Standard adaptive optics systems measure the aberrations in the wavefronts of a beacon guide star caused by atmospheric turbulence, which limits the corrected field of view to the isoplanatic patch, the solid angle over which the optical aberration is roughly constant. For imaging systems that require a corrected field of view larger than the isoplanatic angle, a three-dimensional estimate of the aberration is required. We are developing a wide-field imaging Shack-Hartmann wavefront sensor (WFS) that will characterize turbulence over a large field of view tens of times the size of the isoplanatic angle. The technique will find application in horizontal and downward looking remote sensing scenarios where high resolution imaging through extended atmospheric turbulence is required. The laboratory prototype system consists of a scene generator, turbulence simulator, a Shack Hartman WFS arm, and an imaging arm. The system has a high intrinsic Strehl ratio, is telecentric, and diffraction limited. We present preliminary data and analysis from the system.

Since its invention in the early seventies, the Shack-Hartmann wavefront sensor has seen a wide variety of applications and has had great success in the fields of Adaptive Optics and Ophthalmology, where interferometry is usually impractical. Its application to optical shop testing has been less visible perhaps because shop environments can be manipulated to sufficiently remove vibration and turbulence to a degree that can support interferometry. However, with the growing need to accurately test aspheric optics, the Shack-Hartmann has an advantage; its dynamic range can be manipulated through the design of the lenslet array, rather than being directly tied to the wavelength of light and therefore lessen the need for expensive null optics.When the Shack-Hartmann is pushed to the limits of dynamic range, several issues must be dealt with. First, to reach the limits of dynamic range, those limits must be well understood. This dissertation presents a graphical approach to designing the Shack-Hartmann sensor that makes the trade-off between sensitivity and dynamic range, and accuracy and resolution intuitively clear. Next, the spots that once landed neatly in the region behind each lenslet, may now wander several lenslets away and the data reduction must be able handle this. This dissertation presents a novel and robust method for sorting these widely wondering spots and is shown to work in measurements of highly aspheric elements. Finally, in the high dynamic range regime, induced aberrations can severely limit the accuracy of the instrument. In this dissertation, these non-linear and measurement-dependent errors are studied in detail and a method of compensation is presented along with experimental results that illustrate the efficacy of the approach.

Ocular wavefront sensing is vital to improving our understanding of the human eye and to developing advanced vision correction methods, such as adaptive optics, customized contact lenses, and customized laser refractive surgery. It is also a necessary technique for high-resolution imaging of the retina. The most commonly used wavefront sensing method is based on the Shack-Hartmann wavefront sensor. Since Junzhong Liang's first application of Shack-Hartmann wavefront sensing for the human eye in 1994, the method has quickly gained acceptance and popularity in the ophthalmic industry. Several commercial Shack-Hartmann eye aberrometers are currently available. While the existing aberrometers offer reasonable measurement accuracy and reproducibility, they do have a limited dynamic range. Although rare, highly aberrated eyes do exists (corneal transplant, keratoconus, post-lasik) that cannot be measured with the existing devices. Clinicians as well as optical engineers agree that there is room for improvement in the performance of these devices "Although the optical aberrations of normal eyes have been studied by the Shack-Hartmann technique, little is known about the optical imperfections of abnormal eyes. Furthermore, it is not obvious that current Shack-Hartmann aberrometers are robust enough to successfully measure clinically abnormal eyes of poor optical quality" Larry Thibos, School of Optometry, Indiana University. The ultimate goal for ophthalmic aberrometers and the main objective of this work is to increase the dynamic range of the wavefront sensor without sacrificing its sensitivity or accuracy. In this dissertation, we attempt to review and integrate knowledge and techniques from previous studies as well as to propose our own analytical approach to optimizing the optical design of the sensor in order to achieve the desired dynamic range. We present the underlying theory that governs the relationship between the performance metrics of the sensor: dynamic range, sensitivity, spatial resolution, and accuracy. We study the design constraints and trade-offs and present our system optimization method in detail. To validate the conceptual approach, a complex simulation model was developed. The comprehensive model was able to predict the performance of the sensor as a function of system design parameters, for a wide variety of ocular wavefronts. This simulation model did confirm the results obtained with our analytical approach. The simulator itself can now be used as a standalone tool for other Shack-Hartmann sensor designs. Finally, we were able to validate our theoretical work by designing and building an experimental prototype. We present some of the more practical design aspects, such as illumination choices and tolerance analysis methods. The prototype validated the conceptual approach used in the design and was able to demonstrate a vast increase in dynamic range while maintaining accurate and repeatable measurements.

L’optique adaptative classique est limitée par l'anisoplanétisme. Pour remédier à cette limitation, de nouveaux concepts, appelés optiques adaptatives grand champ, ont été développés. Ces systèmes analysent la turbulence atmosphérique dans le volume, ce qui accroît le champ de correction. Ces techniques requièrent une connaissance précise du profil de Cn2. Mon étude consiste à valider sur le ciel une nouvelle technique de mesure du profil de Cn2, appelée CO-SLIDAR, à partir des corrélations des mesures de pentes et de scintillation réalisées avec un analyseur Shack-Hartmann sur étoile binaire. Elle s’organise autour de deux grands axes. On réalise d’abord une simulation bout-en-bout de la reconstruction du profil de Cn2 dans un cas concret d’observation astronomique. On peut ainsi étudier l’impact des différentes sources d’erreur sur la reconstruction du profil de Cn2. Ceci nous permet d’améliorer la procédure d’estimation du profil de Cn2, en prenant en compte les bruits de détection. La deuxième partie de mon étude se consacre à la validation expérimentale. On dimensionne et caractérise en laboratoire un banc d’acquisition, le banc ProMeO. Ceci conduit à une bonne connaissance du fonctionnement du banc et nous permet de corriger certains effets instrumentaux. Le banc ProMeO est finalement couplé au télescope MeO de 1,5 m de diamètre. Les données acquises permettent une reconstruction du profil de Cn2, du sol jusqu’à 17 km, avec une résolution de 600 m. Les profils obtenus par la méthode CO-SLIDAR sont comparés avec succès à des profils issus de données météorologiques. L’ensemble de ces travaux constitue la première validation sur le ciel de la méthode CO-SLIDAR. / Classical adaptive optics is limited by anisoplanatism. New concepts, known as Wide Field Adaptive Optics systems, have been developed in order to go beyond this limitation. These systems analyse atmospheric turbulence within a volume, increasing the correction field. These techniques require a precise knowledge of the Cn2 profile. The purpose of my thesis is the on-sky validation of a new measurement method of the Cn2 profile, called CO-SLIDAR, using correlations of slopes and of scintillation, both measured with a Shack-Hartmann on a binary star. My study is organized as follows. First, we perform an end-to-end simulation of the reconstruction of the Cn2 profile in a practical astronomical case. We can thus examine the impact of the different error sources on the reconstruction of the Cn2 profile. This allows us to improve the reconstruction method, taking into account the detection noises. The second part is dedicated to the experimental validation. We design and characterize an acquisition bench, the ProMeO bench. This leads to a good knowledge of the bench's operation and we can compensate for some instrumental effects. The ProMeO bench is then coupled to the MeO 1.5 m telescope. The acquired data allow the estimation of the Cn2 profile, from the ground up to 17 km, with a resolution of 600 m. The CO-SLIDAR profiles are successfully compared with profiles estimated from meteorological data. This work is the first on-sky validation of the CO-SLIDAR method.

Cette thèse commence par une étude approfondie des méthodes d’estimation de décalage sous-pixeliques rapides. Une comparaison complète est effectuée prenant en compte problèmes d’estimation de décalage existant dans des applications réelles, à savoir, avec différentes conditions de SNR, différentes grandeurs de déplacement, la non préservation de la contrainte de luminosité constante, l’aliasing et, surtout, la limitation des ressources de calcul. Sur la base de cette étude, en collaboration avec le CNES (l’agence spatiale française), deux problèmes qui sont cruciaux pour l’optique numérique des satellites d’observation de la terre sont analysés. Nous étudions d’abord le problème de correction de front d’onde dans le contexte de l’optique actif. Nous proposons un algorithme pour mesurer les aberrations de front d’onde sur un senseur de type Shack-Hartmann (SHWFS en anglais) en observant la terre. Nous proposons ici une revue de l’état de l’art des méthodes pour le SHWFS utilisé sur des scènes étendues (comme la terre) et concevons une nouvelle méthode pour améliorer l’estimation de front d’onde, en utilisant une approche basée sur l’équation du flot optique. Nous proposons également deux méthodes de validation afin d’assurer une estimation correcte du front d’onde sur les scènes étendues. Tandis que la première est basée sur une adaptation numérique des bornes inférieures (théoriques) pour le recalage d’images, la seconde méthode défausse rapidement les paysages en se basant sur la distribution des gradients. La deuxième application de satellite abordée est la conception numérique d’une nouvelle génération de senseur du type Time Delay Integration (TDI). Dans ce nouveau concept, la stabilisation active en temps réel du TDI est réalisée pour étendre considérablement le temps d’intégration, et donc augmenter le RSB des images. Les lignes du TDI ne peuvent pas être fusionnées directement par addition parce que leur position est modifiée par des microvibrations. Celles-ci doivent être compensées en temps réel avec une précision sous-pixellique. Nous étudions les limites fondamentales théoriques de ce problème et proposons une solution qui s’en approche. Nous présentons un système utilisant la convolution temporelle conjointement à une estimation en ligne du bruit de capteur, à une estimation de décalage basée sur les gradients et à une méthode multiimage non conventionnelle pour mesurer les déplacements globaux. Les résultats obtenus sont concluants sur les fronts de la précision et de la complexité. Pour des modèles de transformation plus complexes, une nouvelle méthode effectuant l’estimation précise et robuste des modèles de mise en correspondance des points d’intérêt entre images est proposée. La difficulté provenant de la présence de fausses correspondances et de mesures bruitées conduit à un échec des méthodes de régression traditionnelles. En vision par ordinateur, RANSAC est certainement la méthode la plus utilisée pour surmonter ces difficultés. RANSAC est capable de discriminer les fausses correspondances en générant de façon aléatoire des hypothèses et en vérifiant leur consensus. Cependant, sa réponse est basée sur la seule itération qui a obtenu le consensus le plus large, et elle ignore toutes les autres hypothèses. Nous montrons ici que la précision peut être améliorée en agrégeant toutes les hypothèses envisagées. Nous proposons également une stratégie simple qui permet de moyenner rapidement des transformations 2D, ce qui réduit le coût supplémentaire de calcul à quantité négligeable. Nous donnons des applications réelles pour estimer les transformations projectives et les transformations homographie + distorsion. En incluant une adaptation simple de LO-RANSAC dans notre cadre, l’approche proposée bat toutes les méthodes de l’état de l’art. Une analyse complète de l’approche proposée est réalisée, et elle démontre un net progrès en précision, stabilité et polyvalence. / This thesis starts with an in-depth study of fast and accurate sub-pixel shift estimationmethods. A full comparison is performed based on the common shift estimation problems occurring in real-life applications, namely, varying SNR conditions, differentdisplacement magnitudes, non-preservation of the brightness constancy constraint, aliasing, and most importantly, limited computational resources. Based on this study, in collaboration with CNES (the French space agency), two problems that are crucial for the digital optics of earth-observation satellites are analyzed.We first study the wavefront correction problem in an active optics context. We propose a fast and accurate algorithm to measure the wavefront aberrations on a Shack-HartmannWavefront Sensor (SHWFS) device observing the earth. We give here a review of state-of-the-art methods for SHWFS used on extended scenes (such as the earth) and devise a new method for improving wavefront estimation, based on a carefully refined approach based on the optical flow equation. This method takes advantage of the small shifts observed in a closed-loop wavefront correction system, yielding improved accuracy using fewer computational resources. We also propose two validation methods to ensure a correct wavefront estimation on extended scenes. While the first one is based on a numerical adaptation of the (theoretical) lower bounds of image registration, the second method rapidly discards landscapes based on the gradient distribution, inferred from the Eigenvalues of the structure tensor.The second satellite-based application that we address is the numerical design of a new generation of Time Delay Integration (TDI) sensor. In this new concept, active real-time stabilization of the TDI is performed to extend considerably the integration time, and therefore to boost the images SNR. The stripes of the TDI cannot be fused directly by addition because their position is altered by microvibrations. These must be compensated in real time using limited onboard computational resources with high subpixel accuracy. We study the fundamental performance limits for this problem and propose a real-time solution that nonetheless gets close to the theoretical limits. We introduce a scheme using temporal convolution together with online noise estimation, gradient-based shift estimation and a non-conventional multiframe method for measuring global displacements. The obtained results are conclusive on the fronts of accuracy and complexity and have strongly influenced the final decisions on the future configurations of Earth observation satellites at CNES.For more complex transformation models, a new image registration method performing accurate robust model estimation through point matches between images is proposed here. The difficulty coming from the presence of outliers causes the failure of traditional regression methods. In computer vision, RANSAC is definitely the most renowned method that overcomes such difficulties. It discriminates outliers by randomly generating minimalist sampled hypotheses and verifying their consensus over the input data. However, its response is based on the single iteration that achieved the largest inlier support, while discarding all other generated hypotheses. We show here that the resulting accuracy can be improved by aggregating all hypotheses. We also propose a simple strategy that allows to rapidly average 2D transformations, leading to an almost negligible extra computational cost. We give practical applications to the estimation of projective transforms and homography+distortion transforms. By including a straightforward adaptation of the locally optimized RANSAC in our framework, the proposed approach improves over every other available state-of-the-art method. A complete analysis of the proposed approach is performed, demonstrating its improved accuracy, stability and versatility.

Con el cambio del siglo XX al XXI, la importancia de las tecnologías ópticas, como herramientas esenciales para otras ciencias, está llamando la atención en diferentes ámbitos científicos y económicos. El desarrollo de técnicas relacionadas con la imagen óptica aparece en diferentes puntos de vista como por ejemplo, la tecnología de la información y de las comunicaciones, la salud humana y las ciencias de la vida, los sensores ópticos y nuevas lámparas para una mejora en el consumo de energía, el desarrollo de equipos destinados a procesos de fabricación en la industria, etc. Las aplicaciones en la industria han tenido un gran impacto económico: por ejemplo, todos los circuitos integrados de semiconductores que se producen en el mundo se fabrican mediante litografía óptica. El desarrollo de la industria de semiconductores ha dado un impulso a la investigación básica y al desarrollo de técnicas ópticas: la disminución de los tamaños en la fabricación implica la exigencia de nuevos materiales, nuevos componentes ópticos, nuevas fuentes de iluminación. En la actualidad, la mayoría de la población europea es usuaria de la Tecnología de la Información y de la Comunicación (del inglés, "Information Communication Technology"), por ejemplo a través de ordenadores personales, telefonía móvil, electrónica empleada en medicina, internet, control de robots inteligentes, detección de obstáculos para la guía de un vehículo,. y la calidad de este tipo de productos aumenta considerablemente cada pocos años para un mismo precio (un factor ~2 cada 3 años). La base de tal progreso se debe, en gran parte, al rápido progreso en la calidad de los componentes que se emplean en esta ICT, como por ejemplo, los circuitos integrados y su conexión con otros dispositivos. La industria semiconductora se está preparando para promover una reducción del detalle más pequeño en los circuitos integrados, por debajo de los 130 nanómetros. Tal reducción requiere una evaluación de la ausencia de gradientes ondulatorios y abruptos con una precisión de 10 nanómetros para el caso particular de obleas de 300 milímetros de diámetro. El diámetro actual standard de las obleas es de 200 milímetros aunque actualmente ya se están produciendo obleas de 300 milímetros y el objetivo es fabricar obleas todavía más grandes. Además, la velocidad de procesado aumentará hasta 100 obleas por hora. Así, el control en la producción y pulido de obleas requiere una instrumentación para la medición rápida de la topografía tridimensional que en la actualidad, no está disponible técnicamente. Otro de los problemas que aparece en la industria semiconductora concierne a los substratos que forman las obleas. La tecnología actual permite producir detalles muy pequeños mediante procesos litográficos. Esto exige mayores requerimientos en la planitud de las obleas sobre las que se depositan repetidamente circuitos integrados. El problema consiste en que la inspección de la planitud requiere mucho tiempo, varias horas para una única oblea. Otro de los problemas con los que se encuentra la industria semiconductora es el procesado de las obleas. Después de la deposición de cada substrato, se neutraliza depositando una capa muy delgada de SiO2. Antes de la siguiente deposición, la oblea se somete a procesos de pulido químicos y mecánicos para conseguir de nuevo la planitud deseada. Se trata de un proceso lento que aumenta el coste de producción. Sin embargo, en un futuro inmediato se fabricarán obleas de 450 mm de diámetro mientras que las actuales son de 200 mm; de forma que se podrán depositar más circuitos integrados ganando tiempo y reduciendo el coste de producción. La situación es similar en otros campos, como por ejemplo, los dispositivos de cristal líquido: en la línea de producción se requiere un rápido control de la topografía tridimensional de dichos cristales, que tampoco está disponible en la actualidad. En este caso las dimensiones pueden llegar a ser de 1m por 1m.

L'optique adaptative classique est limitée par l'anisoplanétisme. Pour remédier à cette limitation, de nouveaux concepts, appelés optiques adaptatives grand champ, ont été développés. Ces systèmes analysent la turbulence atmosphérique dans le volume, ce qui accroît le champ de correction. Ces techniques requièrent une connaissance précise du profil de Cn2. Mon étude consiste à valider sur le ciel une nouvelle technique de mesure du profil de Cn2, appelée CO-SLIDAR, à partir des corrélations des mesures de pentes et de scintillation réalisées avec un analyseur Shack-Hartmann sur étoile binaire. Elle s'organise autour de deux grands axes. On réalise d'abord une simulation bout-en-bout de la reconstruction du profil de Cn2 dans un cas concret d'observation astronomique. On peut ainsi étudier l'impact des différentes sources d'erreur sur la reconstruction du profil de Cn2. Ceci nous permet d'améliorer la procédure d'estimation du profil de Cn2, en prenant en compte les bruits de détection. La deuxième partie de mon étude se consacre à la validation expérimentale. On dimensionne et caractérise en laboratoire un banc d'acquisition, le banc ProMeO. Ceci conduit à une bonne connaissance du fonctionnement du banc et nous permet de corriger certains effets instrumentaux. Le banc ProMeO est finalement couplé au télescope MeO de 1,5 m de diamètre. Les données acquises permettent une reconstruction du profil de Cn2, du sol jusqu'à 17 km, avec une résolution de 600 m. Les profils obtenus par la méthode CO-SLIDAR sont comparés avec succès à des profils issus de données météorologiques. L'ensemble de ces travaux constitue la première validation sur le ciel de la méthode CO-SLIDAR.

Shack-Hartmann wavefront sensors are commonly used in optical alignment, ophthalmology, astronomy, adaptive optics and commercial optical testing. Wavefront error measurement yields Zernike polynomials which provide useful data for alignment correction calculations. In this thesis a practical alignment method of a helmet visor is proposed based on the wavefront error measurements. The optical system is modeled in Zemax software in order to collect the Zernike polynomial data necessary to relate the error measurements to the positioning of the visor. An artificial neural network based computer program is designed and trained with the data obtained from Zernike simulation in Zemax software and then the program is able to find how to invert the misalignments in the system. The performance of this alignment correction method is compared with the optical test setup measurements.

The continuous improvements of optical design tools and manufacturing technologies of free-form optical elements, allow the creation of new complex-shaped lenses that improve the performance of traditional optical systems and make possible new optical applications. The quality of fabrication of complex-shaped lenses depends on the possibility of measurement of the shape along the manufacturing process. Moreover, the measurement of the shape of fabricated lenses is a usual quality control process conducted by the manufacturing industry to ensure the quality of commercial lenses. The measurement of complex-shaped optical surfaces has been usually done with mechanical contact stylus, to get higher resolutions within the larger dynamic range required. However, stylus devices have important drawbacks as a slow measurement speed due to make a point by point measurement, and specially the risk of damage of extremely polished surfaces of the lenses due to the drag of the stylus across them. As opposed to those mechanical contact devices of measurement, there are several non destructive optical techniques like interferometry and deflectometry based on the Shack-Hartmann sensor of spherical microlenses, which are much faster due to make a full-field measurement in a single shot. Despite this advantage, these two techniques have a more limited dynamic range of measurement than stylus devices, which does not allow to measure most complex-shaped lenses. Therefore, solutions to extend the dynamic range of those full-field optical techniques are needed, like changing the conventional Shack-Hartmann’s array of microspheres for an array of more appropriate microlenses and the compensation of the tested lens by means of “inverse” additional optical elements to reduce its complexity. Otherwise, once an optical element has been tested, it is required to finally reconstruct its shape from the discrete data obtained in the measurement. In the lenses’ field, the modal Zernike representation is commonly used to reconstruct the shape. However, to describe complex shapes with steep local changes, zonal representations fit better. Among them, it must be mentioned the B-Spline representation, which is used by the ophthalmic lenses’ manufacturers in the design and modelling of complex progressive surfaces of lenses of this type. The current thesis describes various optical solutions to measure and represent the shape of commercial complex-shaped lenses, particularly applied to progressive addition lenses personalized to the user. The developed solutions are: - It is implemented the B-Spline cubic representation to reconstruct complex wavefronts and get direct information of their local amplitudes, by means of fitting the local wavefront slopes that output from a Shack-Hartmann wavefront sensor. It is compared the fitting quality of B-Spline and circular Zernike representations in a set of simulated wavefronts of different complexity. To quantify the fitting quality in similar conditions as experimentally, two complementary parameters which account for the differences between the reconstructed wavefront and the simulated wavefront with added noise (fitting RMS error) and between the reconstructed wavefront and the simulated wavefront without noise (wavefront RMS error) are used. The fitting quality is analyzed in terms of the degree of Zernike polynomial and in terms of the number of subzones that divides the whole wavefront domain (breakpoints) for the B-Spline representation. - It is developed a Shack-Hartmann wavefront sensor based on a cylindrical microlens array and a proprietary algorithm that processes the line patterns detected, to extend the dynamic range of the conventional Shack-Hartmann sensor of spherical microlenses. After making a conceptual design of the sensor and evaluating the performance of various configurations in terms of the measurement field, spatial resolution, vertical resolution and dynamic range by means of a proprietary ray trace program, two wavefront sensors are built: a first sensor with an unique array of microcylinders placed in a rotary mount that allows positioning the microcylinders in horizontal and vertical directions, and a second more evolved sensor with two equal arrays of microcylinders placed in horizontal and vertical directions, which reaches the same measurement speed as the Shack-Hartmann sensor of spherical microlenses. The sensor is applied to characterize by transmission a set of three different prescriptions commercial progressive addition lenses with designs customized to wearers that move their eyes, their head, and half the eyes and the head when doing a visual task. From the characterization process, the spatially resolved aberrations, the iso-power maps, the iso-cylinder maps and the cylinders’ axis maps of the lenses are obtained. - It is designed and built an active optics system to compensate the wavefront transmitted by complex-shaped lenses. As the active device to make the wavefront compensation, it is used a commercial phase-only modulator based on a parallel-aligned liquid crystal, which has the advantages of a high spatial resolution and an accurate response in open-loop mode. The response is characterized experimentally. As opposed to the abovementioned advantages, the phase modulator has the lack of decreasing its diffraction efficiency as increases the amplitude of the modulated phase. This means that non phase-modulated light, which corresponds to the zero order of diffraction that outputs from the modulator, is superimposed to phase-modulated light of interest. To solve this problem, a pinhole spatial filter that blocks the zero order diffraction light is implemented in the system. The active optics system is proposed as a dynamic null-test to make the quality control of complex-shaped lenses with a reduced cost in time and money over the traditional static null-tests. As a demonstration of the application, an active null-test of a commercial progressive addition lens personalized to the user with distance null power and two dioptres of addition is successfully made. / Las continuas mejoras en las herramientas de diseño óptico y en las tecnologías de fabricación de formas arbitrarias (free-form) de elementos ópticos, permiten el desarrollo de nuevas lentes de formas más complejas, posibilitando nuevas aplicaciones ópticas y mejorando las prestaciones de los sistemas ópticos clásicos. Para la fabricación precisa de lentes de formas complejas es determinante la posibilidad de medida de su forma. Asimismo, la medida final de la forma de lentes fabricadas es un proceso habitual de control de calidad llevado a cabo por la industria fabricante, para garantizar la calidad de las lentes comerciales desarrolladas. La medida de superficies ópticas con formas complejas se ha llevado a cabo, tradicionalmente, con instrumentos de medida por contacto mecánico (stylus), para garantizar buenas resoluciones de medida y abarcar el gran rango dinámico normalmente necesario. No obstante, estos sistemas presentan importantes inconvenientes como la lentitud por ser una medida punto a punto, y especialmente el riesgo de dañado de las superficies extremadamente pulidas de las lentes a causa del contacto y arrastre del stylus. Frente a estos sistemas metrológicos con contacto mecánico, diferentes técnicas no destructivas de tipo óptico como las interferométricas y el sensor Shack-Hartmann clásico de microlentes esféricas, más rápidas al medir la superficie en su conjunto, se han mostrado como buenas alternativas. Aún así, estos dos métodos tienen unos rangos dinámicos de medida más limitados que los de los stylus, lo que típicamente los incapacita para medir lentes de formas complejas. Se hace por tanto necesario desarrollar soluciones para extender el rango dinámico de medida de estas técnicas ópticas de campo completo (full-field), como pueden ser la modificación del sensor Shack-Hartmann convencional de microlentes esféricas por otros tipos de microlentes más apropiados y la compensación previa de la lente a medir mediante la utilización de elementos ópticos “inversos” a ella para reducir su complejidad. Por otra parte, una vez medido un determinado elemento óptico, resulta necesario reconstruir su forma a partir de las medidas discretas obtenidas. En el ámbito de las lentes, la representación modal de polinomios circulares de Zernike es la más utilizada para reconstruir la forma medida. Sin embargo, a la hora de describir formas complejas con cambios locales importantes o formas arbitrarias, las representaciones de tipo zonal resultan más efectivas. Entre ellas, cabe destacar la representación zonal de B-Splines, que es la empleada por la industria oftálmica en el diseño y modelización de las superficies progresivas complejas de lentes de este tipo. La presente tesis describe diversas soluciones ópticas de medida y representación de las características ópticas de lentes comerciales de formas complejas, con particular aplicación a lentes oftálmicas de adición progresiva personalizadas al usuario. Las soluciones desarrolladas son las siguientes: - Se implementa la representación de B-Splines cúbicos para reconstruir frentes de onda complejos y extraer informaciones locales de amplitud, mediante ajuste de las pendientes locales medibles por un sensor de frente de onda de tipo Shack-Hartmann. Se realiza un estudio comparativo de la calidad de la anterior representación y de la representación de Zernike para ajustar diferentes frentes de onda simulados de distinta complejidad, empleándose dos parámetros complementarios para cuantificar la calidad de ajuste, que son el error del frente de onda reconstruido respecto al frente de onda simulado con ruido (error RMS ajuste) y el error del frente de onda reconstruido respecto al frente de onda simulado sin ruido (error RMS frente), de manera que se extraigan conclusiones de la calidad de ajuste en condiciones similares a las experimentales. La calidad de los ajustes se analiza en función del grado del polinomio de Zernike y del número de subzonas de división del dominio del frente de onda (breakpoints) para la representación cúbica de B-Spline. - Se desarrolla un sensor de frente de onda de tipo Shack-Hartmann basado en matrices de microlentes cilíndricas que, junto con un algoritmo de procesado de los patrones de líneas detectados que también se desarrolla, extiende el rango dinámico clásico del sensor Shack-Hartmann equivalente de microlentes esféricas. Una vez realizado el diseño conceptual del sensor y evaluadas las prestaciones metrológicas (campo de medida, resolución espacial, resolución vertical y rango dinámico) de diversas configuraciones del mismo mediante un programa propio de trazado de rayos, se construyen dos sensores: un primer sensor con una única matriz de microcilindros montada sobre un soporte rotador que permite orientar los microcilindros en las direcciones horizontal y vertical, y un segundo sensor más evolucionado con dos matrices de microcilindros horizontales y verticales, que equipara la velocidad de medida con la del sensor Shack-Hartmann convencional de microlentes esféricas. Se aplica el sensor a la caracterización por transmisión de un conjunto de lentes comerciales de adición progresiva personalizadas para personas movedoras de ojos, movedoras de cabeza y movedoras de ojos y cabeza a partes iguales, de tres prescripciones diferentes: OD 0 Ad.2, OD -1 +1 0º Ad.2, y OD -1 +1 135º Ad.2, obteniéndose las aberraciones espacialmente resueltas de las lentes, así como también sus mapas de iso-potencia, de iso-cilindro y de orientación del cilindro. - Se diseña y construye un sistema óptico de compensación activa del frente de onda transmitido por lentes con formas complejas. Como elemento activo de compensación se utiliza un modulador de fase comercial basado en un cristal líquido de moléculas paralelas, que proporciona una modulación pura de la fase (sin modulación de intensidad), una elevada resolución espacial y una respuesta de gran calidad en bucle abierto. La caracterización de dicha respuesta se realiza experimentalmente. En contrapartida a las anteriores ventajas citadas, el modulador presenta un punto débil debido a su naturaleza difractiva, apreciable en forma de un decremento en la eficiencia de difracción para altas amplitudes de modulación de fase, que se traduce en luz parásita no modulada en fase correspondiente al orden cero de difracción que se superpone a la luz modulada en fase de interés. Como solución a este problema se implementa en el sistema un filtro espacial de tipo pinhole que bloquea la luz indeseada de orden cero. El sistema de compensación activa desarrollado se propone como null-test dinámico para el control de calidad de lentes complejas, de manera que suponga una reducción de costes económicos y en tiempo respecto a las convencionales soluciones null-test estáticas. Como demostración del mismo, se lleva a cabo el null-test activo una lente comercial progresiva personalizada con potencia nula de lejos y dos dioptrías de adición.

Reconstruction of continuous signals from a number of their discrete samples is central to digital signal processing. Digital devices can only process discrete data and thus processing the continuous signals requires discretization. After discretization, possibility of unique reconstruction of the source signals from their samples is crucial. The classical sampling theory provides bounds on the sampling rate for unique source reconstruction, known as the Nyquist sampling rate. Recently a new sampling scheme, Compressive Sensing (CS), has been formulated for sparse signals. CS is an active area of research in signal processing. It has revolutionized the classical sampling theorems and has provided a new scheme to sample and reconstruct sparse signals uniquely, below Nyquist sampling rates. A signal is called (approximately) sparse when a relatively large number of its elements are (approximately) equal to zero. For the class of sparse signals, sparsity can be viewed as prior information about the source signal. CS has found numerous applications and has improved some image acquisition devices. Interesting instances of CS can happen, when apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In such cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of the required samples for accurate reconstruction. A general CS problem can be transformed to an equivalent optimization problem. In this thesis, a special case of CS with side information about the feasible region of the equivalent optimization problem is studied. It is shown that in such cases uniqueness and stability of the equivalent optimization problem still holds. Then, an efficient reconstruction method is proposed. To demonstrate the practical value of the proposed scheme, the algorithm is applied on two real world applications: image deblurring in optical imaging and surface reconstruction in the gradient field. Experimental results are provided to further investigate and confirm the effectiveness and usefulness of the proposed scheme.