OPTIMAL SHAPE IN ELECTROMAGNETIC SCATTERING BY SMALL ASPHERICAL PARTICLES

We consider the question of optimal shapes, e.g., those causing minimal extinction among all shapes of equal volume. Guided by the isoperimetric property of a sphere, relevant in the geometrical optics limit of scattering by large particles, we examine an analogous question in the low frequency (electrostatics) approximation, seeking to disentangle electric and geometric contributions. To that end, we survey the literature on shape functionals and focus on ellipsoids, giving a simple proof of spherical optimality for the coated ellipsoidal particle. Monotonic increase with asphericity in the low frequency regime for orientation-averaged induced dipole moments and scattering cross-sections is also shown. Additional physical insight is obtained from the Rayleigh-Gans (transparent) limit and eccentricity expansions. We propose connecting low and high frequency regime in a single minimum principle valid for all size parameters, provided that reasonable size distributions of randomly oriented aspherical particles wash out the resonances for intermediate size parameters. This proposal is further supported by the sum rule for integrated extinction.

Conformación de Superficies Reflectoras de Sistemas Dobles de Tipo Offset con Alimentadores descritos en Campo Próximo

This work discusses an iterative procedure of shaping offset dual-reflector antennas based on geometrical optics considering both far-field and near-field measurements of amplitude and phase from the feed horn. The surfaces synthesized will transform a known radiation field of a feed to a desired aperture distribution. This technique is applied for both circular and elliptical apertures and has the advantage to simplify the problem compared with existing techniques based on solving nonlinear differential equations. A MATLAB tool has been developed to implement the shaping algorithms. This procedure is applied for the design of a 1.1 m high-gain antenna for the ESA’s Solar Orbiter spacecraft. This antenna operating at X-band will manage high data rate and high efficiency communications with Earth stations.

A canonical UTD solution for electromagnetic scattering by an electrically large impedance circular cylinder illuminated by an obliquely incident plane wave

A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder

Con esta tesis ”Desarrollo de una Teoría Uniforme de la Difracción para el Análisis de los Campos Electromagnéticos Dispersados y Superficiales sobre un Cilindro” hemos iniciado una nueva línea de investigación que trata de responder a la siguiente pregunta: ¿cuál es la impedancia de superficie que describe una estructura de conductor eléctrico perfecto (PEC) convexa recubierta por un material no conductor? Este tipo de estudios tienen interés hoy en día porque ayudan a predecir el campo electromagnético incidente, radiado o que se propaga sobre estructuras metálicas y localmente convexas que se encuentran recubiertas de algún material dieléctrico, o sobre estructuras metálicas con pérdidas, como por ejemplo se necesita en determinadas aplicaciones aeroespaciales, marítimas o automovilísticas. Además, desde un punto de vista teórico, la caracterización de la impedancia de superficie de una estructura PEC recubierta o no por un dieléctrico es una generalización de varias soluciones que tratan ambos tipos de problemas por separado. En esta tesis se desarrolla una teoría uniforme de la difracción (UTD) para analizar el problema canónico del campo electromagnético dispersado y superficial en un cilindro circular eléctricamente grande con una condición de contorno de impedancia (IBC) para frecuencias altas. Construir una solución basada en UTD para este problema canónico es crucial en el desarrollo de un método UTD para el caso más general de una superficie arbitrariamente convexa, mediante el uso del principio de localización de los campos electromagnéticos a altas frecuencias. Esta tesis doctoral se ha llevado a cabo a través de una serie de hitos que se enumeran a continuación, enfatizando las contribuciones a las que ha dado lugar. Inicialmente se realiza una revisión en profundidad del estado del arte de los métodos asintóticos con numerosas referencias. As í, cualquier lector novel puede llegar a conocer la historia de la óptica geométrica (GO) y la teoría geométrica de la difracción (GTD), que dieron lugar al desarrollo de la UTD. Después, se investiga ampliamente la UTD y los trabajos más importantes que pueden encontrarse en la literatura. As í, este capítulo, nos coloca en la posición de afirmar que, hasta donde nosotros conocemos, nadie ha intentado antes llevar a cabo una investigación rigurosa sobre la caracterización de la impedancia de superficie de una estructura PEC recubierta por un material dieléctrico, utilizando para ello la UTD. Primero, se desarrolla una UTD para el problema canónico de la dispersión electromagnética de un cilindro circular eléctricamente grande con una IBC uniforme, cuando es iluminado por una onda plana con incidencia oblicua a frecuencias altas. La solución a este problema canónico se construye a partir de una solución exacta mediante una expansión de autofunciones de propagación radial. Entonces, ésta se convierte en una nueva expansión de autofunciones de propagación circunferencial muy apropiada para cilindros grandes, a través de la transformación de Watson. De esta forma, la expresión del campo se reduce a una integral que se evalúa asintóticamente, para altas frecuencias, de manera uniforme. El resultado se expresa según el trazado de rayos descrito en la UTD. La solución es uniforme porque tiene la importante propiedad de mantenerse continua a lo largo de la región de transición, a ambos lados de la superficie del contorno de sombra. Fuera de la región de transición la solución se reduce al campo incidente y reflejado puramente ópticos en la región iluminada del cilindro, y al campo superficial difractado en la región de sombra. Debido a la IBC el campo dispersado contiene una componente contrapolar a causa de un acoplamiento entre las ondas TEz y TMz (donde z es el eje del cilindro). Esta componente contrapolar desaparece cuando la incidencia es normal al cilindro, y también en la región iluminada cuando la incidencia es oblicua donde el campo se reduce a la solución de GO. La solución UTD presenta una muy buena exactitud cuando se compara numéricamente con una solución de referencia exacta. A continuación, se desarrolla una IBC efectiva para el cálculo del campo electromagnético dispersado en un cilindro circular PEC recubierto por un dieléctrico e iluminado por una onda plana incidiendo oblicuamente. Para ello se derivan dos impedancias de superficie en relación directa con las ondas creeping y de superficie TM y TE que se excitan en un cilindro recubierto por un material no conductor. Las impedancias de superficie TM y TE están acopladas cuando la incidencia es oblicua, y dependen de la geometría del problema y de los números de onda. Además, se ha derivado una impedancia de superficie constante, aunque con diferente valor cuando el observador se encuentra en la zona iluminada o en la zona de sombra. Después, se presenta una solución UTD para el cálculo de la dispersión de una onda plana con incidencia oblicua sobre un cilindro eléctricamente grande y convexo, mediante la generalización del problema canónico correspondiente al cilindro circular. La solución asintótica es uniforme porque se mantiene continua a lo largo de la región de transición, en las inmediaciones del contorno de sombra, y se reduce a la solución de rayos ópticos en la zona iluminada y a la contribución de las ondas de superficie dentro de la zona de sombra, lejos de la región de transición. Cuando se usa cualquier material no conductor se excita una componente contrapolar que tiende a desaparecer cuando la incidencia es normal al cilindro y en la región iluminada. Se discuten ampliamente las limitaciones de las fórmulas para la impedancia de superficie efectiva, y se compara la solución UTD con otras soluciones de referencia, donde se observa una muy buena concordancia. Y en tercer lugar, se presenta una aproximación para una impedancia de superficie efectiva para el cálculo de los campos superficiales en un cilindro circular conductor recubierto por un dieléctrico. Se discuten las principales diferencias que existen entre un cilindro PEC recubierto por un dieléctrico desde un punto de vista riguroso y un cilindro con una IBC. Mientras para un cilindro de impedancia se considera una impedancia de superficie constante o uniforme, para un cilindro conductor recubierto por un dieléctrico se derivan dos impedancias de superficie. Estas impedancias de superficie están asociadas a los modos de ondas creeping TM y TE excitadas en un cilindro, y dependen de la posición y de la orientación del observador y de la fuente. Con esto en mente, se deriva una solución UTD con IBC para los campos superficiales teniendo en cuenta las dependencias de la impedancia de superficie. La expansión asintótica se realiza, mediante la transformación de Watson, sobre la representación en serie de las funciones de Green correspondientes, evitando as í calcular las derivadas de orden superior de las integrales de tipo Fock, y dando lugar a una solución rápida y precisa. En los ejemplos numéricos realizados se observa una muy buena precisión cuando el cilindro y la separación entre el observador y la fuente son grandes. Esta solución, junto con el método de los momentos (MoM), se puede aplicar para el cálculo eficiente del acoplamiento mutuo de grandes arrays conformados de antenas de parches. Los métodos propuestos basados en UTD para el cálculo del campo electromagnético dispersado y superficial sobre un cilindro PEC recubierto de dieléctrico con una IBC efectiva suponen un primer paso hacia la generalización de una solución UTD para superficies metálicas convexas arbitrarias cubiertas por un material no conductor e iluminadas por una fuente electromagnética arbitraria. ABSTRACT With this thesis ”Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder” we have initiated a line of investigation whose goal is to answer the following question: what is the surface impedance which describes a perfect electric conductor (PEC) convex structure covered by a material coating? These studies are of current and future interest for predicting the electromagnetic (EM) fields incident, radiating or propagating on locally smooth convex parts of highly metallic structures with a material coating, or by a lossy metallic surfaces, as for example in aerospace, maritime and automotive applications. Moreover, from a theoretical point of view, the surface impedance characterization of PEC surfaces with or without a material coating represents a generalization of independent solutions for both type of problems. A uniform geometrical theory of diffraction (UTD) is developed in this thesis for analyzing the canonical problem of EM scattered and surface field by an electrically large circular cylinder with an impedance boundary condition (IBC) in the high frequency regime, by means of a surface impedance characterization. The construction of a UTD solution for this canonical problem is crucial for the development of the corresponding UTD solution for the more general case of an arbitrary smooth convex surface, via the principle of the localization of high frequency EM fields. The development of the present doctoral thesis has been carried out through a series of landmarks that are enumerated as follows, emphasizing the main contributions that this work has given rise to. Initially, a profound revision is made in the state of art of asymptotic methods where numerous references are given. Thus, any reader may know the history of geometrical optics (GO) and geometrical theory of diffraction (GTD), which led to the development of UTD. Then, the UTD is deeply investigated and the main studies which are found in the literature are shown. This chapter situates us in the position to state that, as far as we know, nobody has attempted before to perform a rigorous research about the surface impedance characterization for material-coated PEC convex structures via UTD. First, a UTD solution is developed for the canonical problem of the EM scattering by an electrically large circular cylinder with a uniform IBC, when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transformation, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the GO or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution. Then, an effective IBC is developed for the EM scattered field on a coated PEC circular cylinder illuminated by an obliquely incident plane wave. Two surface impedances are derived in a direct relation with the TM and TE surface and creeping wave modes excited on a coated cylinder. The TM and TE surface impedances are coupled at oblique incidence, and depend on the geometry of the problem and the wave numbers. Nevertheless, a constant surface impedance is found, although with a different value when the observation point lays in the lit or in the shadow region. Then, a UTD solution for the scattering of an obliquely incident plane wave on an electrically large smooth convex coated PEC cylinder is introduced, via a generalization of the canonical circular cylinder problem. The asymptotic solution is uniform because it remains continuous across the transition region, in the vicinity of the shadow boundary, and it recovers the ray optical solution in the deep lit region and the creeping wave formulation within the deep shadow region. When a coating is present a cross-polar field term is excited, which vanishes at normal incidence and in the deep lit region. The limitations of the effective surface impedance formulas are discussed, and the UTD solution is compared with some reference solutions where a very good agreement is met. And in third place, an effective surface impedance approach is introduced for determining surface fields on an electrically large coated metallic circular cylinder. Differences in analysis of rigorouslytreated coated metallic cylinders and cylinders with an IBC are discussed. While for the impedance cylinder case a single constant or uniform surface impedance is considered, for the coated metallic cylinder case two surface impedances are derived. These are associated with the TM and TE creeping wave modes excited on a cylinder and depend on observation and source positions and orientations. With this in mind, a UTD based method with IBC is derived for the surface fields by taking into account the surface impedance variation. The asymptotic expansion is performed, via the Watson transformation, over the appropriate series representation of the Green’s functions, thus avoiding higher-order derivatives of Fock-type integrals, and yielding a fast and an accurate solution. Numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large. Thus, this solution could be efficiently applied in mutual coupling analysis, along with the method of moments (MoM), of large conformal microstrip array antennas. The proposed UTD methods for scattered and surface EM field analysis on a coated PEC cylinder with an effective IBC are considered the first steps toward the generalization of a UTD solution for large arbitrarily convex smooth metallic surfaces covered by a material coating and illuminated by an arbitrary EM source.

Free-form optical systems for nonimaging applications : Sistemas ópticos anamórficos para aplicaciones anidólicas

La óptica anidólica es una rama de la óptica cuyo desarrollo comenzó a mediados de la década de 1960. Este relativamente nuevo campo de la óptica se centra en la transferencia eficiente de la luz, algo necesario en muchas aplicaciones, entre las que destacamos los concentradores solares y los sistemas de iluminación. Las soluciones de la óptica clásica a los problemas de la transferencia de energía de la luz sólo son adecuadas cuando los rayos de luz son paraxiales. La condición paraxial no se cumple en la mayoría de las aplicaciones para concentración e iluminación. Esta tesis contiene varios diseños free-form (aquellos que no presentan ninguna simetría, ni de rotación ni lineal) cuyas aplicaciones van destinadas a estos dos campos. El término nonimaging viene del hecho de que estos sistemas ópticos no necesitan formar una imagen del objeto, aunque no formar la imagen no es una condición necesaria. Otra palabra que se utiliza a veces en lugar de nonimaging es la palabra anidólico, viene del griego "an+eidolon" y tiene el mismo significado. La mayoría de los sistemas ópticos diseñados para aplicaciones anidólicas no presentan ninguna simetría, es decir, son free-form (anamórficos). Los sistemas ópticos free-form están siendo especialmente relevantes durante los últimos años gracias al desarrollo de las herramientas para su fabricación como máquinas de moldeo por inyección y el mecanizado multieje. Sin embargo, solo recientemente se han desarrollado técnicas de diseño anidólicas capaces de cumplir con estos grados de libertad. En aplicaciones de iluminación el método SMS3D permite diseñar dos superficies free-form para controlar las fuentes de luz extensas. En los casos en que se requiere una elevada asimetría de la fuente, el objeto o las restricciones volumétricos, las superficies free-form permiten obtener soluciones de mayor eficiencia, o disponer de menos elementos en comparación con las soluciones de simetría de rotación, dado que las superficies free-form tienen más grados de libertad y pueden realizar múltiples funciones debido a su naturaleza anamórfica. Los concentradores anidólicos son muy adecuados para la captación de energía solar, ya que el objetivo no es la reproducción de una imagen exacta del sol, sino sencillamente la captura de su energía. En este momento, el campo de la concentración fotovoltaica (CPV) tiende hacia sistemas de alta concentración con el fin de compensar el gasto de las células solares multi-unión (MJ) utilizadas como receptores, reduciendo su área. El interés en el uso de células MJ radica en su alta eficiencia de conversión. Para obtener sistemas competitivos en aplicaciones terrestres se recurre a sistemas fotovoltaicos de alta concentración (HCPV), con factores de concentración geométrica por encima de 500x. Estos sistemas se componen de dos (o más) elementos ópticos (espejos y/o lentes). En los sistemas presentados a lo largo de este trabajo se presentan ejemplos de concentradores HCPV con elementos reflexivos como etapa primaria, así como concentradores con elementos refractivos (lente de Fresnel). Con la necesidad de aumentar la eficiencia de los sistemas HCPV reales y con el fin de proporcionar la división más eficiente del espectro solar, células conteniendo cuatro o más uniones (con un potencial de alcanzar eficiencias de más del 45% a una concentración de cientos de soles) se exploran hoy en día. En esta tesis se presenta una de las posibles arquitecturas de división del espectro (spectrum-splitting en la literatura anglosajona) que utilizan células de concentración comercial. Otro campo de aplicación de la óptica nonimaging es la iluminación, donde es necesario proporcionar un patrón de distribución de la iluminación específico. La iluminación de estado sólido (SSL), basada en la electroluminiscencia de materiales semiconductores, está proporcionando fuentes de luz para aplicaciones de iluminación general. En la última década, los diodos emisores de luz (LED) de alto brillo han comenzado a reemplazar a las fuentes de luz convencionales debido a la superioridad en la calidad de la luz emitida, elevado tiempo de vida, compacidad y ahorro de energía. Los colimadores utilizados con LEDs deben cumplir con requisitos tales como tener una alta eficiencia, un alto control del haz de luz, una mezcla de color espacial y una gran compacidad. Presentamos un colimador de luz free-form con microestructuras capaz de conseguir buena colimación y buena mezcla de colores con una fuente de LED RGGB. Una buena mezcla de luz es importante no sólo para simplificar el diseño óptico de la luminaria sino también para evitar hacer binning de los chips. La mezcla de luz óptica puede reducir los costes al evitar la modulación por ancho de pulso y otras soluciones electrónicas patentadas para regulación y ajuste de color. Esta tesis consta de cuatro capítulos. Los capítulos que contienen la obra original de esta tesis son precedidos por un capítulo introductorio donde se presentan los conceptos y definiciones básicas de la óptica geométrica y en el cual se engloba la óptica nonimaging. Contiene principios de la óptica no formadora de imagen junto con la descripción de sus problemas y métodos de diseño. Asimismo se describe el método de Superficies Múltiples Simultáneas (SMS), que destaca por su versatilidad y capacidad de controlar varios haces de rayos. Adicionalmente también se describe la integración Köhler y sus aplicaciones en el campo de la energía fotovoltaica. La concentración fotovoltaica y la iluminación de estado sólido son introducidas junto con la revisión de su estado actual. El Segundo y Tercer Capítulo contienen diseños ópticos avanzados con aplicación en la concentración solar principalmente, mientras que el Cuarto Capítulo describe el colimador free-form con surcos que presenta buena mezcla de colores para aplicaciones de iluminación. El Segundo Capítulo describe dos concentradores ópticos HCPV diseñados con el método SMS en tres dimensiones (SMS3D) que llevan a cabo integración Köhler en dos direcciones con el fin de proporcionar una distribución de irradiancia uniforme libre de aberraciones cromáticas sobre la célula solar. Uno de los diseños es el concentrador XXR free-form diseñado con el método SMS3D, donde el espejo primario (X) y la lente secundaria (R) se dividen en cuatro sectores simétricos y llevan a cabo la integración Köhler (proporcionando cuatro unidades del array Köhler), mientras que el espejo intermedio (X) presenta simetría rotacional. Otro concentrador HCPV presentado es el Fresnel-RXI (FRXI) con una lente de Fresnel funcionando como elemento primario (POE) y una lente RXI como elemento óptico secundario (SOE), que presenta configuración 4-fold con el fin de realizar la integración Köhler. Las lentes RXI son dispositivos nonimaging conocidos, pero su aplicación como elemento secundario es novedosa. Los concentradores XXR y FRXI Köhler son ejemplos académicos de muy alta concentración (más de 2,000x, mientras que los sistemas convencionales hoy en día no suelen llegar a 1,000x) preparados para las células solares N-unión (con N>3), que probablemente requerirán una mayor concentración y alta uniformidad espectral de irradiancia con el fin de obtener sistemas CPV terrestres eficientes y rentables. Ambos concentradores están diseñados maximizando funciones de mérito como la eficiencia óptica, el producto concentración-aceptancia (CAP) y la uniformidad de irradiancia sobre la célula libre de la aberración cromática (integración Köhler). El Tercer Capítulo presenta una arquitectura para la división del espectro solar basada en un módulo HCPV con alta concentración (500x) y ángulo de aceptancia alto (>1º) que tiene por objeto reducir ambas fuentes de pérdidas de las células triple unión (3J) comerciales: el uso eficiente del espectro solar y la luz reflejada de los contactos metálicos y de la superficie de semiconductor. El módulo para la división del espectro utiliza el espectro solar más eficiente debido a la combinación de una alta eficiencia de una célula de concentración 3J (GaInP/GaInAs/Ge) y una de contacto posterior (BPC) de concentración de silicio (Si), así como la técnica de confinamiento externo para la recuperación de la luz reflejada por la célula 3J con el fin de ser reabsorbida por la célula. En la arquitectura propuesta, la célula 3J opera con su ganancia de corriente optimizada (concentración geométrica de 500x), mientras que la célula de silicio trabaja cerca de su óptimo también (135x). El módulo de spectrum-splitting consta de una lente de Fresnel plana como POE y un concentrador RXI free-form como SOE con un filtro paso-banda integrado en él. Tanto POE como SOE realizan la integración Köhler para producir homogeneización de luz sobre la célula. El filtro paso banda envía los fotones IR en la banda 900-1,150nm a la célula de silicio. Hay varios aspectos prácticos de la arquitectura del módulo presentado que ayudan a reducir la complejidad de los sistemas spectrum-splitting (el filtro y el secundario forman una sola pieza sólida, ambas células son coplanarias simplificándose el cableado y la disipación de calor, etc.). Prototipos prueba-de-concepto han sido ensamblados y probados a fin de demostrar la fabricabilidad del filtro y su rendimiento cuando se combina con la técnica de reciclaje de luz externa. Los resultados obtenidos se ajustan bastante bien a los modelos y a las simulaciones e invitan al desarrollo de una versión más compleja de este prototipo en el futuro. Dos colimadores sólidos con surcos free-form se presentan en el Cuarto Capítulo. Ambos diseños ópticos están diseñados originalmente usando el método SMS3D. La segunda superficie ópticamente activa está diseñada a posteriori como una superficie con surcos. El diseño inicial de dos espejos (XX) está diseñado como prueba de concepto. En segundo lugar, el diseño RXI free-form es comparable con los colimadores RXI existentes. Se trata de un diseño muy compacto y eficiente que proporciona una muy buena mezcla de colores cuando funciona con LEDs RGB fuera del eje óptico como en los RGB LEDs convencionales. Estos dos diseños son dispositivos free-form diseñados con la intención de mejorar las propiedades de mezcla de colores de los dispositivos no aplanáticos RXI con simetría de revolución y la eficiencia de los aplanáticos, logrando una buena colimación y una buena mezcla de colores. La capacidad de mezcla de colores del dispositivo no-aplanático mejora añadiendo características de un aplanático a su homólogo simétrico sin pérdida de eficiencia. En el caso del diseño basado en RXI, su gran ventaja consiste en su menor coste de fabricación ya que el proceso de metalización puede evitarse. Aunque algunos de los componentes presentan formas muy complejas, los costes de fabricación son relativamente insensibles a la complejidad del molde, especialmente en el caso de la producción en masa (tales como inyección de plástico), ya que el coste del molde se reparte entre todas las piezas fabricadas. Por último, las últimas dos secciones son las conclusiones y futuras líneas de investigación. ABSTRACT Nonimaging optics is a branch of optics whose development began in the mid-1960s. This rather new field of optics focuses on the efficient light transfer necessary in many applications, among which we highlight solar concentrators and illumination systems. The classical optics solutions to the problems of light energy transfer are only appropriate when the light rays are paraxial. The paraxial condition is not met in most applications for the concentration and illumination. This thesis explores several free-form designs (with neither rotational nor linear symmetry) whose applications are intended to cover the above mentioned areas and more. The term nonimaging comes from the fact that these optical systems do not need to form an image of the object, although it is not a necessary condition not to form an image. Another word sometimes used instead of nonimaging is anidolic, and it comes from the Greek “an+eidolon” and has the same meaning. Most of the optical systems designed for nonimaging applications are without any symmetry, i.e. free-form. Free-form optical systems become especially relevant lately with the evolution of free-form tooling (injection molding machines, multi-axis machining techniques, etc.). Nevertheless, only recently there are nonimaging design techniques that are able to meet these degrees of freedom. In illumination applications, the SMS3D method allows designing two free-form surfaces to control very well extended sources. In cases when source, target or volumetric constrains have very asymmetric requirements free-form surfaces are offering solutions with higher efficiency or with fewer elements in comparison with rotationally symmetric solutions, as free-forms have more degrees of freedom and they can perform multiple functions due to their free-form nature. Anidolic concentrators are well suited for the collection of solar energy, because the goal is not the reproduction of an exact image of the sun, but instead the collection of its energy. At this time, Concentration Photovoltaics (CPV) field is turning to high concentration systems in order to compensate the expense of multi-junction (MJ) solar cells used as receivers by reducing its area. Interest in the use of MJ cells lies in their very high conversion efficiency. High Concentration Photovoltaic systems (HCPV) with geometric concentration of more than 500x are required in order to have competitive systems in terrestrial applications. These systems comprise two (or more) optical elements, mirrors and/or lenses. Systems presented in this thesis encompass both main types of HCPV architectures: concentrators with primary reflective element and concentrators with primary refractive element (Fresnel lens). Demand for the efficiency increase of the actual HCPV systems as well as feasible more efficient partitioning of the solar spectrum, leads to exploration of four or more junction solar cells or submodules. They have a potential of reaching over 45% efficiency at concentration of hundreds of suns. One possible architectures of spectrum splitting module using commercial concentration cells is presented in this thesis. Another field of application of nonimaging optics is illumination, where a specific illuminance distribution pattern is required. The Solid State Lighting (SSL) based on semiconductor electroluminescence provides light sources for general illumination applications. In the last decade high-brightness Light Emitting Diodes (LEDs) started replacing conventional light sources due to their superior output light quality, unsurpassed lifetime, compactness and energy savings. Collimators used with LEDs have to meet requirements like high efficiency, high beam control, color and position mixing, as well as a high compactness. We present a free-form collimator with microstructures that performs good collimation and good color mixing with RGGB LED source. Good light mixing is important not only for simplifying luminaire optical design but also for avoiding die binning. Optical light mixing may reduce costs by avoiding pulse-width modulation and other patented electronic solutions for dimming and color tuning. This thesis comprises four chapters. Chapters containing the original work of this thesis are preceded by the introductory chapter that addresses basic concepts and definitions of geometrical optics on which nonimaging is developed. It contains fundamentals of nonimaging optics together with the description of its design problems, principles and methods, and with the Simultaneous Multiple Surface (SMS) method standing out for its versatility and ability to control several bundles of rays. Köhler integration and its applications in the field of photovoltaics are described as well. CPV and SSL fields are introduced together with the review on their background and their current status. Chapter 2 and Chapter 3 contain advanced optical designs with primarily application in solar concentration; meanwhile Chapter 4 portrays the free-form V-groove collimator with good color mixing property for illumination application. Chapter 2 describes two HCPV optical concentrators designed with the SMS method in three dimensions (SMS3D). Both concentrators represent Köhler integrator arrays that provide uniform irradiance distribution free from chromatic aberrations on the solar cell. One of the systems is the XXR free-form concentrator designed with the SMS3D method. The primary mirror (X) of this concentrator and secondary lens (R) are divided in four symmetric sectors (folds) that perform Köhler integration; meanwhile the intermediate mirror (X) is rotationally symmetric. Second HCPV concentrator is the Fresnel-RXI (FRXI) with flat Fresnel lens as the Primary Optical Element (POE) and an RXI lens as the Secondary Optical Element (SOE). This architecture manifests 4-fold configuration for performing Köhler integration (4 array units), as well. The RXI lenses are well-known nonimaging devices, but their application as SOE is novel. Both XXR and FRXI Köhler HCPV concentrators are academic examples of very high concentration (more than 2,000x meanwhile conventional systems nowadays have up to 1,000x) prepared for the near future N-junction (N>3) solar cells. In order to have efficient and cost-effective terrestrial CPV systems, those cells will probably require higher concentrations and high spectral irradiance uniformity. Both concentrators are designed by maximizing merit functions: the optical efficiency, concentration-acceptance angle (CAP) and cell-irradiance uniformity free from chromatic aberrations (Köhler integration). Chapter 3 presents the spectrum splitting architecture based on a HCPV module with high concentration (500x) and high acceptance angle (>1º). This module aims to reduce both sources of losses of the actual commercial triple-junction (3J) solar cells with more efficient use of the solar spectrum and with recovering the light reflected from the 3J cells’ grid lines and semiconductor surface. The solar spectrum is used more efficiently due to the combination of a high efficiency 3J concentration cell (GaInP/GaInAs/Ge) and external Back-Point-Contact (BPC) concentration silicon (Si) cell. By employing external confinement techniques, the 3J cell’s reflections are recovered in order to be re-absorbed by the cell. In the proposed concentrator architecture, the 3J cell operates at its optimized current gain (at geometrical concentration of 500x), while the Si cell works near its optimum, as well (135x). The spectrum splitting module consists of a flat Fresnel lens (as the POE), and a free-form RXI-type concentrator with a band-pass filter embedded in it (as the SOE), both POE and SOE performing Köhler integration to produce light homogenization. The band-pass filter sends the IR photons in the 900-1,150nm band to the Si cell. There are several practical aspects of presented module architecture that help reducing the added complexity of the beam splitting systems: the filter and secondary are forming a single solid piece, both cells are coplanar so the heat management and wiring is simplified, etc. Two proof-of-concept prototypes are assembled and tested in order to prove filter manufacturability and performance, as well as the potential of external light recycling technique. Obtained measurement results agree quite well with models and simulations, and show an opened path to manufacturing of the Fresnel RXI-type secondary concentrator with spectrum splitting strategy. Two free-form solid V-groove collimators are presented in Chapter 4. Both free-form collimators are originally designed with the SMS3D method. The second mirrored optically active surface is converted in a grooved surface a posteriori. Initial two mirror (XX) design is presented as a proof-of-concept. Second, RXI free-form design is comparable with existing RXI collimators as it is a highly compact and a highly efficient design. It performs very good color mixing of the RGGB LED sources placed off-axis like in conventional RGB LEDs. Collimators described here improve color mixing property of the prior art rotationally symmetric no-aplanatic RXI devices, and the efficiency of the aplanatic ones, accomplishing both good collimation and good color mixing. Free-form V-groove collimators enhance the no-aplanatic device's blending capabilities by adding aplanatic features to its symmetric counterpart with no loss in efficiency. Big advantage of the RXI design is its potentially lower manufacturing cost, since the process of metallization may be avoided. Although some components are very complicated for shaping, the manufacturing costs are relatively insensitive to the complexity of the mold especially in the case of mass production (such as plastic injection), as the cost of the mold is spread in many parts. Finally, last two sections are conclusions and future lines of investigation.

Antenas básicas para comunicaciones móviles

Debido al gran auge en las comunicaciones móviles, los terminales cada vez son más finos a la par que más grandes, pues cada vez los usuarios quieren tener terminales delgados pero con pantallas mayores. Por ello, el objetivo principal del proyecto es aprender y analizar las antenas usadas en los teléfonos móviles, concretamente las antenas impresas. En los últimos años con el aumento de los servicios ofrecidos por los terminales móviles se han ido añadiendo distintas bandas de frecuencia en las que trabajan estos terminales. Por ello, ha sido necesario diseñar antenas que no funcionen únicamente en una banda de frecuencia, sino antenas multibanda, es decir, antenas capaces de funcionar en las distintas bandas de frecuencias. Para realizar las simulaciones y pruebas de este proyecto se utilizó el software FEKO, tanto el CAD FEKO como el POST FEKO. El CAD FEKO se empleó para el diseño de la antena, mientras que el POST FEKO sirvió para analizar las simulaciones. Por último, hay que añadir que FEKO aunque está basado en el Método de los Momentos (MoM) es una herramienta que puede utilizar varios métodos numéricos. Además del MoM puede utilizar otras técnicas (por separado o hibridizadas) como son el Métodos de Elementos Finitos (FEM), Óptica Física (PO), Lanzamiento de rayos con Óptica Geométrica (RL-GO), Teoría Uniforme de la Difracción (UTD), Método de las Diferencias Finitas en el Dominio del Tiempo (FDTD), ... ABSTRACT. Because of the boom in mobile communications, terminals are thinner and so large, because users want to thin terminals but with large screens. Therefore, the main objective of the project is to learn and analyse the antennas used in mobile phones, specifically printed antennas. In recent years with the rise of the services offered by mobile terminals have been adding different frequency bands in which these terminals work. For that reason, it has been necessary to design antennas that not work only in a frequency band, but multiband antennas, i.e., antennas capable of operating in different frequency bands. For performing simulations and testing in this project will be used software FEKO, as the CAD FEKO and POST FEKO. The CAD FEKO is used for the design of the antenna, whereas the POST FEKO is used for simulation analysis. Finally, it has to add that FEKO is based on the Method of Moments (MoM) but also it can use several numerical methods. Besides the MoM, FEKO can use other techniques (separated or hybridized) such as the Finite Element Method (FEM), Physical Optics (PO), Ray-launching Geometrical Optics (RL-GO), Uniform Theory of Diffraction (UTD), Finite Difference Time Domain (FDTD) …

The mathematical works of Isaac Barrow ... /

Includes reprints of the original title pages, dated 1683, 1669, and 1670 respectively.

Opuscules mathématiques, ou Mémoires sur différens sujets de géométrie, de méchanique, d'optique, d'astronomie &c.

Vol. 5 is in 2 pts., paged continuously.

Applications de géométrie et de méchanique : à la marine aux ponts et chaussées, etc., pour faire suite aux Développements de géométrie /

I. De la stabilité des corps flottants -- II. Du tracé des routes Isolées -- III. Sur le tracé des routes, dans les débiais et les rembials -- IV. Sur les routes sulvies par la lumiére et par les corps élastiques, en général, dans les phénoménes de la réflexion et de la réfraction -- V. Examen théorique de la structure des vaisseaux angials.

Temporal Coding of Volumetric Imagery

'Image volumes' refer to realizations of images in other dimensions such as time, spectrum, and focus. Recent advances in scientific, medical, and consumer applications demand improvements in image volume capture. Though image volume acquisition continues to advance, it maintains the same sampling mechanisms that have been used for decades; every voxel must be scanned and is presumed independent of its neighbors. Under these conditions, improving performance comes at the cost of increased system complexity, data rates, and power consumption.

This dissertation explores systems and methods capable of efficiently improving sensitivity and performance for image volume cameras, and specifically proposes several sampling strategies that utilize temporal coding to improve imaging system performance and enhance our awareness for a variety of dynamic applications.

Video cameras and camcorders sample the video volume (x,y,t) at fixed intervals to gain understanding of the volume's temporal evolution. Conventionally, one must reduce the spatial resolution to increase the framerate of such cameras. Using temporal coding via physical translation of an optical element known as a coded aperture, the compressive temporal imaging (CACTI) camera emonstrates a method which which to embed the temporal dimension of the video volume into spatial (x,y) measurements, thereby greatly improving temporal resolution with minimal loss of spatial resolution. This technique, which is among a family of compressive sampling strategies developed at Duke University, temporally codes the exposure readout functions at the pixel level.

Since video cameras nominally integrate the remaining image volume dimensions (e.g. spectrum and focus) at capture time, spectral (x,y,t,\lambda) and focal (x,y,t,z) image volumes are traditionally captured via sequential changes to the spectral and focal state of the system, respectively. The CACTI camera's ability to embed video volumes into images leads to exploration of other information within that video; namely, focal and spectral information. The next part of the thesis demonstrates derivative works of CACTI: compressive extended depth of field and compressive spectral-temporal imaging. These works successfully show the technique's extension of temporal coding to improve sensing performance in these other dimensions.

Geometrical optics-related tradeoffs, such as the classic challenges of wide-field-of-view and high resolution photography, have motivated the development of mulitscale camera arrays. The advent of such designs less than a decade ago heralds a new era of research- and engineering-related challenges. One significant challenge is that of managing the focal volume (x,y,z) over wide fields of view and resolutions. The fourth chapter shows advances on focus and image quality assessment for a class of multiscale gigapixel cameras developed at Duke.

Along the same line of work, we have explored methods for dynamic and adaptive addressing of focus via point spread function engineering. We demonstrate another form of temporal coding in the form of physical translation of the image plane from its nominal focal position. We demonstrate this technique's capability to generate arbitrary point spread functions.

Phenomenological model of visual acuity

We propose in this work a model for describing visual acuity (VV) as a function of defocus and pupil diameter. Although the model is mainly based on geometrical optics, it also incorporates nongeometrical effects phenomenologically. Compared to similar visual acuity models, the proposed one considers the effect of astigmatism and the variability of best corrected VV among individuals; it also takes into account the accommodation and the “tolerance to defocus,” the latter through a phenomenological parameter. We have fitted the model to the VV data provided in the works of Holladay et al. and Peters, showing the ability of this model to accurately describe the variation of VV against blur and pupil diameter. We have also performed a comparison between the proposed model and others previously published in the literature. The model is mainly intended for use in the design of ophthalmic compensations, but it can also be useful in other fields such as visual ergonomics, design of visual tests, and optical instrumentation.

Geometrical parameter analysis of a high-sensitivity fiber optic angular displacement sensor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Transforming transformation optics via generalised refraction

Generalised refraction is a topic which has, thus far, garnered far less attention than it deserves. The purpose of this thesis is to highlight the potential that generalised refraction has to offer with regards to imaging and its application to designing new passive optical devices. Specifically in this thesis we will explore two types of gener- alised refraction which takes place across a planar interface: refraction by generalised confocal lenslet arrays (gCLAs), and refraction by ray-rotation sheets. We will show that the corresponding laws of refraction for these interfaces produce, in general, light-ray fields with non-zero curl, and as such do not have a corresponding outgoing waveform. We will then show that gCLAs perform integral, geometrical imaging, and that this enables them to be considered as approximate realisations of metric tensor interfaces. The concept of piecewise transformation optics will be introduced and we will show that it is possible to use gCLAs along with other optical elements such as lenses to design simple piecewise transformation-optics devices such as invisibility cloaks and insulation windows. Finally, we shall show that ray-rotation sheets can be interpreted as performing geometrical imaging into complex space, and that as a consequence, ray-rotation sheets and gCLAs may in fact be more closely related than first realised. We conclude with a summary of potential future projects which lead naturally from the results of this thesis.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

A positional FEM Formulation for geometrical non-linear analysis of shells

This work presents a fully non-linear finite element formulation for shell analysis comprising linear strain variation along the thickness of the shell and geometrically exact description for curved triangular elements. The developed formulation assumes positions and generalized unconstrained vectors as the variables of the problem, not displacements and finite rotations. The full 3D Saint-Venant-Kirchhoff constitutive relation is adopted and, to avoid locking, the rate of thickness variation enhancement is introduced. As a consequence, the second Piola-Kirchhoff stress tensor and the Green strain measure are employed to derive the specific strain energy potential. Curved triangular elements with cubic approximation are adopted using simple notation. Selected numerical simulations illustrate and confirm the objectivity, accuracy, path independence and applicability of the proposed technique.