurements of 131 different dust samples. The scattering of the measurements about the model can mainly be explained by changes in morphology and dielectric properties, and to a lesser degree by the width of the particle size distribution.These results are expected to significantly advance our capacity to exploit and interpret polarimetric remote sensing observations of morphologically complex and chemically heterogeneous aerosol. This will be important for constraining Earth-system climate and air-quality forecasting models, and for evaluating and improving parameterisations of aerosol processes in these environmental modelling system