This thesis is devoted to improve our knowledge on the theory of polarized line formation in a magneto-turbulent medium, and in a scattering dominated magnetized medium, where partial redistribution (PRD) effects become important. Thus the thesis consists of two parts. In the first part we carry out a detailed investigation on the effect of random magnetic fields on Zeeman line radiative transfer. In the second part we develop the theory of polarized line formation in the presence of arbitrary magnetic fields and with PRD. We present numerical methods of solution of the relevant transfer equation in both part-I and II. In Chapter I we give a general introduction, that describes the basic physical concepts required in both parts of the thesis. Chapters 2-6 deal with the part-I, namely stochastic polarized Zeeman line formation. Chapters 7-10 deal with part –II, namely the theory and numerics of polarized line formation in scattering media. Chapter II is devoted to the future outlook on the problems described in part-I and II of the thesis. Appendices are devoted to additional mathematical details. Part-I of the Thesis: Stochastic polarized line formation in magneto-turbulent media Magneto-convection on the Sun has a size spectrum that spans several orders of magnitudes and hence develops turbulent elements or eddies the sizes of which are much smaller than the spatial resolution of current spectro-polarimeters (about 0.2 arcsec or 150km at the photospheric level). We were thus strongly motivated to consider the Zeeman effect in a medium where the magnetic field is random with characteristic scales of variation comparable to the radiative transfer characteristic scales. In Chapter 2, we consider the micro-turbulent limit and study the mean zeeman absorption matrix in detail. The micro-turbulent limit refers to the case when the scales of fluctuations of the random field are much smaller than the photon mean free paths associated to the line formation. The ‘mean’ absorption and anomalous dispersion coefficients are calculated for random fields with a non-Zero mean value - isotropic or anisotropic Gaussian distributions that are azimuthally invariant about the direction of the mean field. The averaging method is described in detail, and fairly explicit expressions for the mean coefficients are established. A detailed numerical investigation of the mean coefficients illustrates two simple effects of the magnetic field fluctuations: (i) broadening of the components by fluctuations of the field strength, leaving the π-components unchanged, and (ii) averaging over the angular dependence of the π and components. Angular averaging can modify the frequency profiles of the mean coefficients quite drastically, namely, the appearance of an unpolarized central component in the diagonal absorption coefficient, even when the mean field is in the direction of the line-of-sight. For isotropic fluctuations, the mean coefficients can be expressed in terms of generalized Voigt and Faraday-Voigt functions, which are related to the derivatives of the Voigt and Faraday-Voigt functions. In chapter 3, we study these functions in detail. Simple recurrence relations are established and used for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are also derived. In Chapter 4, we consider the Zeeman effect from a magnetic field which has a finite correlation length(meso-turbulence) that can be varied from zero to infinity and thus made comparable to the photon mean free-path. The random vector magnetic field B is modeled by a Kubo-Anderson process – a piecewise constant Markov process characterized by a correlation length and a probability distribution function(PDF) for the random values of the magnetic field. The micro- and macro-turbulent limits are recovered when the correlation length goes to zero or infinity respectively. Mean values and rms fluctuations around the mean values are calculated numerically for a random magnetic field with isotropic Gaussian fluctuations. The effects of a finite correlation length are discussed in detail. The rms fluctuations of the Stokes parameters are shown to be very sensitive to the correlation length of the magnetic field. It is suggested to use them as a diagnostic tools to determine the scale of unresolved features in the solar atmosphere. In Chapter 5, using statistical approach, we analyze the effects of random magnetic fields on Stokes line profiles. We consider the micro and macro-turbulent regimes, which provide bounds for more general random fields with finite scales of variations. The mean Stokes parameters are obtained in the micro-turbulent regime, by first averaging the Zeeman absorption matrix Φ over the PDF P(B) of the magnetic field and then solving the concerned radiative transfer equation. In the macro-turbulent regime, the mean solution is obtained by averaging the emergent solution over P(B). In this chapter, we consider the same Gaussian PDFs that are used to construct (Φ) in chapter 2. Numerical simulations of magneto-convection and analysis of solar magnetograms provide the empirical PDF for the magnetic field line-of-sight component on the solar atmosphere. In Chapter 6, we explore the effects of different kinds of PDFs on Zeeman line formation. We again consider the limits of micro and macro-turbulence. The types of PDFs considered are: (a) Voigt function and stretched exponential type PDFs for fields with fixed direction but fluctuating strength. (b) Cylindrically symmetrical power law for the angular distribution of magnetic fields with given field strength. (c) Composite PDFs accounting for randomness in both strength and direction obtained by combining a Voigt function or a stretched exponential with an angular power law. The composite PDF proposed has an angular distribution peaked about the vertical direction for strong fields and is nearly isotropically distributed for weak fields, which could mimic solar surface random fields. We also describe how the averaging technique for a normal Zeeman triplet may be generalized to the more common case of anomalous Zeeman splitting patterns. Part-II of the Thesis: Polarized line formation in scattering media-Theory and numerical methods Many of the strongest and most conspicuous lines in the Second Solar Spectrum are strong lines that are formed rather high, often in the chromosphere above the temperature minimum. From the standard, unpolarized and non-magnetic line-formation theory such lines are known to be formed under the conditions that are very far from local thermodynamic equilibrium. They are characterized by broad damping wings surrounding the line core. Doppler shifts in combination with collisions cause photons that are absorbed at a given frequency to be redistributed in frequency across the line profile in a complex way during the scattering process. Two idealized, limiting cases to describe this redistribution are “frequency coherence” and “complete redistribution” (CRD), but the general theory that properly combines these two limiting cases goes under the name “partial frequency redistribution” (PRD). Resonance lines which are usually strong can be properly modeled only when PRD is taken into account. To use these strong lines for magnetic field diagnostics we need a line scattering theory of PRD in the presence of magnetic fields of arbitrary strength. In the second part of the thesis we develop such a theory and derive the polarized PRD matrices. These matrices are then used in the polarized line transfer equation to compute the emergent Stokes parameters. Polarized scattering in spectral lines is governed by a 4 x 4 matrix that describes how the Stokes vector is scattered in all directions and redistributed in frequency within the line. In Chapter 7, using a classical approach we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction, and for a J = 0 → 1 → 0 transition. This case of arbitrary magnetic fields is called the Hanle-Zeeman regime, since it covers both the partially overlapping weak and strong-field regimes, in which the Hanle and Zeeman effects respectively dominate the scattering polarization. In this general regime the angle-frequency correlations that describe the so-called PRD are intimately coupled to the polarization properties. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of J quantum numbers. In chapter 8 , we show explicitly that for a J = 0 → 1 → 0 scattering transition there exists an equivalence between the Hanle-Zeeman redistribution matrix that is derived through quantum electrodynamics(Bommier 1997b) and the one derived in Chapter 7 starting from the classical, time-dependent oscillator theory of Bommier & Stenflo (1999). This equivalence holds for all strengths and directions of the magnetic field. Several aspects of the Hanle-Zeeman redistribution matrix are illustrated, and explicit algebraic expressions are given, which are of practical use for the polarized line transfer computations. In chapter 9, we solve the polarized radiative transfer equation numerically, taking into account both the Zeeman absorption matrix and the Hanle-Zeeman redistribution matrix. We compute the line profiles for arbitrary field strengths, and scattering dominated line transitions. We use a perturbation method (see eg. Nagendra et al. 2002) to solve the Hanle-Zeeman line transfer problem. The limiting cases of weak field Hanle scattering and strong field Zeeman true absorption are retrieved. The ilntermediate regime, where both Zeeman absorption and scattering effects are important, is studied in some detail. Numerical method used to solve the Hanle-Zeeman line transfer problem in Chapter 9 is computationally expensive. Hence it is necessary to develop fast iterative methods like PALI (Polarized Approximate Lambda Iteration). As a first step in this direction we develop such a method in Chapter 10 to solve the transfer problem with weak field Hanle scattering. We use a ‘redistribution matrix’ with coupling between frequency redistribution and polarization and no domain decomposition. Such a matrix is constructed by angle-averaging the frequency dependent terms in the exact weak field Hanle redistribution matrix for a two-level atom with unpolarized ground level (that can be obtained by taking the weak field limit of the Hanle-Zeeman redistribution matrix). In the past, the PALI technique has been applied to redistribution matrices in which frequency redistribution is ‘decoupled’ from scattering polarization, the decoupling being achieved by an adequate decomposition of the frequency space into several domains. In this chapter, we examine the consequences of frequency space decomposition, and the resulting decoupling between the frequency redistribution and polarization, on the solution of the polarized transfer equation for the Stokes parameters.

Der Strahlungstransport stellt eine von drei Arten des Wärmetransports zwischen Gebieten unterschiedlicher Temperatur dar. Eine der einfachsten Formen bildet der Strahlungstransport im Vakuum, ein Vorgang, der im kosmischen Umfeld, beispielsweise bei der Energieübertragung von einem Stern auf seine Planeten, beobachtbar ist. Hierbei ist es hinreichend, sich auf die Betrachtung von Oberflächen zu beschränken. Strahlungstransport kann jedoch auch in semitransparenten Medien, wie biologischem Gewebe oder Glas, beobachtet werden. Das Medium, in dem der Strahlungstransport erfolgt, wirkt sich durch Vorgänge wie Absorption, Emission, Reflexion oder Streuung auf den Strahlungstransport aus. Für die Modellierung des Strahlungstransports in einem solchen Umfeld können verschiedene Modelle, darunter das Strahlenmodell, genutzt werden. Dieses Modell beschreibt den Wärmetransport anhand einer skalaren Größe, die Strahlungsintensität genannt wird. Betrachtet wird die Strahlungsintensität in diesem Modell entlang eines Strahls in eine vorgegebene Richtung. Die mathematische Darstellung des Strahlenmodells des Strahlungstransports in partizipierenden Medien führt auf eine richtungsabhängige Integro-Differentialgleichung. Ist die Richtungsabhängigkeit nicht von Interesse, so kann der Übergang zu einer winkelintegrierten Form erfolgen. Dieser Übergang führt schließlich auf ein System schwach singulärer fredholmscher Integralgleichungen zweiter Art. Dieses charakterisiert nun nicht mehr die erwähnte Strahlungsintensität, sondern beschreibt die sogenannte Einstrahlung sowie den Strahlungsfluss. Das System singulärer Integralgleichungen kann mittels eines Galerkin-Ansatzes numerisch gelöst werden. Geht man von einer hinreichenden Glattheit des Randes aus, kann die Kompaktheit des Operators der Integralgleichungen gezeigt werden. Dies wiederum erlaubt Rückschlüsse auf die Existenz und Eindeutigkeit einer Lösung. Ein Augenmerk bei der Ermittlung der Galerkin-Näherung ist auf die Bestimmung der singulären Integrale der Galerkin-Diskretisierung zu richten. Für die Bestimmung multidimensionaler, singulärer Integrale stellt die Arbeit das Verfahren der hierarchischen Integration vor. Basierend auf einer Zerlegung des Integrationsgebietes, erfolgt die Beschreibung singulärer Integrale durch ein Gleichungssystem, dessen rechte Seite nur von regulären Integralen abhängig ist. Können diese regulären Integrale sowie die Lösung des Gleichungssystems exakt bestimmt werden, so sind auch die singulären Integrale exakt bestimmt. Bei einer numerischen Bestimmung der regulären Integrale ist die Fehlerordnung ausschlaggebend für den Fehler der singulären Integrale. Als Integrationsgebiete werden Hyperwürfel beliebiger Dimension sowie Simplizes bis einschließlich Dimension 3 als Integrationsgebiete betrachtet. Als Voraussetzungen an den Kern des Doppelintegrals sind nur die Eigenschaften der Translationsinvarianz sowie der Homogenität zu richten. Kann ein nicht translationsinvarianter oder nicht homogener Kern eines Integrals in Summanden zerlegt werden, die selbst translationsinvariant und homogen sind, ist auch die Bestimmung solcher Integrale möglich. Darüber hinaus stellt die Arbeit Verbindungen zu dem Begriff des Hadamard partie finie her. Auf diese Weise lässt sich das Verfahren der hierarchischen Integration für beliebige Dimensionen und beliebige Singularitätsordnungen anwenden. Die Strahlungstransportgleichung ist im Allgemeinen mittels eines Galerkin-Ansatzes lösbar, führt jedoch auf eine voll besetzte Systemmatrix. Numerische Beispiele beleuchten daher Methoden der Matrixkompression mittels hierarchischer Matrizen sowie der direkten Erzeugung schwach besetzter Matrizen über regulären Gittern und Gittern mit hängenden Knoten und skizziert Ansätze zur Parallelisierung auf entsprechenden Computersystemen.

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A novel technique for measuring gas temperature and spectral particle emissivity in high-temperature gas-particle streams is presented. The main application of this optical sensor is to improve the process control of batch unit operations, such as steelmaking furnaces. The spectral emission profile of CO and CO2 and the continuous particle emission in the 3.5 to 5 μm wavelength region was recorded and analyzed in real time with a low-resolution passive sensor. The sensor consisted of light collecting optics, a dispersion element (grating spectrometer) and a 64-pixel pyroelectric array. Wavelength and radiance calibrations were performed. The temperature of the gas-particle medium (Tg+p) followed from the least-squares minimization of the difference between the measured radiance in the 4.56-4.7 μm region –which saturates due to the large CO2 concentrations and path lengths in industrial furnaces– and the corresponding blackbody radiance. Particle emissivity (εp) was calculated at 3.95 μm from an asymptotic approximation of the Radiative Transfer Equation that yields the emerging radiance from a semi-infinite particle cloud. The major source of error in the magnitude of Tg+p and εp could come from particle scattering. Through the method of embedded invariance an expression was developed to estimate the lowering effect of particle size and volume fraction on the saturation of the 4.56-4.7 μm CO2 emission region. An iterative procedure for correcting the values of the gas-particle temperature and particle emissivity was applied to the datasets from the two industrial tests. Results from the measurement campaigns with the infrared sensor prototype at two full-scale furnaces are presented. A proof-of-concept test at a coal-fired boiler for electricity production was followed by more extensive measurements at a Basic Oxygen Furnace (BOF) for steelmaking. The second test provided temperature and particle emissivity profiles for eight heats, which highlighted the simplicity of the technique in obtaining in-situ measurements for modeling studies. Through the analysis of the particle emissivity profile in the BOF and the definition of a new variable –the minimum carbon time– a novel end-point strategy to stop the injection of high-purity oxygen during low-carbon heats in BOF converters was proposed.

A novel technique for measuring gas temperature and spectral particle emissivity in high-temperature gas-particle streams is presented. The main application of this optical sensor is to improve the process control of batch unit operations, such as steelmaking furnaces. The spectral emission profile of CO and CO2 and the continuous particle emission in the 3.5 to 5 μm wavelength region was recorded and analyzed in real time with a low-resolution passive sensor. The sensor consisted of light collecting optics, a dispersion element (grating spectrometer) and a 64-pixel pyroelectric array. Wavelength and radiance calibrations were performed. The temperature of the gas-particle medium (Tg+p) followed from the least-squares minimization of the difference between the measured radiance in the 4.56-4.7 μm region –which saturates due to the large CO2 concentrations and path lengths in industrial furnaces– and the corresponding blackbody radiance. Particle emissivity (εp) was calculated at 3.95 μm from an asymptotic approximation of the Radiative Transfer Equation that yields the emerging radiance from a semi-infinite particle cloud. The major source of error in the magnitude of Tg+p and εp could come from particle scattering. Through the method of embedded invariance an expression was developed to estimate the lowering effect of particle size and volume fraction on the saturation of the 4.56-4.7 μm CO2 emission region. An iterative procedure for correcting the values of the gas-particle temperature and particle emissivity was applied to the datasets from the two industrial tests. Results from the measurement campaigns with the infrared sensor prototype at two full-scale furnaces are presented. A proof-of-concept test at a coal-fired boiler for electricity production was followed by more extensive measurements at a Basic Oxygen Furnace (BOF) for steelmaking. The second test provided temperature and particle emissivity profiles for eight heats, which highlighted the simplicity of the technique in obtaining in-situ measurements for modeling studies. Through the analysis of the particle emissivity profile in the BOF and the definition of a new variable –the minimum carbon time– a novel end-point strategy to stop the injection of high-purity oxygen during low-carbon heats in BOF converters was proposed.

La disponibilité de nouveaux moyens d’acquisition en télédétection, satellitaire (PLEIADES, HYPXIM), aéroportée ou par drone (UAV) à très haute résolution spatiale ouvre la voie à leur utilisation pour l’étude de milieux complexes telles que les villes. En particulier, la connaissance de la ville pour l’étude des îlots de chaleur, la planification urbaine, l’estimation de la biodiversité de la végétation et son état de santé nécessite au préalable une étape de classification des matériaux qui repose sur l’utilisation de l’information spectrale accessible en télédétection hyperspectrale 0,4-2,5μm. Une des principales limitations des méthodes de classification réside dans le non traitement des zones à l’ombre. Des premiers travaux ont montré qu’il était possible d’exploiter l’information radiative dans les ombres des bâtiments. En revanche, les méthodes actuelles ne fonctionnent pas dans les ombres des arbres du fait de la porosité de leur couronne. L’objectif de cette thèse vise à caractériser les propriétés optiques de surface à l’ombre de la végétation arborée urbaine au moyen d’outils de transfert radiatif et de correction atmosphérique. L’originalité de ce travail est d’étudier la porosité d’un arbre via la grandeur de transmittance de la couronne. La problématique a donc été abordée en deux temps. Premièrement, la caractérisation de la transmittance d’un arbre isolé a été menée avec l’utilisation de l’outil DART à travers la mise en œuvre d’un plan d’expériences et d’études de sensibilité qui ont permis de la relier à des paramètres biophysiques et externes. Une campagne de mesures terrain a ensuite été réalisée afin d’évaluer son estimation à partir de différents niveaux de modélisation de l’arbre, dont un modèle réel acquis par mesures lidar terrestre. Deuxièmement, une nouvelle méthode de correction atmosphérique 3D adaptée à la végétation urbaine, ICARE-VEG, a été développée à partir des résultats précédents. Une campagne aéroportée et de mesures terrain UMBRA a été dédiée à sa validation. Ses performances comparées à d’autres outils existants ouvrent de larges perspectives pour l’interprétation globale d’une image par télédétection et pour souligner la complexité de modéliser des processus physiques naturels à une échelle spatiale très fine. / The new advances in remote sensing acquisitions at very high spatial resolution, either spaceborne (PLEIADES, HYPXIM), airborne or unmanned aerial vehicles borne, open the way for the study of complex environments such as urban areas. In particular, the better understanding of urban heat islands, urban planning, vegetation biodiversity, requires the knowledge of detailed material classification mapsbased on the use of spectral information brought by hyperspectral imagery 0.4-2.5μm. However, one of the main limitations of classification methods relies on the absence of shadow processing. Past studies have demonstrated that spectral information was possible to be extracted from shadows cast by buildings. But existing methods fail in shadows cast by trees because of their crown porosity. The objective of this thesis aims to characterize surface optical properties in urban tree shadows by means of radiative transfer and atmospheric correction tools. The originality of this work is to study the tree crown porosity through the analysis of the tree crown transmittance. Therefore, the issue has been divided into two parts. Firstly, an experimental design with the use of DART tool has been carried out in order to examine the relationships between the transmittance of an isolated tree and different biophysical and external variables. Then, the estimation of the tree crown transmittance has been assessed with several tree 3D modelling strategies derived from reference terrestrial lidar acquisitions. Secondly, a new atmospheric correction method appropriate to the processing of tree shadows, ICARE-VEG, was implemented fromthese previous results. An airborne and field campaign UMBRA was dedicated to its validation. Moreover, its performances was compared to other existing tools. Finally, the conclusions open large outlooks to the overall interpretation of remote sensing images and highlight the complexity to model physical natural processes with finer spatial resolutions.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The SNABP [40SiO2.30Na2CO3.1Al2O3.25B2O3.PbO2 (mol%)] glass system, nanostructured with PbS Quantum Dots (QDs) and/or doped with Er3+ ions, was successfully synthesized by the Fusion Method, when it was subjected to appropriate thermal annealing. The glass transition temperatures (Tg) were obtained by Differential Thermal Analyze (DTA), in which it was possible to define a suitable temperature to be used in the thermal annealing of the synthesized samples. As results of these thermal annealing, the formation and growth of PbS QDs have occurred in the glass environment. The optical properties of samples were investigated by Optical Absorption (OA), Photoluminescence (PL), and Photoluminescence with Temporal Resolution (PLTR). Moreover, the Atomic Force Microscopy (AFM) and X-Ray Diffractometry were employed in study of morphological and structural properties of samples, respectively. The size dispersions of PbS QDs were determined from OA spectra. Once using both the Method and OA data, it was also possible to estimate the average diameters of these nanoparticles, which grow with the increase in annealing time. The characteristic transitions of Er3+ ions were clearly identified in OA spectra. In addition, it was observed that the increase in annealing time of samples had provoked amplification in the overlapping between PL bands of both the PbS QDs and Er3+ ions, as well as with the absorption 4I15/2 -> 4I13/2 of these ions. Thus, the PLTR measurements have confirmed the decrease in lifetime of the 4I13/2 level (of Er3+ ions), with the amplification in the overlapping of PL emissions. Finally, as a main result of this work, it was proved that the SNABP glass system, nanostructured with PbS QDs and doped with Er3+ ions, displays to be quite favorable to the radiative energy transfer process (from PbS QDs to Er3+ ions), as well as the occurrence of stimulated emission of 4I13/2 level. / O sistema vítreo SNABP [40SiO2.30Na2CO3.1Al2O3.25B2O3.PbO2 (mol%)] nanoestruturado com pontos quânticos (PQs) de PbS e/ou dopados com íons Er3+ foi sintetizado com sucesso pelo Método de Fusão, quando submetido a tratamentos térmicos apropriados. As temperaturas de transição vítrea (Tg) foram obtidas por Análise Térmica Diferencial (DTA), em que foi possível definir uma temperatura adequada para ser utilizada nos tratamentos térmicos das amostras sintetizadas. Como resultados desses tratamentos térmicos, a formação e crescimento dos PQs de PbS ocorreram no ambiente vítreo. As propriedades ópticas das amostras foram investigadas por Absorção Óptica (AO), Fotoluminescência (PL) e Fotoluminescência com Resolução Temporal (PLRT). Além disso, a Microscopia de Força Atômica (AFM) e Difratometria de Raios-X (DRX) foram empregadas no estudo das propriedades morfológicas e estruturais das amostras, respectivamente. As dispersões de tamanho dos PQs de PbS foram determinadas a partir dos espectros de AO. Com a utilização do Método e os dados de AO, foi também possível estimar os diâmetros médios dessas nanopartículas, que aumentaram com o aumento no tempo de tratamento térmico. As transições características dos íons Er3+ foram claramente identificadas nos espectros de AO. Em adição, foi observado que o aumento no tempo de tratamento das amostras provocou um aumento na sobreposição entre as bandas de PL dos PQs de PbS e dos íons Er3+, bem como com a absorção 4I15/2 -> 4I13/2 desses íons. Assim, as medidas de PLRT confirmaram o decréscimo no tempo de vida do nível 4I13/2 (dos íons Er3+) com o aumento dessa sobreposição das emissões de PL. Finalmente, como principal resultado deste trabalho, foi comprovado que o sistema vítreo SNABP nanoestruturado com PQs de PbS dopados com íons Er3+ mostrou-se bastante favorável ao processo de transferência de energia radiativa (dos PQs de PbS para os íons Er3+), bem como a ocorrência da emissão estimulada do nível 4I13/2. / Mestre em Física

Le transfert radiatif dû aux gaz joue un rôle important dans les applications industrielles comme les chambres de combustion, les sciences atmosphériques, etc. Plusieurs modèles ont été proposées pour estimer les propriétés radiatives des gaz. Le plus précis est l'approche dite Raie Par Raie (RPR). Cependant, cette méthode implique un coût de calcul excessif qui la rend inappropriée pour la plupart des applications. Néanmoins, elle reste la méthode de référence que nous utiliserons pour l'évaluation d’autres modèles approchés. Le modèle de coefficient d’absorption corrélé (Ck) est généralement suffisant pour de nombreuses applications. Cette méthode est réputée précise lorsque petits gradients de température sont rencontrés au sein du gaz. Toutefois, si le milieu gazeux est soumis à d'importants gradients de température, la méthode Ck peut conduire à des erreurs qui peuvent atteindre 50% en termes de flux radiatifs par rapport à des simulations de RPR. Le but de cette thèse est de proposer une version améliorée de la méthode Ck, appelée l'approche de coefficient d’absorption corrélé en multi spectral (MSCk). La principale différence entre les modèles Ck et MSCk est que, dans l'approche Ck les intervalles spectraux sur lesquels les propriétés radiatives des gaz sont moyennées sont choisis contiguës alors que, dans l’approche MSCk, ces intervalles sont construits afin d'assurer que le coefficient d'absorption soit corrélé sur ces intervalles. Par conséquent, l'hypothèse de corrélation dans l’approche MSCk est mieux adaptée que dans l’approche Ck. La construction de ces intervalles spectraux (en utilisant la méthode de classification automatique de données fonctionnelles) est détaillée. Cette approche est évaluée par rapport à la référence RPR dans plusieurs cas test. Ces cas traitent de mélanges de gaz (H2O-N2 et H2O-CO2-N2) dans l’intervalle de température [300-3000K]. Les résultats montrent que la méthode MSCk permet d'obtenir de meilleures précisions que les méthodes Ck tout en restant acceptable en termes de coût de calcul. / Radiative heat transfer of gas plays an important role in industrial applications such as in combustion chambers, atmospheric sciences, etc. Several models [11] have been proposed to estimate the radiative properties of gases. The most accurate one is the Line-By-Line (LBL) approach. However, this technique involves excessive computation cost which makes it inappropriate for most applications. Nevertheless, it remains the reference approach for the assessment of other approximate models. The Correlated k-distribution method (Ck) [11] was shown to be a relevant choice for many applications. This method performs usually well, when only small temperature gradients are involved [21]. However, if the gaseous medium is subject to large temperature gradients, it may lead to errors that can reach 50% in terms of radiative heat fluxes when compared to LBL simulations [21]. The aim of the present paper is to propose an enhanced version of the Ck method, called the Multi-Spectral Correlated k-distribution approach (MSCk). The main difference between Ck and MSCk models is that in the Ck approach spectral intervals over which the radiative properties of the gas are averaged are chosen contiguous whereas, in the MSCk technique, those intervals are built in order to ensure that the absorption coefficient are scaled over them [27]. Accordingly, the usual assumption of correlated spectrum used in k-distribution approaches for the treatment of non uniformities is more acceptable in the MSCk case than in the Ck one. The building of those spectral intervals (using Functional Data Clustering, [52]) is detailed and the approach is assessed against LBL reference data in several test cases. These cases involve H2O-N2 and H2O-CO2-N2 mixtures in the [300-3000K] temperature range. Results show that the MSCk method enables to achieve better accuracies than Ck methods while remaining acceptable in terms of computational cost.

Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

Ces travaux de recherche portent sur le développement d'un système original de fusion de données de diffusion électromagnétique et optique par des milieux denses et complexes. La méthode, à la fois théorique, numérique et expérimentale, permet la fusion des signatures de diffusion hyperspectrales, polarimétriques et angulaires d'un milieu d'étude. Un système expérimental multi-capteurs comprenant une source laser supercontinuum est présenté pour mesurer les signatures de diffusion de différentes cibles. Des modèles directs de simulation physique ont aussi été développés via : (i) une approche dite « top-down » qui modélise les signatures à partir de paramètres macroscopiques (ex. rugosité, indices optiques effectifs) ou (ii) une approche dite « bottom-up » qui modélise les signatures à partir de paramètres microscopiques (ex. distribution en taille, géométrie, concentration, indices optiques et structuration des diffuseurs) en résolvant soit l'équation de transfert radiatif ou directement les équations de Maxwell. Des méthodes inverses appliquées sur les signatures mesurées sont développées pour retrouver simultanément les paramètres d’intérêt du milieu analysé. Les avancées de ces travaux permettent une amélioration de la compréhension des phénomènes de diffusion électromagnétiques et optiques par des milieux denses et complexes tels que les surfaces rugueuses, les revêtements, les nanomatériaux, les suspensions colloïdales ou les agrégats fractals d'aérosols ultrafins. Les domaines d'applications de ces travaux sont l'aéronautique (ex. peintures d'aéronefs), l'imagerie aéroportée ou satellite (ex. imagerie active hyperspectrale ou polarimétrique), la sécurité et la défense (ex. matériaux pour la furtivité) ou bien les sciences de l'atmosphère (ex. systèmes LiDAR, suivi de pollution, suies), l'industrie chimique (ex. suspensions colloïdales) ou le biomédical (ex. diagnostic de tumeurs et mélanomes). / This work reports the development of an original data fusion system dedicated to electromagnetic and light scattering by dense and complex media. The dissertation encompasses the theoretical, numerical and experimental studies. The output of the data fusion system is a fused hyperspectral, polarimetric and angular scattering signature. An experimental multi-sensor and supercontinuum laser-based system is presented to measure the scattering signatures for various targets. Direct physical simulation models were developed using a two-level modelling scheme: (i) a top-down approach is used to model signatures from macro-physical parameters, e.g. the surface roughness or the effective refractive index and, (ii) a bottom-up approach is used to model signatures from microphysical parameters, e.g. the size distribution, the geometry, the concentration, the refractive index and the structuration of the scatterers, by solving the radiative transfer equation or directly the Maxwell's equations. Inversion schemes are deployed to retrieve these parameters by inverting the experimental signatures. The advancements described throughout this dissertation will serve to improve understanding of electromagnetic and light scattering by dense and complex media such as rough surfaces, coatings, nanomaterials, colloidal suspension and fractal aggregates of ultrafine aerosols. This study has relevant applications in fields as diverse as aeronautics (e.g. aircraft paint coatings), remote-sensing (e.g. hyperspectral, polarimetric, active or passive imaging), security and defense (e.g. furtive materials), atmospheric science (e.g. black carbon or soot characterization, LiDAR systems), chemical engineering (e.g. colloidal suspensions), or biomedical (e.g. tumor and melanoma diagnostic).