Um sistema multi-feixe de pinças ópticas baseado na técnica de contraste de fase da ordem zero pode apresentar vantagens significativas sobre sistemas mecanicamente complexos e sensíveis ao alinhamento, e sobre tecnologias que, apesar de serem similares, requerem a customização de componentes ópticos. Porém, ao nosso conhecimento, este sistema até agora não tem sido implementado experimentalmente. Neste trabalho tem-se desenvolvido, como prova de princípio, o primeiro sistema baseado na técnica de contraste de fase da ordem zero gerador de múltiplas pinças ópticas. Esta técnica da óptica de Fourier utiliza conceitos do contraste de fase de Zernike e técnicas de codificação de dois pixels para gerar padrões de intensidade no plano da imagem que são diretamente relacionados a distribuições de fase no plano de entrada do sistema, o qual é formado por um modulador espacial de luz (SLM). Esta dissertação de mestrado descreve detalhadamente os passos tomados com o propósito de utilizar os campos estruturados de luz gerados pelo sistema de contraste de fase da ordem zero para aprisionar esferas de 2 µm de diâmetro de sílica fundida. Neste trabalho apresentamos os fundamentos teóricos do aprisionamento óptico e da técnica de contraste de fase da ordem zero, seguidos pela implementação de experimentos independentes em cada modalidade, e finalmente apresentamos a integração de ambos os sistemas dentro um sistema único de pinças ópticas multi-feixe. Apesar da baixa eficiência óptica do sistema, foi possível implementar um sistema de pinças ópticas duplas. Finalizamos o nosso trabalho na discussão detalhada das limitações do nosso arranjo óptico e comentamos sobre potenciais melhorias para aumentar a rigidez das pinças ópticas e a qualidade geral do sistema. / A multi-beam optical trapping system based on the zero order phase contrast technique may offer significant advantages over mechanically-complex, alignment-sensitive optical trapping systems, and over technologies that, though similar, require the customization of optics components. However, to our knowledge, such a system has not been yet implemented experimentally. We have developed, as a proof of principle, what we think is the first system based on the zero order phase contrast technique to successfully generate multiple optical traps. This Fourier optics technique makes use of existing concepts of Zernike phase contrast and two-pixel encoding techniques to generate intensity patterns in the image plane that are directly related to phase distributions in the input plane, which is comprised by a spatial light modulator (SLM). This master\'s dissertation describes in detail the steps taken towards using the structured light fields generated by a zero order phase contrast system to trap 2 µm diameter fused silica beads. We present the theoretical foundations of optical trapping and the zero order phase contrast technique, followed by the implementation of independent laboratory experiments in each modality, and finally integrate both systems into a single optical setup for multi-beam trapping. In spite of the low optical efficiency of the system, we were able to implement dual optical traps. We finalize by discussing in detail the limitations of our experimental setup in and comment on potential improvements to increase the stiffness of the optical traps and the overall quality of the system.

L’instrumentation multi-pupille permet de repousser les limitations actuelles des diamètres des télescopes monolithiques. L’alignement des sous-pupilles est donc une problématique incontournable pour les futurs projets de télescopes au sol comme dans l’espace. Un Analyseur de Surface d’Onde (ASO) est alors nécessaire pour mesurer les aberrations spécifiques au cas multi-pupille que sont le piston différentiel (différence de marche entre les sous-pupilles), le tip et le tilt (basculements différentiels entre les sous-pupilles). Nous nous attachons à réaliser des ASOs non supervisés et simples d’implantation, permettant l’alignement total d’un instrument multi-pupille. L’algorithme ELASTIC repose sur l’analyse de la corrélation entre deux images focales prises successivement, différant par une perturbation maîtrisée et appliquée directement sur les sous-pupilles. ELASTIC permet d’une part d’estimer les grandes erreurs de tip/tilt, pour effectuer un alignement géométrique et d’autre part de stabiliser le tip/tilt pendant la minimisation des grandes erreurs de piston, pour l’alignement interférométrique. Enfin, un second algorithme appelé LAPD permet, au moyen de deux images prises simultanément dans un plan focal et dans un plan légèrement défocalisé, d’estimer les petites erreurs de piston/tip/tilt pour le cophasage fin. Ces différents algorithmes sont caractérisés au moyen de simulations numériques, pour différents types de télescopes multi-pupilles. Nous démontrons expérimentalement les briques de la chaîne d’alignement sur un instrument à 6 sous-pupilles. Ces ASOs permettent de simplifier le dimensionnement des futurs télescopes. / The resolution of a telescope is ultimately limited by its aperture diameter, but the size of mirrors is bounded by current technology to about 10m on the ground and to a few meters in space. To overcome this limitation, interferometry consists in making an array of sub-apertures interfere; the resulting instrument is called an interferometer or a multi-aperture telescope. To reach the diffraction limit of such instruments, all sub-apertures must be phased to within a small fraction of wavelength. A critical sub-system of interferometers is the Cophasing Sensor (CS), whose goal is to measure the relative positioning errors between the sub-apertures (differential piston, tip and tilt), which are the specific low-order aberration of an interferometer and the main source of wave-front degradation. We aim to develop unsupervised and easy-to-implement CSs for the global multi-aperture telescope alignment. ELASTIC algorithm provides a solution for large amplitude tip/tilt error measurement from a modified cross-spectrum of two diversity images, allowing the geometrical alignment. ELASTIC also provides tip/tilt stability for the large amplitude piston error minimization, called the interferometric alignment. Finally a second algorithm called LAPD uses focal and slightly defocused images for the small amplitude piston/tip/tilt error measurement, allowing the fine phasing. Numerical simulations of several types of multi-aperture telescopes are performed in order to test our algorithms. We experimentally demonstrate the efficiency of the different algorithms on a 6-sub-aperture instrument. These algorithms should simplify the design of the future telescopes.

The objectives of the present project were to set up, optimise and characterise a digitalholographic microscopy (DHM) laboratory set-up designed for the study of eyetissue and to implement and optimise digital data processing and noise reductionroutines. This work is part of a collaborative project aiming to provide quantitativemethods for the in vitro and in vivo characterisation of human corneal transparency.The laboratory set-up is based on a commercial laboratory microscope with zoomfunction (a “macroscope”). In continuation of previous work, we completed and optimised,and extended a software for holographic signal processing and numericalpropagation of the wavefront.To characterise the set-up and quantify its performances for standard operationand in its DHM configuration, we compare the magnification and resolution to theoreticalvalues for a given set of parameters. We determined the magnification factorand the rotation angle between the object and camera planes. With a laser wavelengthof 532 nm, a x1 objective and a zoom setting of x2.9 (which corresponds to aplane sample wavefront), we measured a magnification of 1.68. With the same parameters,we measure a holographic resolution of about 11 m. The wavefront phasecould be determined with a precision of a fraction of the wavelength.We subsequently performed analysis of the relative contribution of coherent noiseand implemented and evaluated several noise reduction routines. While the impactof coherent noise remained visible in the amplitude image, interferometric precisionwas obtained for the phase of the wavefront and the set-up was considered qualifiedfor its intended use for corneal characterisation.A first test measurement was performed on primate cornea.Subsequent work will address the further quantitative characterisation of the setupfor the full set of parameters (objectives, zoom positions, wavelengths), test measurementson samples with known transmission and light scattering properties (e.g.solutions of PMMA beads) and the comparison of the results with the predictions ofa theoretical model, and measurements on animal and human tissue.

This thesis explores how the diffraction pattern in the near-field region of a chromium feature edge on a photomask gets altered for three scenarios: First, an analytical study using the Fresnel diffraction integral is performed that investigates what happens when the thin-mask approximation is omitted and the chromium layer is given a thickness. Another analytical study is performed where the edges of a test feature are altered to simulate deviations in the linewidth or a translation of the whole feature, image subtraction is then used to create a difference pattern by subtracting a reference diffraction pattern from the diffraction pattern created by the altered test feature. Lastly, a numerical study using Fourier optics is performed to investigate the effect that introducing four common defects: extrusions, intrusions, dark spots, and pinholes, around the edge will have on the diffraction pattern by subtracting the diffraction pattern from a reference half-plane and again analyzing the resulting difference pattern. Introducing a thickness to the chromium layer alters the diffraction pattern by creating a small crease around the area of the edge in reflective mode, resulting in something similar to a double edge. The high optical density of chromium nullified any effect the thickness had when viewing the system through transmission mode. A linear relation between a change in linewidth or translation of a feature and the peak intensity of the difference pattern is observed that might be used for edge detection. The defect diameter of an extrusion or intrusion seems to correlate in a quadratic way with the peak fringe intensity of the subtracted difference pattern along the x-axis as the defect is fully visible. For a dark spot or pinhole defect being translated away from a chromium edge, the central fringe along the y-axis of the difference pattern follows a sinusoidal curve as it translates further away from the edge. The amplitude of this curve is related to the defect size.

Nous avons développé un microscope tomographique diffractif en réflexion, qui permet d’observer la surface d’un échantillon avec une résolution latérale améliorée comparée à un microscope holographique conventionnel. À partir des même données expérimentales (les hologrammes acquis sous différents angles d’illumination), des mesures à haute précision longitudinale peuvent être réalisées sur la surface d’un échantillon purement réfléchissant, par reconstruction du profil de hauteur à partir de la phase. Cette méthode d’imagerie multimodale présente plusieurs avantages comparée aux mesures en holographie interférométrique classique : amélioration de la résolution latérale sur la partie diffractive, déroulement de phase facilité, réduction du bruit cohérent, l’ensemble étant associé à la grande précision longitudinale fournie par les mesures de phase. Nous montrons ces possibilités en imageant divers échantillons minces. / We have developed a tomographic diffractive microscope in reflection, which permits observation of sample surfaces with an improved lateral resolution, compared to a conventional holographic microscope. From the same set of data, high-precision measurements can be performed on the shape of the reflective surface by reconstructing the phase of the diffracted field. doing so allows for several advantages compared to classical holographic interferometric measurements: improvement in lateral resolution, easier phase unwrapping, reduction of the coherent noise, combined with the high-longitudinal precision provided by interferometric phase measurements. We demonstrate these capabilities by imaging various test samples.

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise.

The ongoing merger of the digital and optical components of the modern microscope is creating opportunities for new measurement techniques, along with new challenges for optical modelling. This thesis investigates several such opportunities and challenges which are particularly relevant to biomedical imaging. Fourier optics is used throughout the thesis as the underlying conceptual model, with a particular emphasis on three--dimensional Fourier optics. A new challenge for optical modelling provided by digital microscopy is the relaxation of traditional symmetry constraints on optical design. An extension of optical transfer function theory to deal with arbitrary lens pupil functions is presented in this thesis. This is used to chart the 3D vectorial structure of the spatial frequency spectrum of the intensity in the focal region of a high aperture lens when illuminated by linearly polarised beam. Wavefront coding has been used successfully in paraxial imaging systems to extend the depth of field. This is achieved by controlling the pupil phase with a cubic phase mask, and thereby balancing optical behaviour with digital processing. In this thesis I present a high aperture vectorial model for focusing with a cubic phase mask, and compare it with results calculated using the paraxial approximation. The effect of a refractive index change is also explored. High aperture measurements of the point spread function are reported, along with experimental confirmation of high aperture extended depth of field imaging of a biological specimen. Differential interference contrast is a popular method for imaging phase changes in otherwise transparent biological specimens. In this thesis I report on a new isotropic algorithm for retrieving the phase from differential interference contrast images of the phase gradient, using phase shifting, two directions of shear, and non--iterative Fourier phase integration incorporating a modified spiral phase transform. This method does not assume that the specimen has a constant amplitude. A simulation is presented which demonstrates good agreement between the retrieved phase and the phase of the simulated object, with excellent immunity to imaging noise.

L'Europe prépare actuellement le plus grand télescope du monde : l'European Extremely Large Telescope (E-ELT). Prévu vers 2026, ce télescope géant permettra de répondre à des questions fondamentales de l'astrophysique contemporaine. L'imagerie d'objets astrophysiques depuis des télescopes au sol est cependant perturbée par l'atmosphère qui réduit la capacité des instruments au sol à distinguer les objets proches. L'Optique Adaptative (OA) permet de restaurer cette résolution angulaire en corrigeant en temps réel (via un miroir déformable) le front d'onde perturbé par l'atmosphère (mesuré par l'Analyseur de Surface d'Onde (ASO)). Jusqu'à récemment, la majorité des systèmes d'OA utilisaient des ASO Shack-Hartmann (SH). Des concepts concurrents basés sur le filtrage optique de Fourier (le senseur Pyramide ou l'analyseur Zernike) viennent cependant d'être mis en fonctionnement et leurs résultats semblent surpasser les performances du SH. En vue de leur potentielle utilisation sur les ELTs, cette thèse vise à consolider leur compréhension théorique ainsi qu'à optimiser ces ASO basés sur le filtrage de Fourier. Cette thèse développe un cadre mathématique qui décrit sous un unique formalisme ces ASO. Il permet de généraliser les designs préexistants -passant ainsi d'ASO uniques à des "classes d'ASO"- en transformant leurs grandeurs caractéristiques à l'origine fixées en degrés de liberté. Les classes Pyramide et Zernike sont donc explorées dans le but d'optimiser ces ASO au regard des attentes expérimentales. Des configurations inédites de la classe Pyramide -ASO que l'on appelle Pyramides aplaties- s'avèrent notamment prometteuses et font l'objet d'une étude plus poussée. / Europe is currently preparing the largest telescope of the world: the European Extremely Large Telescope (E-ELT). Planned by 2026, this huge telescope will allow to answer fundamental questions of contemporary astrophysics. However, images of astrophysical objects done by ground based telescopes suffer from the atmospheric turbulence which reduces the capacity of instruments to distinguish objects too close to each other. The Adaptive Optics (AO) allows to restore this loss of angular resolution by correcting (thanks to a deformable mirror) in real time the perturbed wave front (measured by the WaveFront Sensor (WFS)).Until very recently, the majority of AO systems had used the Shack-Hartmann (SH) WFS. New concepts based on Fourier filtering (the Pyramid or the Zernike WFSs) have however just been put in operation in several professional observatories and their results seem to outperform the SH. Since they would potentially be chosen for the AO systems of the future ELTs, this thesis aims to consolidate their theoretical understanding and to optimize these Fourier based WFSs.We firstly develop a mathematical framework which describes all these WFSs under an unique formalism. It allows to generalize the pre-existent designs -a WFS thus becomes a "WFS class"- by considering their optical parameters as flexible quantities. We then explored the two Pyramid and Zernike classes to identify the influence of class' parameters on performance criteria in order to optimize optical designs with regard to the instrumental requirements. New configurations of the Pyramid class -that we called Flattened pyramids- show promising behaviors and are studied in details.

The present study analyses three beam shaping approaches with respect to a light-efficient generation of i) patterns and ii) multiple spots by means of a generic optical 4f-setup. 4f approaches share the property that due to the one-to-one relationship between output intensity and input phase, the need for time-consuming, iterative calculation can be avoided. The resulting low computational complexity offers a particular advantage compared to the widely used holographic principles and makes them potential candidates for real-time applications. The increasing availability of high-speed phase modulators, e.g. on the basis of MEMS, calls for an evaluation of the performances of these concepts. Our second interest is the applicability of 4f methods to high-power applications. We discuss the variants of 4f intensity shaping by phase modulation from a system-level point of view which requires the consideration of application relevant boundary conditions. The discussion includes i) the micro mirror based phase manipulation combined with amplitude masking in the Fourier plane, ii) the Generalized Phase Contrast, and iii) matched phase-only correlation filtering combined with GPC. The conceptual comparison relies on comparative figures of merit for energy efficiency, pattern homogeneity, pattern image quality, maximum output intensity and flexibility with respect to the displayable pattern. Numerical simulations illustrate our findings.

Spatial Light Modulators (SLMs) based on Micro-Opto-Electro-Mechanical Systems (MOEMS) are increasingly being used in various fields of optics and enable novel functionalities. The technology features frame rates from a few kHz to the MHz range as well as resolutions in the megapixel range. The field continues to make rapid progress, but technological advancements are always associated with high expenditure. Against this background, this dissertation addresses the question: What contribution can optical system design make to the further development of MOEMS-SLM-based modulation? A lens is a simple example of an optical system. This dissertation deals with system design based on Fourier optics in which the wave properties of light are exploited. On this basis, arrays of micromirrors can modulate light properties in a spatially resolved manner. For example, tilt-mirrors can control the intensity distribution in an image plane. In this dissertation variations of the aperture required for this are investigated. In addition to known absorbing apertures, phase filters in particular are investigated, which apply a spatially distributed delay effect to the light wave. This dissertation proposes the combination of MOEMS-SLMs with static, pixelated elements in the same system. These may be pixelated phase masks, also known as diffractive optical elements (DOEs). Analogously, pixelated polarizer arrays and absorbing photomasks exist. The combination of SLMs and static elements allows new degrees of freedom in system design. This thesis proposes new modulation systems based on MOEMS tilt-mirror SLMs. These systems use analog tilt-mirror arrays for the simultaneous modulation of intensity and phase as well as intensity and polarization. The proposed systems thus open up new possibilities for MOEMS-based spatial light modulation. Their properties are validated and investigated by numerical simulations. System properties and limitations are derived from these near and far field simulations. This dissertation shows that the modulation of different MOEMS-SLM types can be fundamentally changed by system design. Piston mirror arrays are classically used for phase modulation and tilt-mirror arrays for intensity modulation. This thesis proposes the use of subpixel phase structures. Their use approximately provides tilt-mirrors with the phase-modulating effect of piston-mirrors. In order to achieve this, a new optimization method is presented. Piston-mirror arrays are available only to a limited extent. By contrast, tilt-mirror arrays are well established. In combination with subpixel phase features, tilt-mirrors may replace piston-mirrors in some applications. These and other challenges of MOEMS-SLM technology can be adequately addressed on the basis of system design. / Räumliche Lichtmodulatoren (Spatial Light Modulators, SLMs) auf Basis von Mikro-Opto-Elektro-Mechanischen Systemen (MOEMS) finden zunehmend Anwendung in verschiedensten Teilgebieten der Optik und ermöglichen neuartige Funktionalitäten. Die Technik ermöglicht Frameraten von einigen kHz bis in den MHz-Bereich sowie Auflösungen bis in den Megapixelbereich. Der Fachbereich macht nach wie vor rasche Fortschritte, technologische Weiterentwicklungen sind aber stets mit hohem Aufwand verbunden. Vor diesem Hintergrund widmet sich diese Arbeit der Frage: Welchen Beitrag kann optisches Systemdesign zur Weiterentwicklung der MOEMS-SLM-basierten Modulation leisten? Bereits eine Linse stellt ein Beispiel für ein optisches System dar. Diese Dissertation beschäftigt sich mit Systemdesign auf Basis der Fourier-Optik, bei der die Welleneigenschaften des Lichts genutzt werden. Auf dieser Basis können Arrays von Mikrospiegeln die flächige Verteilung von Licht einstellen. Beispielsweise können Kippspiegel die Intensitätsverteilung in einer Bildebene steuern. In dieser Dissertation werden Variationen der dafür nötigen Apertur untersucht. Neben bekannten absorbierenden Blenden werden insbesondere Phasenfilter untersucht, welche eine flächig verteilte Verzögerungswirkung auf die Lichtwelle aufbringen. Diese Dissertation schlägt die Kombination von MOEMS-SLMs mit statischen, pixelierten Elementen im selben System vor. Hierbei kann es sich um pixelierte Phasenmasken handeln, auch bekannt als diffraktive optische Elemente (DOEs). Analog existieren pixelierte Polarisatorarrays und absorbierende Fotomasken. Die Kombination von SLMs und statischen Elementen ermöglicht neue Freiheiten im Systemdesign. Diese Arbeit schlägt neue Modulationssysteme auf Basis von MOEMS-Kippspiegel-SLMs vor. Diese Systeme nutzen analoge Kippspiegelarrays für die simultane Modulation von Intensität und Phase sowie von Intensität und Polarisation. Die vorgeschlagenen Systeme eröffnen damit neue Möglichkeiten für die MOEMS-basierte Flächenlichtmodulation. Ihre Eigenschaften werden mithilfe von numerischen Simulationen validiert und untersucht. Aus diesen Nah- und Fernfeldsimulationen werden Systemeigenschaften und Limitierungen abgeleitet. Es wird in dieser Arbeit gezeigt, dass die Modulation verschiedener MOEMS-SLM-Typen auf Basis des Systementwurfs fundamental verändert werden kann. Senkspiegelarrays werden klassischerweise zur Modulation der Phase eingesetzt und Kippspiegelarrays zur Modulation der Intensität. Diese Arbeit schlägt die Nutzung von Subpixel-Phasenstrukturen vor. Diese verleihen Kippspiegeln näherungsweise die phasenmodulierende Wirkung von Senkspiegeln. Um dies zu erreichen, wird ein neuartiges Optimierungsverfahren vorgestellt. Senkspiegelarrays sind nur in geringem Umfang verfügbar. Im Gegensatz dazu sind Kippspiegelarrays gut etabliert. In Kombination mit Subpixel-Phasenstrukturen könnten Kippspiegel in einigen Anwendungen Senkspiegel ersetzen. Diese und andere Herausforderungen der MOEMS-SLM-Technologie lassen sich auf der Grundlage des Systemdesigns adäquat adressieren.