The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical Observatory telescope in Sutherland, and our attempt to validate it with simultaneous Shack-Hartmann wavefront sensor images.

Wavefront sensing is an old yet fundamental problem in adaptive optics. Traditional wavefront sensors are limited to time-consuming measurements, complicated and expensive setup, or low theoretically achievable resolution. In this thesis, we introduce an optically encoded and computationally decodable novel approach to the wavefront sensing problem: the Coded Shack-Hartmann. Our proposed Coded Shack-Hartmann wavefront sensor is inexpensive, easy to fabricate and calibrate, highly sensitive, accurate, and with high resolution. Most importantly, using simple optical flow tracking combined with phase smoothness prior, with the help of modern optimization technique, the computational part is split, efficient, and parallelized, hence real time performance has been achieved on Graphics Processing Unit (GPU), with high accuracy as well. This is validated by experimental results. We also show how optical flow intensity consistency term can be derived, using rigor scalar diffraction theory with proper approximation. This is the true physical law behind our model. Based on this insight, Coded Shack-Hartmann can be interpreted as an illumination post-modulated wavefront sensor. This offers a new theoretical approach for wavefront sensor design.

Traditionally, adaptive optics (AO) systems for microscopy have focused on AO at the pupil plane, however this produces poor performance in samples with both spatially-variant aberrations, such as non-flat sample interfaces, and spatially-invariant aberrations, such as spherical aberration due to a difference between the sample index of refraction and the sample for which the objective was designed. Here, we demonstrate well-corrected, wide field-of-view (FOV) microscopy by simultaneously correcting the two types of aberrations using two AO loops. Such an approach is necessary in wide-field applications where both types of aberration may be present, as each AO loop can only fully correct one type of aberration. Wide FOV corrections are demonstrated in a trans-illumination microscope equipped with two deformable mirrors (DMs), using a partitioned aperture wavefront (PAW) sensor to directly control the DM conjugated to the sample interface and a sensor-less genetic algorithm to control the DM conjugated to the objective’s pupil.

Optical images of astronomical objects viewed through ground-based telescopes are blurred by the atmosphere. The atmosphere is turbulent and as a consequence the density of air is not evenly distributed. This results in random, time-varying variations in refractive index. The wave-fronts passing through the atmosphere become aberrated, degrading the quality of the images. One solution is to include an adaptive optics system in the telescope. The system estimates the aberration of the wave-fronts and compensates the wave-front in real time using a corrector element, typically a deformable mirror. An important problem is how to estimate the aberrations optimally using only a small amount of light. This procedure is called wave-front sensing and is the subject of the research of this thesis. For turbulence with Kolmogorov statistics, the wave-front slope contains 87% of the energy of the aberrations. Hence, it is crucial to estimate the slope accurately. The displacement of an image is directly proportional to the wave-front slope and is used to estimate the slope. The conventional way of measuring the average slope of the wave-front in a Shack-Hartmann sensor is from the centroid of the image at the focal plane. It is demonstrated that using the centroid estimator produces an estimate with infinite variance. The Cramer-Rao lower bound (CRLB) is a theoretical lower bound for the variance of an unbiased estimator. The variance of the maximum-likelihood (ML) estimate for the displacement of a diffraction-limited image approaches the CRLB using a relatively small number of photons. The ML estimator is extended to the case where the image is randomly blurred by atmospheric turbulence. It is found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the ML estimator instead of the centroid. Curvature sensors use two defocused images to estimate the wave-front aberrations. It is shown using the CRLB that the focal plane is the optimal plane to measure the slope and the error using defocused images is quantified. The effect of using broadband light on the accuracy of the slope estimate is also investigated. When using laser guide stars, it is not possible to estimate the slope of the wave-front directly from the image because the beam is displaced on both the upward and downward journey. However, the displacement is a weak function of wavelength due to dispersion. In theory, the difference in wave-front slope as a function of wavelength is proportional to the absolute slope. Centering algorithms were implemented on experimental data taken at the Observatoire de Lyon to confirm this relationship. There is strong evidence pointing to a linear relationship between two pairs of differential tilt measurements, but not between the differential and the absolute tilt. However, the data appears to have been affected by a systematic experimental error and a new experiment is needed. Phase retrieval is a non-linear technique used to recover the phase in the Fourier domain using intensity measurements at the image plane and additional constraints. A method is described to solve the phase retrieval problem using linear iterations near the solution, which provides both analytical insight into phase retrieval and numerical results. The algorithm finds the maximum a posteriori estimate of the phase using prior information about the statistics of the noise and the phase and converges well in practice. When phase retrieval is performed on data from subdivided apertures, there is a loss of information regarding the relative piston terms of the subapertures and this error is quantified. It is found that there is a smaller wavefront error when estimating the phase from a full aperture than from a subdivided aperture. Using a combination of intensity measurements from a full and a subdivided aperture is shown to result in a small improvement at very high photon levels only. Curvature sensors measure the wave-front aberrations via a linear relationship between the curvature of the wave-front and the intensity difference between two defocused images. In practice, their performance is limited by their non-linear behaviour, which is characterised by solving simultaneously the irradiance transport equation and the accompanying wave-front transport equation. It is shown how the presence of non-linear geometric terms limits the accuracy of the sensor and how diffraction effects limit the spatial resolution. The effect of photon noise on the sensor is also quantified. A novel technique for deriving wave-front aberrations from two defocused intensity measurements is derived. The intensity defines a probability density function and the method is based on the evolution of the cumulative density function of the intensity. In one dimension, the problem is easily solved using histogram specification with a linear relationship between the wave-front slope and the difference in the abscissas of the histograms. This method is insensitive to scintillation. In two dimensions, the procedure requires the use of the Radon transform. Simulation results demonstrate that very good reconstructions can be attained down to 100 photons in each detector.

The quality of microscopy imaging is often degraded by sample-induced aberrations. Adaptive optics (AO) is a standard approach to counter such aberrations. In common practice of AO, an active optical correction element, usually a deformable mirror (DM), is usually inserted in the pupil plane of the objective lens, namely pupil AO. However, as first proposed in the astronomy community and now gradually recognized by the optical microscopy community, the placement of the DM in a plane conjugate to a primary sample-induced aberration plane can be more advantageous, especially in situations where the aberration is spatially varying and arises mainly from a dominant layer. We refer to this technique as conjugate AO. In this thesis, we describe two novel implementations of sensor-based conjugate AO in wide-field microscopy, as well as the wavefront sensing techniques we developed for these implementations. Our first implementation is in trans-illumination configuration. The wavefront sensor is based on a technique called partitioned aperture wavefront (PAW) sensing, previously developed in our lab for quantitative phase contrast imaging. Our second conjugate AO is implemented with fluorescence microscopy. The wavefront sensing strategy is based on oblique back-illumination. In both implementations, we addressed the key challenges of developing wavefront sensors that are capable of operating with uncollimated light, which exhibits large diverging angles and may arbitrarily distribute as well. We show that both conjugate AO systems and their wavefront sensors are not only robust, well-suited for video-rate imaging, but also provide large corrected field of view, which is only limited by the microscope itself.

Over the past several years, experiments in adaptive optics involving multiple natural and laser guide stars have been carried out at the 1.55 m Kuiper telescope and the 6.5 m MMT telescope. The astronomical imaging improvement anticipated from both ground-layer and tomographic adaptive optics has been calculated. Ground-layer adaptive optics will reduce the effects of atmospheric seeing, increasing the resolution and sensitivity of astronomical observations over wide fields. Tomographic adaptive optics will provide diffraction-limited imaging along a single line of sight, increasing the amount of sky coverage available to adaptive optics correction.A new facility class wavefront sensor has been deployed at the MMT which will support closed-loop adaptive optics correction using a constellation of five Rayleigh laser guide stars and the deformable F/15 secondary mirror. The adaptive optics control loop was closed for the first time around the focus signal from all five laser signals in July of 2007, demonstrating that the system is working properly. It is anticipated that the full high-order ground-layer adaptive optics loop, controlled by the laser signals in conjunction with a tip/tilt natural guide star, will be closed in September 2007, with the imaging performance delivered by the system optimized and evaluated.The work here is intended to be both its own productive scientific endeavor for the MMT, but also as a proof of concept for the advanced adaptive optics systems designed to support observing at the Large Binocular Telescope and future extremely large telescopes such as the Giant Magellan Telescope.

Neste trabalho foi desenvolvido um novo método voltado para a caracterização de lentes térmicas em materiais fotônicos, utilizados como meios ativos no desenvolvimento de lasers. Este método baseia-se em interferometria por padrão de speckle eletrônico (ESPI), utilizando dois lasers de diodo multímodo sintonizados a diferentes freqüências. Com o ajuste desta diferença, foi possível escolher uma resolução apropriada para medirmos as variações geradas no raio de curvatura da frente de onda, relacionados ao efeito térmico. Para os nossos experimentos escolhemos uma amostra vítrea de aluminato de cálcio dopado com 4% de érbio; e potências de bombeio incidentes de até 1,76 mW do laser de bombeio. Os lasers de diodo foram sintonizados para ter um intervalo de contorno por volta de 120 m. Com o aumento da potência absorvida pela amostra, observamos a diminuição da curvatura da frente de onda incidente na CCD, devido ao aumento da potência da lente térmica gerada. Através de uma análise paraxial dos feixes, foi feita uma aproximação para obtermos os valores das lentes para cada configuração, apresentando comprimentos focais de 131,39 mm a 42,76 mm. / In this work we will develop a new method focused on the caracterization of thermal lenses effect in photonic materials used as active media in lasers design. This method is based on electronic speckle pattern interferometry (ESPI) using two multimode diode lasers tuned to different frequencies. Adjusting this difference we can achieve an appropriate resolution to measure the variability generated within the curvature radius of the wavefront due to thermal lens effect. For our experiments we chose a vitreous sample of calcium aluminate doped with 4% erbium and incident pump powers ranging to 1.76mW. The diode lasers were tuned to have a contour interval of around 120m. With addition in power absorbed by the sample, we observed a decrease in the curvature radius incident on the camera due to increased power of the thermal lens generated. Through a paraxial of the wavefront, an approach was made to obtain the values of the lenses for each configuration, with focal lengths ranging from 131.39 mm to 42.76 mm.

This work explores remote sensing of planetary atmospheres and their circumstellar surroundings. The terrestrial ionosphere is a highly variable space plasma embedded in the thermosphere. Generated by solar radiation and predominantly composed of oxygen ions at high altitudes, the ionosphere is dynamically and chemically coupled to the neutral atmosphere. Variations in ionospheric plasma density impact radio astronomy and communications. Inverting observations of 83.4 nm photons resonantly scattered by singly ionized oxygen holds promise for remotely sensing the ionospheric plasma density. This hypothesis was tested by comparing 83.4 nm limb profiles recorded by the Remote Atmospheric and Ionospheric Detection System aboard the International Space Station to a forward model driven by coincident plasma densities measured independently via ground-based incoherent scatter radar. A comparison study of two separate radar overflights with different limb profile morphologies found agreement between the forward model and measured limb profiles. A new implementation of Chapman parameter retrieval via Markov chain Monte Carlo techniques quantifies the precision of the plasma densities inferred from 83.4 nm emission profiles. This first study demonstrates the utility of 83.4 nm emission for ionospheric remote sensing. Future visible and ultraviolet spectroscopy will characterize the composition of exoplanet atmospheres; therefore, the second study advances technologies for the direct imaging and spectroscopy of exoplanets. Such spectroscopy requires the development of new technologies to separate relatively dim exoplanet light from parent star light. High-contrast observations at short wavelengths require spaceborne telescopes to circumvent atmospheric aberrations. The Planet Imaging Concept Testbed Using a Rocket Experiment (PICTURE) team designed a suborbital sounding rocket payload to demonstrate visible light high-contrast imaging with a visible nulling coronagraph. Laboratory operations of the PICTURE coronagraph achieved the high-contrast imaging sensitivity necessary to test for the predicted warm circumstellar belt around Epsilon Eridani. Interferometric wavefront measurements of calibration target Beta Orionis recorded during the second test flight in November 2015 demonstrate the first active wavefront sensing with a piezoelectric mirror stage and activation of a micromachine deformable mirror in space. These two studies advance our ``close-to-home'' knowledge of atmospheres and move exoplanetary studies closer to detailed measurements of atmospheres outside our solar system.

Neste trabalho foi desenvolvido um novo método voltado para a caracterização de lentes térmicas em materiais fotônicos, utilizados como meios ativos no desenvolvimento de lasers. Este método baseia-se em interferometria por padrão de speckle eletrônico (ESPI), utilizando dois lasers de diodo multímodo sintonizados a diferentes freqüências. Com o ajuste desta diferença, foi possível escolher uma resolução apropriada para medirmos as variações geradas no raio de curvatura da frente de onda, relacionados ao efeito térmico. Para os nossos experimentos escolhemos uma amostra vítrea de aluminato de cálcio dopado com 4% de érbio; e potências de bombeio incidentes de até 1,76 mW do laser de bombeio. Os lasers de diodo foram sintonizados para ter um intervalo de contorno por volta de 120 m. Com o aumento da potência absorvida pela amostra, observamos a diminuição da curvatura da frente de onda incidente na CCD, devido ao aumento da potência da lente térmica gerada. Através de uma análise paraxial dos feixes, foi feita uma aproximação para obtermos os valores das lentes para cada configuração, apresentando comprimentos focais de 131,39 mm a 42,76 mm. / In this work we will develop a new method focused on the caracterization of thermal lenses effect in photonic materials used as active media in lasers design. This method is based on electronic speckle pattern interferometry (ESPI) using two multimode diode lasers tuned to different frequencies. Adjusting this difference we can achieve an appropriate resolution to measure the variability generated within the curvature radius of the wavefront due to thermal lens effect. For our experiments we chose a vitreous sample of calcium aluminate doped with 4% erbium and incident pump powers ranging to 1.76mW. The diode lasers were tuned to have a contour interval of around 120m. With addition in power absorbed by the sample, we observed a decrease in the curvature radius incident on the camera due to increased power of the thermal lens generated. Through a paraxial of the wavefront, an approach was made to obtain the values of the lenses for each configuration, with focal lengths ranging from 131.39 mm to 42.76 mm.

L’imagerie d’exoplanètes est limitée par deux obstacles intrinsèques : le faible écart angulaire entre planète et étoile, et le très faible flux lumineux en provenance de la planète par rapport à la lumière de l’étoile. Le premier obstacle est surmonté par l’utilisation de très grands télescopes, de la classe des dix mètres de diamètre, et éventuellement depuis le sol de systèmes d’optique adaptative, qui permettent d’atteindre de hautes résolutions angulaires. Le deuxième obstacle est surmonté par l’utilisation de coronographes. Les coronographes sont des instruments conçus pour filtrer la lumière de l’étoile tout en laissant passer la lumière de l’environnement circumstellaire. Cependant, toute aberration optique en amont du coronographe engendre des fuites de lumière stellaire à travers le coronographe. Ces fuites se traduisent par un fouillis de tavelures dans les images scientifiques, tavelures qui cachent d’éventuelles planètes. Il est donc nécessaire de mesurer et de corriger les aberrations quasi-statiques à l’origine des tavelures. Cette thèse présente des contributions théoriques, numériques et expérimentales à la mesure et à la correction des aberrations des imageurs coronographiques. La première partie décrit le contexte et présente la méthode de la diversité de phase coronographique, un formalisme qui considère l’analyse de surface d’onde post-coronographique comme un problème inverse posé dans un cadre bayésien. La deuxième partie concerne l’imagerie depuis le sol. Elle présente tout d’abord une expression analytique permettant de modéliser l’imagerie coronographique en présence de turbulence, puis l’extension de la méthode de diversité de phase coronographique à la mesure depuis les télescopes au sol donc en présence de turbulence résiduelle, et enfin une validation en laboratoire de cette méthode étendue. La troisième partie est consacrée aux futurs imageurs spatiaux à très hauts contrastes pour lesquels il faut corriger non pas seulement la phase mais tout le champ complexe. Elle présente la validation en laboratoire de la mesure d’un champ complexe d’aberrations par diversité de phase coronographique, ainsi que des premiers résultats d’extinction de la lumière en plan focal par une méthode non linéaire, le non-linear dark hole. / Exoplanet imaging has two intrinsic limitations, namely the small angular separation between the star and the planet, and the very low light flux from the planet compared to the starlight. The first limitation is overcome by using very large telescopes of the ten-metre diameter class, and, for ground-based telescopes, adaptive optics systems, which allow high angular resolution imaging. The second limitation is overcome by using a coronagraph. Coronagraphs are optical devices which filter the starlight while granting passage to the light coming from the stellar environment. However, any optical aberration upstream of the coronagraph causes some of the starlight to leak through the coronagraph. This unfiltered starlight in turn causes speckles in the scientific images, and the light of the planets that could be there is lost among the speckles. Consequently, measurement and correction of the quasi-static aberration which generate the speckles are necessary for the exoplanet imagers to achieve their full potential. This thesis introduces theoretical, numerical, and experimental contributions to the topic of measurement and correction of the aberrations in coronagraphic imagers. The first part describes the context and introduces coronagraphic phase diversity, which is a Bayesian inverse problem formalism for post-coronagraphic wave-front sensing. The second part is focused on ground-based imaging. It introduces an analytic expression for coronagraphic imaging through turbulence, the extension of coronagraphic phase diversity to on-sky measurement through residual turbulence, and a laboratory validation of the extended method. The third part is concerned with future high-contrast space-based imagers, which will require not only phase correction, but a full complex wave-front correction. It presents the laboratory validation of coronagraphic phase diversity as a post-coronagraphic complex wave-front sensor, and first results of active contrast enhancement in the focal plane through thecreation of a non-linear dark hole.