While exact methods, such as DDA or T-matrix, can be applied to particles withsizes comparable to the wavelength, computational demands mean that they are size limited. For particles much larger than the wavelength, the Geometric Optics approximation can be employed, but in doing so wave effects, such as interference and diffraction, are ignored. In between these two size extremes there exists a need for computational techniques which are capable of handling the wide array of ice crystal shapes and sizes that are observed in cirrus clouds. The Beam Tracing model developed within this project meets these criteria. It combines aspects of geometric optics and physical optics. Beam propagation is handled by Snell's law and the law of reflection. A beam is divided into reflected and transmitted components each time a crystal facet is illuminated. If the incident beam illuminates multiple facets it is split, with a new beam being formed for each illuminated facet. The phase-dependent electric field amplitude of the beams is known from their ampli- tude (Jones) matrices. These are modified by transmission and reflection matrices, whose elements are Fresnel amplitude coefficients, each time a beam intersects a crystal facet. Phase tracing is carried out for each beam by considering the path that its 'centre ray' would have taken. The local near-field is then mapped, via a surface integral formulation of a vector Kirchhoff diffraction approximation, to the far-field. Once in the far-field the four elements of the amplitude matrix are trans- formed into the sixteen elements of the scattering matrix via known relations. The model is discussed in depth, with details given on its implementation. The physical basis of the model is given through a discussion of Ray Tracing and how this leads to the notion of Beam Tracing. The beam splitting algorithm is described for convex particles followed by the necessary adaptations for concave and/or ab- sorbing particles. Once geometric aspects have been established details are given as to how physical properties of beams are traced including: amplitude, phase and power. How diffraction is implemented in the model is given along with a review of existing diffraction implementations. Comparisons are given, first against a modified Ray Tracing code to validate the geometric optics aspects of the model. Then, specific examples are given for the cases of transparent, pristine, smooth hexagonal columns of four different sizes and orientations; a highly absorbing, pristine, smooth hexagonal column and a highly absorbing, indented, smooth hexagonal column. Analysis of two-dimensional and one-dimensional intensity distributions and degree of linear polarisation results are given for each case and compared with results acquired through use of the Amster- dam Discrete-Dipole Approximation (ADDA) code; with good agreement observed. To the author's best knowledge, the Beam Tracer developed here is unique in its ability to handle concave particles; particles with complex structures and the man- ner in which beams are divided into sub-beams of quasi-constant intensity when propagating in an absorbing medium. One of the model's potential applications is to create a database of known particle scattering patterns, for use in aiding particle classification from images taken by the Small Ice Detector (SID) in-situ probe. An example of creating such a database for hexagonal columns is given.

Study of light rays (light world lines) plays a significant role in many of astro- physical applications. Light rays are mainly studied in terms of so-called grav- itational lensing. However, the majority of studies are mainly focused on light propagation in vacuum. If the refractive and dispersive medium characterised by refractive index n is considered, effects occurring due to the medium presence need to be taken into account, which significantly complicates the problem. In the present thesis, rays propagating through simple refractive and dispersive systems, such as plane differentially sheared medium, are studied. In order to simplify the problem, the Hamiltonian equations of motion are used. The ray trajectories in the vicinity of Kerr black hole as well as accessible regions for the rays are also studied. Radial variation of the medium velocity is considered. Due to the recent increase of publications focused on the gravitational lensing in plasma, a detailed review summarizing the results obtained recently is included. 1

No description available.

The study whose results are presented here was carried out in support of an ongoing larger effort to investigate and understand the impact of coherence and polarization on the performance of instruments intended to monitor the Earth's radiant energy budget. The visibility of fringes produced by a Michelson interferometer is known to be sensitive to the degree to which the incident light beam is monochromatic. Therefore, the Michelson interferometer has significant potential as a tool for quantifying the degree of temporal coherence of a quasi-monochromatic light beam. Simulation of the performance of an optical instrument using the Monte-Carlo ray-trace (MCRT) method has been shown to be an efficient method for transferring knowledge of the coherence state of a beam of light from one instrument to another. The goal of the effort reported here is to create and experimentally validate an MCRT model for the optical performance of a Michelson interferometer. The effort is motivated by the need to consolidate the knowledge and skills of the investigator in the realm of physical optics, and by the need to make a useful analytical tool available to other investigators in the larger effort. / Master of Science

The manuscript presents my research on hyperbolic Partial Differential Equations (PDE), especially on conservation laws. My works began with this thought in my mind: ''Existence and uniqueness of solutions is not the end but merely the beginning of a theory of differential equations. The really interesting questions concern the behavior of solutions.'' (P.D. Lax, The formation and decay of shock waves 1974). To study or highlight some behaviors, I started by working on geometric optics expansions (WKB) for hyperbolic PDEs. For conservation laws, existence of solutions is still a problem (for large data, $L^\infty$ data), so I early learned method of characteristics, Riemann problem, $BV$ spaces, Glimm and Godunov schemes, \ldots In this report I emphasize my last works since 2006 when I became assistant professor. I use geometric optics method to investigate a conjecture of Lions-Perthame-Tadmor on the maximal smoothing effect for scalar multidimensional conservation laws. With Christian Bourdarias and Marguerite Gisclon from the LAMA (Laboratoire de \\ Mathématiques de l'Université de Savoie), we have obtained the first mathematical results on a $2\times2$ system of conservation laws arising in gas chromatography. Of course, I tried to put high oscillations in this system. We have obtained a propagation result exhibiting a stratified structure of the velocity, and we have shown that a blow up occurs when there are too high oscillations on the hyperbolic boundary. I finish this subject with some works on kinetic équations. In particular, a kinetic formulation of the gas chromatography system, some averaging lemmas for Vlasov equation, and a recent model of a continuous rating system with large interactions are discussed. Bernard Rousselet (Laboratoire JAD Université de Nice Sophia-Antipolis) introduced me to some periodic solutions related to crak problems and the so called nonlinear normal modes (NNM). Then I became a member of the European GDR: ''Wave Propagation in Complex Media for Quantitative and non Destructive Evaluation.'' In 2008, I started a collaboration with Bruno Lombard, LMA (Laboratoire de Mécanique et d'Acoustique, Marseille). We details mathematical results and challenges we have identified for a linear elasticity model with nonlinear interfaces. It leads to consider original neutral delay differential systems.

Submitted by Larissa Vitoria Cardoso Cusielo (larissavitoria@id.uff.br) on 2018-01-17T17:54:08Z No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) JSS-DISSERTACAO-FINAL.pdf: 4070871 bytes, checksum: aed10e06bb72148a505c12d171275694 (MD5) JSS-PRODUTO-FINAL.pdf: 1298696 bytes, checksum: cfe46d7ba1b6853b3911e475c98b30dc (MD5) / Rejected by Biblioteca do Aterrado BAVR (bavr@ndc.uff.br), reason: Prezada Larissa, No campo Departamento, o 1º campo é pra entrar com o Instituto de Ciências Exatas. Att, Eliete on 2018-01-24T16:19:53Z (GMT) / Submitted by Larissa Vitoria Cardoso Cusielo (larissavitoria@id.uff.br) on 2018-03-20T16:57:19Z No. of bitstreams: 3 JSS-DISSERTACAO-FINAL.pdf: 4070871 bytes, checksum: aed10e06bb72148a505c12d171275694 (MD5) JSS-PRODUTO-FINAL.pdf: 1298696 bytes, checksum: cfe46d7ba1b6853b3911e475c98b30dc (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Biblioteca do Aterrado BAVR (bavr@ndc.uff.br) on 2018-03-20T22:39:15Z (GMT) No. of bitstreams: 3 JSS-DISSERTACAO-FINAL.pdf: 4070871 bytes, checksum: aed10e06bb72148a505c12d171275694 (MD5) JSS-PRODUTO-FINAL.pdf: 1298696 bytes, checksum: cfe46d7ba1b6853b3911e475c98b30dc (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-20T22:39:15Z (GMT). No. of bitstreams: 3 JSS-DISSERTACAO-FINAL.pdf: 4070871 bytes, checksum: aed10e06bb72148a505c12d171275694 (MD5) JSS-PRODUTO-FINAL.pdf: 1298696 bytes, checksum: cfe46d7ba1b6853b3911e475c98b30dc (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017 / Marinha do Brasil. Colégio Naval. Angra dos Reis, RJ / Este trabalho tem por finalidade despertar no aluno a predisposição para aprender de forma significativa, em conformidade com a Teoria da Aprendizagem Significativa de David P. Ausubel. Para isso, propomos como estratégia de ensino, o uso de atividades experimentais que devem ser realizadas antes da apresentação dos conteúdos aos alunos. Dessa forma, acreditamos que as atividades experimentais possam atuar como agente motivador, despertando a curiosidade do aluno através da observação direta do fenômeno, e como suporte (ancoragem) para a aprendizagem significativa dos conceitos relativos ao conteúdo que será aprendido. A sequência didática utilizada neste trabalho foi desenvolvida para a aprendizagem dos principais conceitos e teorias relacionados aos fenômenos da reflexão e da refração da luz, presentes na óptica geométrica e aplicados no desenvolvimento de diversos dispositivos usados no cotidiano das pessoas. Com essa finalidade, foi montado um kit de materiais de baixo custo, acompanhado dos roteiros de montagem e aplicação, que permite a realização dos experimentos propostos, diretamente em sala de aula, sem a necessidade de um ambiente exclusivo. Desse modo, acreditamos que, despertando a curiosidade do aluno para as aulas de física, por meio da experimentação, é possível criar as condições necessárias para que ele aprenda de forma mais prazerosa e significativa. / This work aims to awaken in the student the predisposition to learn in a meaningful way, in accordance with The Theoryof Meaningful Learning, from David P. Ausubel. For this, we propose as teaching strategy, the use of experimental activities that must be carried out before the presentation of the contents to the students. Thus, we believe that the experimental activities can act as a motivating agent, arousing the student's curiosity through direct observation of the phenomenon, and as support for meaningful learning of concepts related to the content to be learned. The didactic sequence used in this work was developed for the learning of the main concepts and theories related to the phenomena of reflection and light refraction, present in the geometric optics and applied in the development of various devices used in people's daily lives. For this purpose,was builta kit of low cost materials, together with the constructionand application scripts, which allows the realization of the experiments proposed, directly in the classroom, without the need of an exclusive environment. In this way, we believe that by arousing curiosity of the studentsto physics classes, through experimentation, it is possible to create the conditions necessary for them to learn in a most pleasurable and meaningful way.

An investigation into the light scattering properties of Saharan dust grains is presented. An electrodynamic trap has been used to levitate single dust particles. By adjusting the trap parameters, partial randomisation of the particle orientation has been introduced. While levitated, the particles were illuminated by a laser, and a rotating half-wave retarder enabled selection of vertically or horizontally polarized incident light. A laser diffractometer and linear photodiode array have been used to measure intensity at scattering angles between 0.5° and 177°. Combining these measurements with Fraunhofer diffraction as calculated for a range of appropriately-sized apertures allows the calculation of the phase function and degree of linear polarization. The phase functions and degree of linear polarisation for four case study particles are presented - the phase functions are found to be featureless across most of the scattering region, with none of the halo features or rainbow peaks associated with regularly shaped particles such as hexagonal columns or spheres. Particle models comprised of large numbers of facets have been constructed to resemble the levitated particles. Utilizing Gaussian random sphere methods, increasing levels of roughness have been added to the surfaces of these models. A Geometric Optics model and a related model, Ray Tracing with Diffraction on Facets, have been modified to calculate scattering on these particle reconstructions. Scattering calculations were performed on each of these reconstructions using a range of refractive indices and two rotation regimes – one where the orientations of the reconstructed particle were limited to match those observed when the particle was levitated, and one where the orientation was not limited. Qualitative comparisons are performed on the phase functions and degree of linear polarization, where it is observed that the addition of roughness to the modelled spheroids causes the computed phase functions to increasingly resemble those from the levitated particles. Limiting the orientation of the particles does not affect the scattering noticeably. The addition of a very small absorption coefficient does not change the comparisons considerably. As the absorption coefficient is increased, however, the quality of the comparisons decreases rapidly in all cases but one. The phase functions are quantitatively compared using RMS errors, and further comparison is performed using the asymmetry parameter.

This thesis is about ‘Dual View’ displays. These are displays that can show different images to different people. For example, the driver of a car could view a GPS map, whilst the passenger who looks at the display from a different angle, could watch a movie. This thesis describes some of the research that took the project from an idea to a refined product. Sharp’s first dual view display is prototyped, and problems such as crosstalk between the two views are seen. These problems are analysed and rectified to bring the device up to a high standard. In July 2005 Sharp used this technology to launch the world’s first dual view product. Since then a new design of dual view display has been investigated. This design is theoretically optimised and experimentally tested. The new design is shown to provide dual view with greater head freedom, greater efficiency, and lower crosstalk than the original parallax barrier design.

Submitted by Larissa Vitoria Cardoso Cusielo (larissavitoria@id.uff.br) on 2017-09-05T17:46:23Z No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Robson Torrez Diniz - Dissertação completa versão final.pdf: 3357742 bytes, checksum: 22cf96d445d78898c79f7231e10ebea2 (MD5) PRODUTO VERSÃO FINAL PDF - ROBSON TORRES DINIZ.pdf: 541891 bytes, checksum: 14439f8630e371d9c9aea577fc222c52 (MD5) / Rejected by Biblioteca do Aterrado BAVR (bavr@ndc.uff.br), reason: Titulo em caixa alto on 2017-09-05T19:17:32Z (GMT) / Submitted by Larissa Vitoria Cardoso Cusielo (larissavitoria@id.uff.br) on 2017-09-05T19:38:14Z No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Robson Torrez Diniz - Dissertação completa versão final.pdf: 3357742 bytes, checksum: 22cf96d445d78898c79f7231e10ebea2 (MD5) PRODUTO VERSÃO FINAL PDF - ROBSON TORRES DINIZ.pdf: 541891 bytes, checksum: 14439f8630e371d9c9aea577fc222c52 (MD5) / Approved for entry into archive by Biblioteca do Aterrado BAVR (bavr@ndc.uff.br) on 2017-09-27T20:11:28Z (GMT) No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Robson Torrez Diniz - Dissertação completa versão final.pdf: 3357742 bytes, checksum: 22cf96d445d78898c79f7231e10ebea2 (MD5) PRODUTO VERSÃO FINAL PDF - ROBSON TORRES DINIZ.pdf: 541891 bytes, checksum: 14439f8630e371d9c9aea577fc222c52 (MD5) / Made available in DSpace on 2017-09-27T20:11:28Z (GMT). No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Robson Torrez Diniz - Dissertação completa versão final.pdf: 3357742 bytes, checksum: 22cf96d445d78898c79f7231e10ebea2 (MD5) PRODUTO VERSÃO FINAL PDF - ROBSON TORRES DINIZ.pdf: 541891 bytes, checksum: 14439f8630e371d9c9aea577fc222c52 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Universidade Federal Fluminense. Instituto de Ciências Exatas. Programa de Pós-Graduação em Ensino de Física. Volta Redonda, RJ. / Com o intuito de contribuir para a melhoria do ensino de óptica no ensino médio, este trabalho propõe uma abordagem de ensino potencialmente significativo com uso de experimentação. O objetivo principal do trabalho é apresentar um experimento sobre óptica geométrica, que será introduzido na sala de aula como base da metodologia de ensino. O experimento é constituído de uma base de madeira e uma folha de papel A3 plastificada que servirá de banco óptico para as práticas, além de uma fonte de luz, um espelho plano e um espelho esférico. A proposta do trabalho é fazer com que os alunos possam através de práticas experimentais identificar os principais conceitos relacionados a óptica geométrica. O experimento tem como meta trazer a visualização dos fenômenos relacionados a este assunto e conecta-los com a teoria abordada nas aulas teóricas. Os conceitos serão apresentados experimentalmente em três aulas assim divididas: 1ª Aula – Reflexão da Luz, 2ª Aula – Espelhos Planos e 3ª Aula – Espelhos Esféricos. Desta forma, teremos abordado os assuntos que se relacionam e dependem do conceito de reflexão da luz, tendo então a intenção de facilitar e potencializar o aprendizado dos conceitos teóricos já vistos em sala de aula a fim de propiciar uma aprendizagem potencialmente significativa. Como produto associado a esta Dissertação elaboramos um documento a parte, que poderá ser usado por docentes do ensino médio, a fim de aplicar essa proposta em sala de aula. / In order to contribute to improving the teaching of optics in high school, this dissertation proposes an approach with the use of potentially meaningful teaching with experimentation. The main objective of the study is to present an experiment on geometric optics, which will be introduced in the classroom as basics of the teaching methodology. The experimental apparatus consists of a wooden base and a laminated A3 sheet of paper that will serve as the optical bench to the practical as well as a light source, a plane mirror and a spherical mirror. The purpose of this study is to make students through experimental practices to identify the main concepts related to geometric optics, using mainly light reflection. The experiment aims to allow to visualize the related phenomena to this topic and related them to the theoretical. The concepts will be experimentally presented in three classes divided as follows: 1 st class – Reflection of light, 2 st class – Mirrors Plans and 3 st class – Spherical Mirrors. Thus, we have addressed the issues that relate to and depend on the theoretical concepts discussed in the classrooms to facilitate and enhance learning. As a product of this dissertation, an extra document was prepared so that it can be used for teachers of high school.

Dans ce mémoire, je propose une nouvelle technique optique de mesure de positions relatives 3D, tailles et indices de réfraction d’un ensemble de particules, éclairées par un faisceau laser plan pulsé : l’imagerie interférométrique de Fourier (FII). Dans le cadre de ce travail, les particules sont sphériques, homogènes transparentes et isotropes. Lorsque ces particules sont éclairées, elles se comportent comme des sources d’ondes lumineuses sphériques qui interférent entre elles. L’enregistrement des franges d’interférences et leur analyse par transformation de Fourier peut permettre d’accéder aux caractéristiques des particules. Dans ce mémoire, je décris l’influence des caractéristiques de particules sur les représentations spectrales des franges d’interférences crées par les couples de particules éclairées dans l’espace de Fourier 2D. Les franges d’interférences sont simulées numériquement en utilisant la théorie de Lorenz-Mie. Puis j’aborde le problème inverse en montrant comment il est possible de retrouver les caractéristiques des particules, en me servant de l’optique géométrique et du filtrage spatial par transformation de Fourier. / In this thesis, I propose a new optical technique for measuring 3D relative positions, sizes and refractive indices of a set of particles, which are illuminated by a plane and pulsed laser beam. In this work, the particles are spherical, transparent, homogeneous and isotropic. When these particles are illuminated, they have the behavior of sources of spherical light waves which interfere. The recording of interference fringes and analysisby Fourier transform can measure the characteristics of the particles. I describe the influence of particle characteristics on spectral representations of the interference fringes created by the pairs of particles illuminated in 2D Fourier space. The interference fringes are simulated numerically using the Lorenz-Mietheory. The inverse problem is approached by showing how it is possible to measure the characteristics of particles with geometrical optics and spatial filtering by Fourier transformation.