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The aim of the work described in this thesis is to improve the understanding, implementation, and overall capabilities of structured illumination microscopy (SIM). SIM is a superresolution technique that excels in gentle live-cell volumetric imaging tasks. Many modalities of SIM were developed over the last decade that tailored SIM into the versatile and powerful technique that it is today. Nevertheless, the field of SIM continues to evolve and there is plenty of room for novel concepts. Specifically, in this thesis, a generalised framework for a theoretical description of SIM variants is introduced, the constraints of optical components for a flexible SIM system are discussed and the set-up is realised, the important aspect of deconvolution in SIM is highlighted and further developed, and finally novel SIM modalities introduced that improve its time-resolution, gentleness, and volumetric imaging capabilities. Based on the generalised theory, the computational steps for the extraction of superresolution information from SIM raw data are outlined and the essential concept of spatial frequency un-mixing explained for standard SIM as well as for multifocal SIM. Multifocal SIM hereby acts as a parallelised confocal as well as widefield technique and thus serves as link between the two modalities. Using this novel scheme deconvolution methods for SIM are then further developed to allow a holistic reconstruction procedure. Deconvolution is of great important in the SIM reconstruction process, and hence rigorous derivations of advanced deconvolution methods are provided and further developed to enable generalised ‘multi-image’ Richardson-Lucy deconvolution in SIM, called joint Richardson-Lucy deconvolution (jRL). This approach is demonstrated to robustly produce optically sectioned multifocal SIM images and, through the incorporation of a 3D imaging model, also volumetric standard SIM images within the jRL framework. For standard SIM this approach enabled acquisition speed doubling, because the recovery of superresolved images from a reduced number of raw frames through constrained jRL was made possible. The method is validated in silico and in vitro. For the study of yet faster moving samples deconvolution microscopy is found to be the method of choice. To enable optical sectioning, a key feature of SIM, in deconvolution microscopy, a new modality of optical sectioning microscopy is introduced that can be implemented as a single-shot technique. Via polarised excitation and detection in orthogonal directions in conjunction with structured illumination the theoretical framework is rigorously derived and validated.

Two-photon laser scanning microscopy (2PLSM) allows fluorescence imaging in thick biological samples where absorption and scattering typically degrade resolution and signal collection of 1-photon imaging approaches. The spatial resolution of conventional 2PLSM is limited by diffraction, and the near-infrared wavelengths used for excitation in 2PLSM preclude the accurate imaging of many small subcellular features of neurons. Stimulated emission depletion (STED) microscopy is a superresolution imaging modality which overcomes the resolution limit imposed by diffraction and allows fluorescence imaging of nanoscale features. In this thesis, I describe the development of 2PLSM combined with STED microscopy for superresolution fluorescence imaging of neurons embedded in thick tissue. Furthermore, I describe the application of this method to studying the biophysics connecting synaptic structure and function in dendritic spines.

Thesis advisor: Michael J. Naughton / The nanoscale coaxial cable (nanocoax) has demonstrated sub-diffraction-limited optical confinement in the visible and the near infrared, with the theoretical potential for confinement to scales arbitrarily smaller than the free space wavelength. In the first part of this thesis, I define in clear terms what the diffraction limit is. The conventional resolution formulae used by many are generally only valid in the paraxial limit. I performed a parametric numerical study, employing techniques of Fourier optics, to resolve precisely what that limit should be for nonparaxial (i.e. wide angle) focusing of scalar spherical waves. I also present some novel analytical formulae born out of Debye’s approximation which explain the trends found in the numeric study. These new functional forms remain accurate under wide angle focusing and could materially improve the performance, for example, in high intensity focused ultrasound surgery by further concentrating the power distributed within the point spread function to suppress the side lobes. I also comment of some possible connections to the focusing of electromagnetic waves. In the second part of this thesis I report on a novel fabrication process which yields optically addressable, sub-micron scale, and high aspect ratio metal-insulator-metal nanocoaxes made by atomic layer deposition of Pt and Al2O3. I discuss the observation of optical transmission via the fundamental, TEM-like mode by excitation with a radially polarized optical vortex beam. Also, Laguerre-Gauss beams are shown to overlap well with cylindrical waveguide modes in the nanocoax. My experimental results are based on interrogation with a polarimetric imager and a near-field scanning optical microscope. Various optical apparatus I built during my studies are also reviewed. Numerical simulations were used with uniaxial symmetry to explore 3D adiabatic taper geometries much larger than the wavelength. Finally, I draw some conclusions by assessing the optical performance of the fabricated nanocoaxial structures, and by giving some insights into future directions of investigation. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Seismic imaging is a technique that uses seismic echoes to map and detect underground geological structures. The conventional seismic image has the resolution limit of λ/2, where λ is the wavelength associated with the seismic waves propagating in the subsurface. To exceed this resolution limit, this thesis develops a new imaging method using resonant multiples, which produces superresolution images with twice or even more the spatial resolution compared to the conventional primary reflection image. A resonant multiple is defined as a seismic reflection that revisits the same subsurface location along coincident reflection raypath. This reverberated raypath is the reason for superresolution imaging because it increases the differences in reflection times associated with subtle changes in the spatial location of the reflector. For the practical implementation of superresolution imaging, I develop a post-stack migration technique that first enhances the signal-to-noise ratios (SNRs) of resonant multiples by a moveout-correction stacking method, and then migrates the post-stacked resonant multiples with the associated Kirchhoff or wave-equation migration formula. I show with synthetic and field data examples that the first-order resonant multiple image has about twice the spatial resolution compared to the primary reflection image. Besides resolution, the correct estimate of the subsurface velocity is crucial for determining the correct depth of reflectors. Towards this goal, wave-equation migration velocity analysis (WEMVA) is an image-domain method which inverts for the velocity model that maximizes the similarity of common image gathers (CIGs). Conventional WEMVA based on subsurface-offset, angle domain or time-lag CIGs requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, I present a new WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on synthetic and field datasets validate the efficiency and effectiveness of this method.

Multiframe image superresolution has been an active research area for many years. In this approach image processing techniques are used to combine multiple low-resolution (LR) images capturing different views of an object. These multiple images are generally under-sampled, degraded by optical and pixel blurs, and corrupted by measurement noise. We exploit diversities in the imaging channels, namely, the number of cameras, magnification, position, and rotation, to undo degradations. Using an iterative back-projection (IBP) algorithm we quantify the improvements in image fidelity gained by using multiple frames compared to single frame, and discuss effects of system parameters on the reconstruction fidelity. As an example, for a system in which the pixel size is matched to optical blur size at a moderate detector noise, we can reduce the reconstruction root-mean-square-error by 570% by using 16 cameras and a large amount of diversity in deployment.We develop a new technique for superresolving binary imagery by incorporating finite-alphabet prior knowledge. We employ a message-passing based algorithm called two-dimensional distributed data detection (2D4) to estimate the object pixel likelihoods. We present a novel complexity-reduction technique that makes the algorithm suitable even for channels with support size as large as 5x5 object pixels. We compare the performance and complexity of 2D4 with that of IBP. In an imaging system with an optical blur spot matched to pixel size, and four 2x2 undersampled LR images, the reconstruction error for 2D4 is 300 times smaller than that for IBP at a signal-to-noise ratio of 38dB.We also present a transform-domain superresolution algorithm to efficiently incorporate sparsity as a form of prior knowledge. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular L1 norm as the regularization operator. Secondly we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for L1 norm minimization and also with the linear minimum mean squared error (LMMSE) estimator.

No description available.

Récemment, de nombreuses techniques de microscopie de fluorescence de super-résolution ont été développées pour permettre d'observer de nombreuses structures biologiques au-delà de la limite de diffraction. La microscopie d'illumination structurée (SIM) est l'une de ces technologies. Le principe de la SIM est basé sur l'utilisation d'une grille de lumière harmonique qui permet de translater les hautes fréquences spatiales de l'échantillon vers la région d’observation du microscope. Les méthodes classiques de reconstruction SIM nécessitent une connaissance parfaite de l'illumination de l’échantillon. Cependant, l’implémentation d’un contrôle parfait de l’illumination harmonique sur le plan de l'échantillon n'est pas facile expérimentalement et il présente un grand défi. L’hypothèse de la connaissance parfaite de l’intensité de la lumière illuminant l’échantillon en SIM peut donc introduire des artefacts sur l’image reconstruite de l'échantillon, à cause des erreurs d’alignement de la grille qui peuvent se présenter lors de l’acquisition expérimentale. Afin de surmonter ce défi, nous avons développé dans cette thèse des stratégies de reconstruction «aveugle» qui sont indépendantes de d'illumination. À l'aide de ces stratégies de reconstruction dites «blind-SIM», nous avons étendu la SIM harmonique pour l’appliquer aux cas de «SIM-speckle» qui utilisent des illuminations aléatoires et inconnues qui contrairement à l’illumination harmonique, ne nécessitent pas de contrôle. / Recently, many superresolution fluorescence microscopy techniques have been developed which allow the observation of many biological structures beyond the diffraction limit. Structured illumination microscopy (SIM) is one of them. The principle of SIM is based on using a harmonic light grid which downmodulates the high spatial frequencies of the sample into the observable region of the microscope. The resolution enhancement is highly dependent on the reconstruction technique, which restores the high spatial frequencies of the sample to their original position. Common SIM reconstructions require the perfect knowledge of the illumination pattern. However, to perfectly control the harmonic illumination patterns on the sample plane is not easy in experimental implementations and this makes the experimental setup very technical. Reconstructing SIM images assuming the perfect knowledge of the illumination intensity patterns may, therefore, introduce artifacts on the estimated sample due to the misalignment of the grid that can occur during experimental acquisitions. To tackle this drawback of SIM, in this thesis, we have developed blind-SIM reconstruction strategies which are independent of the illumination patterns. Using the 3D blind-SIM reconstruction strategies we extended the harmonic SIM to speckle illumination microscopy which uses random unknown speckle patterns that need no control, unlike the harmonic grid patterns.

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La mécanique quantique a révolutionné la compréhension du monde microscopique depuis son avènement au XXe siècle. Cependant, les propriétés de la matière condensée restent difficiles à étudier en raison d'une puissance de calcul insuffisante pour simuler numériquement les systèmes à N corps. Une approche alternative consiste à piéger des atomes froids dans des réseaux, dont le comportement est analogue à celui des électrons dans un cristal. Ce système modèle, dont les paramètres peuvent être contrôlés, permet de simuler les phénomènes étudiés.La technique usuellement employée pour confiner les atomes ultrafroids dans un réseau consiste à produire une onde stationnaire résultant de l'intérférence entre deux faisceaux contrapropageants. L'originalité du projet dans lequel s'inscrit cette thèse est de générer un potentiel sublongueur d'onde grâce à la modulation des forces de Casimir au voisinage d'une surface nanostructurée. Le confinement des atomes dans un réseau bidimensionnel avec une faible distance intersite (typiquement 50 nm) permettra ainsi de mieux appréhender les propriétés des matériaux, tels que le graphène.Le travail réalisé au cours de mon doctorat s'est ainsi articulé autour de quatre axes. Tout d'abord, le refroidissement d'atomes de Rubidium 87 a été effectué jusqu'à obtenir un condensat de Bose-Einstein. Puis, des simulations numériques ont été réalisées pour mettre en place une nouvelle méthode d'imagerie sublongueur d'onde, s'appuyant sur le couplage différencié des niveaux atomiques avec un double réseau. Ceci permettra d'activer de façon sélective les sites à détecter pour localiser les atomes avec une précision sublongueur d'onde. Un nouveau système d'imagerie a d'ailleurs été développé pour mieux résoudre les images des distributions atomiques. D'autre part, des simulations numériques ont été réalisées pour anticiper les résultats expérimentaux sur le transport adiabatique au voisinage d'une surface. Enfin, dans le cadre de ma convention CIFRE, une nouvelle architecture laser sera présentée, dans le but d'intéragir avec les atomes de potassium 40 qui seront à refroidir dans la suite du projet dans lequel s'inscrit ma thèse. / Quantum mechanics was a revolution for microscopic systems understanding. However, the study of many-body systems remains a challenge because of computation complexity. Ultracold atoms trapped in lattices offer an alternative way to simulate condensed matter properties. Indeed, their behaviour is similar to the one of electrons in crystals.The common approach for generating optical lattices is to make two laser beams interefere so that we can get a stationary wave that reproduces the potential wells of the crystalline structure. In the new ongoing project, the lattices will be produced by modulation of Casimir-Polder forces nearby a nanostructured surface. Ultracold atoms trapped in a 2D lattice with a short lattice spacing (50 nm) will enable a better understanding of material properties (e.g. graphene).The work I have done during my thesis can be split into in four parts. The first one consisted in cooling Rubidium 87 until Bose-Einstein condensate regime. Then, numerical simulations were performed to set up a new subwavelength imaging technique, based on different couplings between atomic levels with a double lattice. This will make it possible to activate the sites selectively, in order to pinpoint the atoms with subwavelength precision. Moreover, a new imaging system was developped to improve the resolution of the atomic cloud images. I did new calculations in order to predict experimental results on adiabatic atomic transport in the near field of a surface. Finally, a new laser architecture was designed in this thesis, as part of CIFRE convention, in order to cool down potassium 40 atoms, which has to be done in the future.