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Bakalauro darbą „Įstrižojo astigmatizmo kompiuterinis modeliavimas sferiniuose ir asferiniuose lęšiuose“ sudaro įvadas, 5 dėstymo skyriai, išvados ir priedai. Darbe pateikiami 50 paveikslai ir 2 lentelės, cituojami 16 literatūros šaltinių. Darbo apimtis 66 lapai. Darbe apibendrinta literatūra apie lęšių aberacijas, jų įtaką regėjimo kokybei, bei minimalizavimą asferiniais lęšiais. Taip pat pateikiami matematiniai sferinių ir asferinių lęšių modeliai, bei įstrižojo astigmatizmo analizė šiuose lęšiuose. Įvade iškeliami darbo tikslai ir uždaviniai. Pirmajame skyriuje pateikta teorinė medžiaga apie lęšių aberacijas, antrajame – apie sferinius ir asferinius lęšius. Išanalizuoti galimi asferinių lęšių paviršiai ir jų pranašumas prieš sferinius paviršius. Trečiajame skyriuje pateikiamas matematinis spindulių eigos modelis sferiniame paviršiuje. Ketvirtajame – matematinis spindulių eigos modelis asferiniame paviršiuje. Penktajame skyriuje lyginami kompiuterinių modelių pagalba gauti įstrižojo astigmatizmo apibūdinti rezultatai, tangentinėmis paklaidomis. / The bachelor’s thesis „The computer modeling of oblique astigmatism in spherical and aspherical lenses” consists of introduction, 5 chapters, conclusions and attachments. The thesis introduces 50 figures, 2 tables and refers to 16 literary sources. The volume of the work is 66 pages. The work summarizes the literature which describes the lens aberrations, its influence to quality of vision and reduction by using aspheric lenses. There is also included mathematical models of spherical and aspheric lenses, and analysis of oblique astigmatism in them. The introduction sets the aims and the goals of the study. The first chapter contains theoretic material about lens aberrations, the second – about spherical and aspheric lenses, the analysis about available surfaces of aspheric lenses and advantages of them. The third chapter contains mathematical model of light rays pathway in spherical lenses. The fourth chapter contains mathematical model of light rays pathway in aspheric lenses. The fifth chapter contains comparison of oblique astigmatism described as tangential errors in those two models.

Cette thèse a pour objectif ultime d'améliorer notre compréhension de la réflexion de la lumière sur des surfaces micro-courbes, en particulier lorsque les dimensions physiques des surfaces (rayons de courbure de l'ordre de 50-300 μm) sont comparables aux paramètres dimensionnels d'un faisceau optique Gaussien, typique des faisceaux issus d'une fibre optique ou d'un microlaser. A cet effet, une étude théorique et des simulations numériques ont été menées ; elles ont été confrontées à une étude expérimentale. Pour ce faire, la réalisation des micro-miroirs à concavité contrôlée n'étant pas chose aisée, un premier jalon de cette thèse a consisté à atteindre les avancées technologiques nécessaires à la réalisation de tels micro-miroirs(par procédé de gravure plasma de type DRIE) en vue de leur caractérisation expérimentale. Une motivation importante du choix de ce sujet est son potentiel applicatif à la réalisation de micro-bancs optiques sur puce silicium, de sorte à augmenter les capacités de couplage et de manipulation de lumière de façon intégrée dans un espace ultra-compact. A titre d'illustration des possibilités de la nouvelle micro-instrumentation optique que nous proposons, nous avons conçu et réalisé un microsystème de balayage spatial à grand angle (110°) d'un faisceau laser dont le spot optique ne se déforme pas tout au long de l'opération de balayage, ce qui en fait, entre autres, la pièce maîtresse de systèmes portables d'imagerie médicale par tomographie à cohérence optique / The ultimate objective of this thesis is to improve our understanding of light reflection on micro-curved surfaces, especially when the physical dimensions of the surfaces (radii of curvature in the order of 50-300 microns) are comparable to typical dimensional parameters of a Gaussian optical beam, such as those coming from an optical fiber or from a micro-laser. To this end, a theoretical study and numerical simulations were conducted; they were confronted with an experimental study. To do this, the realization of micro-mirrors controlled concavity being not easy, a first step of this thesis was to achieve the technological advances necessary for the realization of such micro-mirrors (by plasma etching method of DRIE type) for their subsequent experimental characterization. An important motivation for choosing this topic is its potential application in the production of micro-optical benches on a silicon chip, so as to increase the coupling efficiencies and capabilities of manipulation of light, in an integrated way and in an ultra compact space. As an illustration of the new micro-optical instrumentation which is attainable, we have designed and implemented a micro-device able of wide-angle (110 °) spatial scanning of a laser beam, the optical spot being not deformed during the scanning operation, which makes this device, the centerpiece of portable medical imaging systems by optical coherence tomography, among others

Orientador: Ermínia de Lourdes Campello Fanti / Banca: Fernanda Soares Pinto Cardona / Banca: Maria Gorete Carreira Andrade / Resumo: Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos "ends" e grupos de dualidade são apresentados. / Abstract: In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant "ends" and duality groups are presented. / Mestre

Made available in DSpace on 2014-06-11T19:30:22Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-03-31Bitstream added on 2014-06-13T19:19:04Z : No. of bitstreams: 1 cellini_cp_me_sjrp.pdf: 781641 bytes, checksum: 70ed1b385d132f8255370c0014be09b4 (MD5) / Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos ends e grupos de dualidade são apresentados. / In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant ends and duality groups are presented.

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