This thesis describes an analytical approach to the optical design of four-mirror anastigmatic optical systems. In all cases investigated here the object is at infinity. In the introduction the field of reflecting, or "catoptric", optical system design is discussed and given some historical context. The concept of the "simplest possible reflecting anastigmat" is raised in connection with Plate Diagram analysis. It is shown that four-plate systems are in general the simplest possible anastigmats, and that four-plate systems comprised of four spherical mirrors are the last family of "simplest possible reflecting anastigmats" for which the complete solution set remains unknown. In chapter 2 third-order aberration coefficients in wavefront measure are derived in a form that is particularly suitable for Plate Diagram analysis. These coefficients are subsequently used to describe the Plate Diagram, and to detail the application of the Plate Diagram to the survey of all possible solutions for four-spherical-mirror anastigmats. The Plate Diagram technique is also generalized to investigate its use as an optical design tool. In the example given a generalized Plate Diagram approach is used to determine solutions for four-mirror anastigmats with a prescribed first-order layout and a minimum number of conicoids. In chapter 3 results are presented for the survey of four-spherical-mirror anastigmats in which all elements are required to be smaller than the primary mirror. Two novel families of four-spherical-mirror anastigmats are presented and these are shown to be the only examples of four-spherical-mirror systems that exist under the given constraints. Chapter 4 gives an example of the application of Plate Diagram analysis to the design of an anastigmatic system with a useful first-order layout and a minimum number of conicoid mirrors. It is shown that systems with useful first-order layouts and only one conicoid mirror can be obtained using this method. In chapter 5 results are presented of the survey of all remaining four-spherical-mirror anastigmatic systems: that is systems in which elements are allowed to exceed the diameter of the entrance pupil, which includes systems with concave and convex primary mirrors. A wide variety of solutions are presented and classified according to both the underlying geometry of the solutions and the first-order layouts. Of these systems only one has been reported in previously published literature. The results presented in this thesis complete the set of "four-plate" reflecting anastigmats, and it can now be said that all possible solutions for four-spherical-mirror anastigmatic systems have been determined.

Thesis (M.S.)--Ohio University, June, 1994. / Title from PDF t.p.

BORRAJO, T. B. Atividades investigativas para o ensino de óptica geométrica. 2017.117 f. Dissertação (Mestrado Nacional Profissional em Ensino de Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by francisco lima (admir@ufc.br) on 2017-06-21T18:09:56Z No. of bitstreams: 1 2017_dis_tbborrajo.pdf: 2234935 bytes, checksum: 28fb00441f75e93f7465f2b7b75ff5ed (MD5) / Approved for entry into archive by Giordana Silva (giordana.nascimento@gmail.com) on 2017-06-23T15:28:55Z (GMT) No. of bitstreams: 1 2017_dis_tbborrajo.pdf: 2234935 bytes, checksum: 28fb00441f75e93f7465f2b7b75ff5ed (MD5) / Made available in DSpace on 2017-06-23T15:28:56Z (GMT). No. of bitstreams: 1 2017_dis_tbborrajo.pdf: 2234935 bytes, checksum: 28fb00441f75e93f7465f2b7b75ff5ed (MD5) Previous issue date: 2017 / In the face of a scene of dissatisfaction and indifference in the process of teaching/learning of science in basic education, we present a proposal for teaching some fundamentals topics of geometrical optics, based on investigative activities that require reflection and reasoning. In it, the students are divided into groups and they need to discuss about ideas, make hypotheses and find ways for prove them. At the end of each class, the group conclusions are confronted with formal knowledge. Making it possible to analyze discrepancies and concordances with the know theory. The methodology is based on the concepts of active learning, sociointeractionism and inquiry based learning. The main focus of the proposal is increase student interest, make him more receptive to new knowledges by problematization and discussion with colleagues and teacher. With this method, it is possible to transform student into an agent in his own process of learning, developing his skills and capabilities in a science education process. / Diante de um cenário de insatisfação e desinteresse no processo de ensino/aprendizagem de ciências na educação básica, apresentamos uma proposta para o ensino de alguns tópicos fundamentais de óptica geométrica, baseada em atividades investigativas que exigem reflexão e raciocínio. Nela, os estudantes são divididos em grupos e precisam debater ideias, construir hipóteses e encontrar meios para comprová-las. Ao final de cada aula, as conclusões dos grupos são confrontadas com o conhecimento formal, possibilitando a análise de discordâncias e concordâncias com a teoria já estabelecida. A metodologia é baseada nos conceitos de aprendizagem ativa, sociointeracionismo e ensino por investigação. O grande foco da proposta é despertar o interesse do aluno, torná-lo mais receptivo aos novos conhecimentos através da problematização e do debate com os colegas e com o professor. A partir de entrevistas com os alunos, observação da sala durante as práticas e análise de relatórios elaborados pelos próprios estudantes, foi possível constatar que eles conseguiram desenvolver, efetivamente, uma atitude científica ao longo das investigações. Com esse método, é possível fazer do estudante um agente no seu próprio processo de aprendizagem, desenvolvendo suas habilidades e capacidades em um processo de educação científica.

The ray formalism is critical to understanding light propagation, yet current pedagogy relies on inadequate 2D representations. We present a system in which real light rays are visualized through an optical system by using a collimated laser bundle of light and a fog chamber. Implementation for remote and immersive access is enabled by leveraging a commercially available 3D viewer and gesture-based remote controlling of the tool via bi-directional communication over the Internet.

No description available.

QC 351 A7 no. 49 / The use of the two -dimensional Fourier transform to compute the form of the optical image has led to new insights into the form of images. The techniques involved are discussed in some detail, and the application to tolerancing of surface errors is used as an ex- ample of the results.

Neste trabalho, construímos novas soluções com simetria esférica ou axial para as equações do campo gravitacional induzido num cenário brana do tipo Randall-Sundrum, onde uma 3-brana com constante cosmológica está imersa num espaço-tempo 5-dimensional conhecido como bulk. Para o caso esfericamente simétrico, com constante cosmológica negativa, obtivemos uma família de soluções numa brana assintoticamente anti-de Sitter, sendo que cada membro desta é diferenciado de outro por uma constante integração C, que fixada proveu-nos soluções de buracos negros ou buracos de minhocas. Com a mesma simetria, geometrias que descrevem buracos de minhoca foram encontradas numa brana assintoticamente de Sitter. Para o caso axialmente simétrico, métricas assintoticamente anti-de Sitter e de Sitter foram construídas no contexto citado. Propriedades óticas, como a rotação do vetor de polarização, foram estudadas, mostrando-nos algumas diferenças entre os mundos brana, tratados como uma teoria de gravitação modificada, e a relatividade geral. / In this work we have constructed new solutions, with axial or spherical symmetry, to the induced gravitational field equations within a Randall-Sundrum type brane world scenario, where a 3-brane with cosmological constant is embedded in a 5-dimensional space-time called bulk. For the spherical case with negative cosmological constant, we have found a family of solutions in an anti-de Sitter brane, where each member of the family is different from another when C is fixed. With a fixed C we have black holes or wormholes. In this same case, with spherical symmetry, we have obtained wormhole solutions in a de Sitter brane. In the same context, for the axially symmetric case, metrics asymptotically anti-de Sitter and de Sitter were built. Optics features, like rotation of polarization vector, have been studied. These features showed some differences between brane worlds, a theory of modified gravity, and the General Relativity.

Pouvoir déterminer la structure et la composition de l’intérieur de la Terre est un enjeu scientifique fondamental, pour la compréhension de l’organisation de la Terre profonde, des mécanismes des séismes et leur localisation en lien avec la prévention du risque sismique, pour la détection et l’exploitation des ressources naturelles telles que l’eau ou les hydrocarbures, ou encore pour toutes les activités de construction et de prévention associées au génie civil. Pour cela, les ondes sismiques sont un outil de choix. L’utilisation d’une approximation haute fréquence pour la modélisation de la propagation des ondes est avantageuse en termes de coût de calcul dès lors que plusieurs centaines, voire milliers, ou plus de longueurs d’ondes doivent être propagées. À la place de l’équation des ondes linéaire, l’approximation haute fréquence fournit trois équations aux dérivées partielles fondamentales. L’équation Eikonal, non linéaire, permet d’obtenir le temps de trajet. Une deuxième équation fournit l’angle d’émergence. L’équation Eikonal et l’équation des angles appartiennent toutes deux à la grande famille des équations de Hamilton-Jacobi. Enfin, l’équation de transport permet de calculer l’amplitude.Le tracé des rais sismiques est une technique lagrangienne qui utilise la méthode des caractéristiques pour obtenir un ensemble d’équations différentielles ordinaires à partir de ces équations aux dérivées partielles. Ces équations peuvent être intégrées facilement, donnant ainsi accès au temps de trajet et à l’amplitude le long des rais. Très largement utilisés dans la communauté géophysique du fait de leur simplicité, les outils de tracé de rais ne sont pas pour autant les plus efficaces et les plus robustes en pratique pour des applications d’imagerie et d’inversion haute résolution. En lieu et place, il peut être utile de résoudre directement les équations aux dérivées partielles par une méthode eulérienne. Durant les trois dernières décennies, une multitude de solveurs ont été développés pour l’équation Eikonal, la plupart utilisant la méthode des différences finies. Ces différents travaux visent à obtenir le meilleur compromis entre précision, coût de calcul, robustesse, facilité d’implémentation et souplesse d’utilisation.Dans cette thèse, je développe une approche différente, se basant principalement sur une méthode Galerkine discontinue. Dans le champ des mathématiques, cette méthode a été largement utilisée pour résoudre les lois de conservation et les équations de Hamilton-Jacobi. Très peu de travaux ont porté sur l'utilisation de cette méthode pour la résolution de l’équation Eikonal statique dans un contexte géophysique, et ce malgré le haut niveau de précision qu'elle apporte. C’est pourquoi, en me basant sur des travaux mathématiques, je propose un nouveau solveur Eikonal adapté au contexte géophysique. Les milieux hétérogènes complexes, anisotropes, et incluant des variations topographiques sont correctement pris en compte, avec une précision sans précédent. En y intégrant de manière robuste une stratégie de balayage rapide, je montre que ce solveur présente une très grande efficacité en deux comme en trois dimensions.J'utilise également ce solveur pour calculer l’angle d’émergence. Je développe par ailleurs un solveur voisin en volumes finis pour la résolution de l’équation de transport, permettant ainsi le calcul de l’amplitude. La variable d’état adjoint pour la tomographie sismique des temps et des pentes vérifiant une équation de transport semblable, je montre qu'on peut également la calculer à l'aide de ce solveur en volumes finis. En conséquence, je propose et analyse un ensemble consistant de solveurs pour la communauté géophysique. Ces outils devraient s’avérer utiles pour une large palette d’applications. Finalement, en guise d’illustration, je les utilise dans des schémas d’imagerie sismique, dans le but de démontrer le bénéfice apporté par une approximation haute fréquence dans ce type de schémas. / Recovering information on the structure and the composition of the Earth's interior is a fundamental issue for a large range ofapplications, from planetology to seismology, natural resources assessment, and civil engineering. Seismic waves are a very powerful tool for that purpose. Using a high-frequency approximation for the numerical modeling of seismic wave propagation is computationally advantageous when hundreds, thousands, or more of wavelengths have to be propagated. Instead of the linear wave equation, the high-frequency approximation yields three fundamental partial differential equations. The nonlinear Eikonal equation leads to traveltime. A second equation is derived for the take-off angle. Both Eikonal and angle equations belong to the wide Hamilton-Jacobi family of equations. In addition, the transport equation leads to the amplitude.As a Lagrangian approach, seismic ray tracing employs the method of characteristics to derive a set of ordinary differential equations from these partial differential equations. They can be easily integrated, thus yielding traveltime and amplitude along rays. Widely used in the geophysical community for their simplicity, the ray-tracing tools might not be the most efficient and robust ones for practical high-resolution imaging and inversion applications. Instead, it might be desirable to directly solve the partial differential equations in an Eulerian way. In the three last decades, plenty of Eikonal solvers have been designed, mostly based on finite-difference methods. Successive works try to find the best compromise between accuracy, computational efficiency, robustness, ease of implementation, and versatility.In this thesis, I develop a different approach, mainly based on the discontinuous Galerkin method. This method has been intensively used in the mathematical field for solving conservation laws and time-dependent Hamilton-Jacobi equations. Only few investigations have been done regarding its use for solving the static Eikonal equation in a geophysical context, despite the high level of accuracy allowed by this method. Therefore, improving upon mathematical studies, I propose a new Eikonal solver suitable for the geophysical context. Complex heterogeneous anisotropic media with non-flat topographies are correctly handled, with an unprecedented accuracy. Combined with a fast-sweeping strategy in a robust way, I show that this new solver exhibits a high computational efficiency, in two dimensions as well as in three dimensions.I also employ this solver for the computation of the take-off angle. I design an additional finite-volume solver for solving the transport equation, leading to the computation of amplitude. With this solver, I also consider the computation of the adjoint-state variable for seismic tomography, since it satisfies a similar transport equation. Eventually, I propose a whole set of consistent solvers to the geophysical community. These tools should be useful in a wide range of applications. As an illustration, I finally use them in advanced seismic imaging schemes, in order to demonstrate the benefit brought by the high-frequency approximation in this kind of schemes.

This thesis analyzes some aspects of electromagnetic wave propagation in double negative materials. Double negative materials have negative refractive indices. They are backward-wave materials. Plane waves undergo negative refraction at interfaces between double positive and double negative media. Causality principle implies these properties. High frequency plane wave scattering from a double negative infinitely long cylinder has been analyzed by using modified Watson transform, geometrical optics and Mie series. Mie series results and the modified Watson transform results have been found to be in good agreement. Hence, the physical mechanism of the scattering has been revealed.

Thesis (doctoral)--Université de Paris, 1867. Thèse de doctorat : Physique : Paris, Faculté des sciences : 1867. / "No. d'ordre: 293" Titre provenant de l'écran-titre. Références bibliogr.