This thesis works through the design of a radar-based system for imaging snowpacks remotely and over large areas to assist in avalanche prediction. The key to such a system is the ability to image volumes of snow at shallow, spatially-varying angles of incidence. To achieve this prerequisite, the design calls for a ground-based Synthetic Aperture Radar (SAR) capable of generating three-dimensional, ultra-high-resolution images of a snowpack. To arrive at design parameters for this SAR, the thesis works through relevant principles in avalanche mechanics, alpine-snowpack geophysics, and electromagnetic scattering theory. The thesis also works through principles of radar, SAR, antenna, and image processing theory to this end. A preliminary system is implemented to test the feasibility of the overall design. The preliminary system demonstrates ultra-high-resolution, three-dimensional imaging capabilities and the ability to image the volume of multiple alpine snowpacks. Images of these snowpacks display the structural patterns indicative of different layers in the snowpacks. Possible attributions of the patterns to physical properties in the snowpack are explored, but conclusions are not arrived at. Finally, lessons from the implementation of this preliminary system are discussed in terms of opportunities to be capitalized upon and problems to be overcome in future systems that more faithfully realize the complete design set forth in the thesis.

This thesis presents the development of a high-resolution ground-based 3D-SAR system and investigates its application to microwave-vegetation studies. The development process of the system is detailed including an enumeration of high-level requirements, discussions on key design issues, and detailed descriptions of the system down to a component level. The system operates on a 5.4 GHz (C-band) signal, provides a synthetic aperture area of 1.7 m x 1.7 m, and offers resolution of 0.75 m x 0.3 m x 0.3 m (range x azimuth x elevation). The system is employed on several trees with varying physical characteristics. The resulting imagery demonstrates successful 3D reconstruction of the trees and some of their internal features. The individual leaves and small branches are not visible due to the system resolution and the size of the wavelength. The foliage's outline and internal density distribution is resolved. Large branches are visible where geometry is favorable. Trunks are always visible due to their size and normal-facing incidence surface and their return has the strongest contribution from their base. The imagery is analyzed for dependencies on radar and tree parameters including: incidence angle, signal frequency, polarization, inclusion size, water content, and species. In the current work, a single frequency (5.4 GHz) and polarization (HH) is used which leaves the door open for future analysis to use other frequencies and polarizations. The improved resolution capabilities of the 3D-SAR system enables more precise backscatter measurements leading to a greater understanding of microwave-vegetation scattering behavior.

The retina is a thin layer of tissue lining the back of the eye and is primarily responsible for sight in vertebrates. The neural retina has a distinct layered structure with three dense nuclear layers, separated by plexiform layers comprising of axons and dendrites, and a layer of photoreceptor segments. The retinal and choroidal vasculatures nourish the retina from either side, with an avascular layer comprised largely of photoreceptor cells. Diseases that directly affect the neural retina like retinal degeneration as well as those of vascular origin like diabetic retinopathy can lead to partial or total blindness. Early detection of these diseases can potentially pave the way for a timely intervention and improve patient prognosis. Current techniques of retinal imaging rely mainly on optical techniques, which have limited depth resolution and depend mainly on the clarity of visual pathway. Magnetic resonance imaging is a versatile tool that has long been used for anatomical and functional imaging in humans and animals, and can potentially be used for retinal imaging without the limitations of optical methods. The work reported in this thesis involves the development of high resolution magnetic resonance imaging techniques for anatomical and functional imaging of the retina in rats. The rats were anesthetized using isoflurane, mechanically ventilated and paralyzed using pancuronium bromide to reduce eye motion during retinal MRI. The retina was imaged using a small, single-turn surface coil placed directly over the eye. The several physiological parameters, like rectal temperature, fraction of inspired oxygen, end-tidal CO2, were continuously monitored in all rats. MRI parameters like T1, T2, and the apparent diffusion coefficient of water molecules were determined from the rat retina at high spatial resolution and found to be similar to those obtained from the brain at the same field strength. High-resolution MRI of the retina detected the three layers in wild-type rats, which were identified as the retinal vasculature, the avascular layer and the choroidal vasculature. Anatomical MRI performed 24 hours post intravitreal injection of MnCl2, an MRI contrast agent, revealed seven distinct layers within the retina. These layers were identified as the various nuclear and plexiform layers, the photoreceptor segment layer and the choroidal vasculature using Mn54Cl2 emulsion autoradiography. Blood-oxygenlevel dependent (BOLD) functional MRI (fMRI) revealed layer-specific vascular responses to hyperoxic and hypercapnic challenges. Relative blood volume of the retina calculated by using microcrystalline iron oxide nano-colloid, an intravascular contrast agent, revealed high blood-volume in the choroidal vasculature. Fractional changes to blood volume during systemic challenges revealed a higher degree of autoregulation in the retinal vasculature compared to the choroidal vasculature, corroborating the BOLD fMRI data. Finally, the retinal MRI techniques developed were applied to detect structural and vascular changes in a rat model of retinal dystrophy. We conclude that retinal MRI is a powerful investigative tool to resolve layer-specific structure and function in the retina and to probe for changes in retinal diseases. We expect the anatomical and functional retinal MRI techniques developed herein to contribute towards the early detection of diseases and longitudinal evaluation of treatment options without interference from overlying tissue or opacity of the visual pathway.

In the past two decades, Fluorescence microscopy has imparted tremendous impact in Biology and Imaging. Several super-resolution Fluorescence imaging techniques (e.g. PALM, STED, STORM, 4Pi and structured illumination) have enabled diff raction-unlimited imaging. But high resolution is limited to a depth of few tens of microns. Thus, deep tissue imaging and simultaneous volume imaging have become a highly sought after feature in Fluorescence microscopy. The research work in this thesis address these issues by using spatial filtering techniques to tailor the point spread function (PSF) which uniquely characterizes the optical sys-tem. The advantage of this approach lies in the fact that intricate details about the focal region can be computed and designed with the help of well established theory and experimentation. In particular, this technique was applied to both spherical and cylindrical lenses. The former was used to generate Bessel-like, non-diffracting beams which demonstrated the ability to penetrate deep inside tissue-like media and thereby yielded an imaging depth of nearly 650μm as compared to about 200μm for a state-of-the-art confocal microscope. The latter gave rise to light-sheet and it's extended version that is ideal for planar imaging at large penetration depths. Another development is the generation of multiple light-sheet illumination pattern that can simultaneously illuminate several planes of the specimen. The proposed multiple light-sheet illumination microscopy (MLSIM) technique may enable volume imaging in Fluorescence microscopy. The first two chapters of this thesis are introductory in nature and provides a general overview of the principles of Fluorescence microscopy and three state-of-the-art Fluorescence imaging techniques; namely confocal, multi-photon and light-sheet based microscopy. Confocal microscopes are widely considered as a standard tool for biologists and this discussion shows that even though they have made signi ficant contributions in the fields of biophysics, biophotonics and nanoscale imaging, their inability to achieve better penetration depth has prevented their use in thick, scattering samples such as biological tissue. The system PSF of a confocal microscope broadens as it goes deeper in-side a scattering sample resulting in poor-resolution thereby destroying the very concept of high resolution, noise-free imaging. Additionally, confocal microscopy suffers from in-creased photo-bleaching due to o -layer (above and below the focal plane) excitation and low temporal resolution since it requires point-by-point scanning mechanism. On the other hand, multi-photon microscopy offers several advantages over confocal microscopy such as reduced photo-bleaching and inherent optical sectioning ability, however, it still lacks in providing high temporal resolution. Light-sheet based microscopy have gained popularity in recent years and promises to deliver high spatio-temporal resolution with minimized photo-bleaching. Recently, a considerable amount of research has been dedicated to further develop this promising technique for a variety of applications. The ability to look deeper inside a biological specimen has profound implications. How-ever, at depths of hundreds of microns, several effects (such as scattering, PSF distortion and noise) deteriorates the image quality and prohibits detailed study of key biological phenomenon. Chapter 3 of this thesis describes the original research work which experimentally addresses to this issue. Here, Bessel-like beam is employed in conjugation with an orthogonal detection scheme to achieve imaging at large penetration depth. Bessel beams are penetrative, non-di ffracting and have self-reconstruction properties making them a natural choice for imaging scattering prone specimens which are otherwise inaccessible by other microscopy imaging techniques such as, Widefield, CLSM, 4PI, Structural illumination microscopy and others. In this case such a Bessel-like beam is generated by masking the back-aperture of the excitation objective with a ring-like spatial filter. The proposed excitation scheme allow continuous scanning by simply translating the detection optics. Additionally, only a pencil-like region of the specimen can be illuminated at a given instance thereby reducing premature photobleaching of neighboring regions. This illumination scheme coupled with orthogonal detection shows the ability of selective imaging from a desired plane deep inside the specimen. In such a configuration, the lateral resolution of the illumination arm determines the axial resolution of the overall imaging system. Such an imaging system is a boon for obtaining depth information from any desired specimen layer that includes nano-particle tracking in thick tissue. Experiments performed by imaging the Fluorescent polymer tagged-CaCO3 particles and yeast cell in a tissue-like gel-matrix demonstrates penetration depth that extends up to 650 m. This will advance the field of fluorescence imaging microscopy and imaging. Similar to the ability to observe deep inside a sample, simultaneous 3D monitoring of whole specimens play a vital role in understanding many developmental process in Biology. At present, light-sheet based microscopy is the prime candidate amongst the various microscopy techniques, that is capable of providing high signal-to-background-ratio as far as planar imaging is concerned. Since spatial filtering technique was found to successfully give rise to novel features (such as large penetration depth) in a fluorescence microscope setup, a logical extension would be to implement a similar approach with a light-sheet based microscope setup. These implementations are discussed in Chapter 4 of this thesis where spatial filtering is employed with cylindrical lenses. For facilitating computational and experimental studies, a vectorial formalism was derived to give an explicit computable integral solution of the electric field generated at the focal region of a cylindrical lens. This representation is based on vectorial diffraction theory and further enables the computation of the point spread function of a cylindrical lens. Commonly used assumptions are made in the derivation such as no back-scattering and negligible contribution from evanescent fields. Stationary phase approximation along with the Fresnel transmission coefficients are employed for evaluating the polarization dependent electric field components. Computational studies were carried out to determine the polarization effects and calculate the system resolution. Experimental comparison of light-sheet intensity pro les show good agreement with the theoretical calculations and hence validate the model. This formalism was derived as a first step since it gives the essential understanding of tightly focused E-fields of a high N.A. cylindrical lens systems and thereby helps in further understanding the effect of spatial filtering. As the next step, generation of extended light-sheet for fluorescence microscopy is pro-posed by introducing a specially designed double-window spatial filter at the back-aperture of a cylindrical lens. The filter allows the light to pass through the periphery and center of a cylindrical lens. When illuminated with a plane wave, the proposed filter results in an extended depth-of-focus along with side-lobes which are due to other interferences in the transverse focal plane. Computational studies show a maximum extension of light-sheet by 3:38 times for single photon excitation, and 3:68 times for multi-photon excitation as compared to state-of-art single plane illumination microscopy (SPIM) system and essentially implies a larger field of view. Finally, generation of multiple light-sheet pattern is proposed and demonstrated using a different spatial filter placed at the back aperture of a cylindrical lens. A complete imaging setup consisting of multiple light-sheets for illumination and an orthogonal detection arm, is implemented for volume imaging in fluorescence microscopy. This proposed scheme is a single shot technique that enables whole volume imaging by simultaneously exciting multiple specimen layers. Experimental results confirm the generation of multiple light-sheets of thickness 6:6 m with an inter-sheet spacing of 13:4 m. Imaging of 3 5 m sized fluorescently coated Yeast cells (encaged in Agarose gel-matrix) is per-formed and conclusively demonstrates the usefulness and potential of multiple light-sheet illumination microscopy (MLSIM) for volume imaging. As part of the future scope of the research work presented in this thesis, the Bessel-beam based improved depth microscopy technique may attract applications in particle tracking deep inside tissues and optical injection apart from fluorescence imaging applications. The vectorial formalism derived for cylindrical lens can be used to predict other, complex optical setups involving cylindrical lenses. Extended light-sheet generation proposed in this work by using appropriate spatial filtering with a cylindrical lens, complements the existing and popular selective plane illumination microscopy technique and may facilitate the study of large biological specimens (such as, full-grown Zebra sh and tissue) with high spatial resolution and reduced photobleaching. Finally, the MLSIM technique presented in this thesis may accelerate the field of developmental biology, cell biology, fluorescence imaging and 3D optical data storage.

Ziel ist die räumliche Abbildung biologischer Materialien (Knochen, Kollagenfibrillen und Zähne) hinsichtlich deren Struktur auf der Nanometerskala mit Hilfe der Nanotomographie. Die Nanotomographie ist eine moderne dreidimensionale Volumenabbildungsmethode auf der Nanometerskala basierend auf der Rasterkraftmikroskopie. Für die Nanotomographie wurden Ätzprotokolle an Zähnen, Kollagenfibrillen und Knochen entwickelt, die einen gleichmäßigen Abtrag bewirken. Lineare Verschiebungen der aufgenommenen Schichten werden mit Hilfe der manuellen Registrierung korrigiert und zu einem Volumenbild rekonstruiert. Ein zentrales Ergebnis sind dabei erste hochaufgelöste Volumenbilder einzelner Kollagenfibrillen im nativen Knochen. Neben der konventionellen Nanotomographie wird ein Ansatz zur automatisierten Nanotomographie mit einer Auflösung von 10 nm am Beispiel des menschlichen Knochens und Zahnes demonstriert. Mit Hilfe von mikroskopischen und elektronenmikroskopischen Techniken wurden die verschiedenen Strukturebenen des humanen Zahn und Knochens abgebildet und die räumlichen Strukturen der TM-AFM-Bilder auf der Mikro- und Nanometerskala eingeordnet. Darüber hinaus konnte mit Hilfe analytischer Messmethoden die chemische Zusammensetzung des kortikalen nativen Knochens erfasst werden und Änderungen durch das Ätzen detektiert werden.

Cette thèse s'inscrit dans le domaine des problèmes inverses en traitement du signal. Elle est consacrée à la conception d'algorithmes de restauration et de séparation de signaux parcimonieux et à leur application à l'approximation de courbes de forces en microscopie de force atomique (AFM), où la notion de parcimonie est liée au nombre de points de discontinuité dans le signal (sauts, changements de pente, changements de courbure). Du point de vue méthodologique, des algorithmes sous-optimaux sont proposés pour le problème de l'approximation parcimonieuse basée sur la pseudo-norme l0 : l'algorithme Single Best Replacement (SBR) est un algorithme itératif de type « ajout-retrait » inspiré d'algorithmes existants pour la restauration de signaux Bernoulli-Gaussiens. L'algorithme Continuation Single Best Replacement (CSBR) est un algorithme permettant de fournir des approximations à des degrés de parcimonie variables. Nous proposons aussi un algorithme de séparation de sources parcimonieuses à partir de mélanges avec retards, basé sur l'application préalable de l'algorithme CSBR sur chacun des mélanges, puis sur une procédure d'appariement des pics présents dans les différents mélanges. La microscopie de force atomique est une technologie récente permettant de mesurer des forces d'interaction entre nano-objets. L'analyse de courbes de forces repose sur des modèles paramétriques par morceaux. Nous proposons un algorithme permettant de détecter les régions d'intérêt (les morceaux) où chaque modèle s'applique puis d'estimer par moindres carrés les paramètres physiques (élasticité, force d'adhésion, topographie, etc.) dans chaque région. Nous proposons finalement une autre approche qui modélise une courbe de force comme un mélange de signaux sources parcimonieux retardées. La recherche des signaux sources dans une image force-volume s'effectue à partir d'un grand nombre de mélanges car il y autant de mélanges que de pixels dans l'image / This thesis handles several inverse problems occurring in sparse signal processing. The main contributions include the conception of algorithms dedicated to the restoration and the separation of sparse signals, and their application to force curve approximation in Atomic Force Microscopy (AFM), where the notion of sparsity is related to the number of discontinuity points in the signal (jumps, change of slope, change of curvature).In the signal processing viewpoint, we propose sub-optimal algorithms dedicated to the sparse signal approximation problem based on the l0 pseudo-norm : the Single Best Replacement algorithm (SBR) is an iterative "forward-backward" algorithm inspired from existing Bernoulli-Gaussian signal restoration algorithms. The Continuation Single Best Replacement algorithm (CSBR) is an extension providing approximations at various sparsity levels. We also address the problem of sparse source separation from delayed mixtures. The proposed algorithm is based on the prior application of CSBR on every mixture followed by a matching procedure which attributes a label for each peak occurring in each mixture.Atomic Force Microscopy (AFM) is a recent technology enabling to measure interaction forces between nano-objects. The force-curve analysis relies on piecewise parametric models. We address the detection of the regions of interest (the pieces) where each model holds and the subsequent estimation of physical parameters (elasticity, adhesion forces, topography, etc.) in each region by least-squares optimization. We finally propose an alternative approach in which a force curve is modeled as a mixture of delayed sparse sources. The research of the source signals and the delays from a force-volume image is done based on a large number of mixtures since there are as many mixtures as the number of image pixels

Ziel ist die räumliche Abbildung biologischer Materialien (Knochen, Kollagenfibrillen und Zähne) hinsichtlich deren Struktur auf der Nanometerskala mit Hilfe der Nanotomographie. Die Nanotomographie ist eine moderne dreidimensionale Volumenabbildungsmethode auf der Nanometerskala basierend auf der Rasterkraftmikroskopie. Für die Nanotomographie wurden Ätzprotokolle an Zähnen, Kollagenfibrillen und Knochen entwickelt, die einen gleichmäßigen Abtrag bewirken. Lineare Verschiebungen der aufgenommenen Schichten werden mit Hilfe der manuellen Registrierung korrigiert und zu einem Volumenbild rekonstruiert. Ein zentrales Ergebnis sind dabei erste hochaufgelöste Volumenbilder einzelner Kollagenfibrillen im nativen Knochen. Neben der konventionellen Nanotomographie wird ein Ansatz zur automatisierten Nanotomographie mit einer Auflösung von 10 nm am Beispiel des menschlichen Knochens und Zahnes demonstriert. Mit Hilfe von mikroskopischen und elektronenmikroskopischen Techniken wurden die verschiedenen Strukturebenen des humanen Zahn und Knochens abgebildet und die räumlichen Strukturen der TM-AFM-Bilder auf der Mikro- und Nanometerskala eingeordnet. Darüber hinaus konnte mit Hilfe analytischer Messmethoden die chemische Zusammensetzung des kortikalen nativen Knochens erfasst werden und Änderungen durch das Ätzen detektiert werden.