Paul Penfield, Jr. / "March 20, 1962." / Army Signal Corps Contract DA 36-039-sc-78108 Department of the Army Task 3-99-20-001 and Project 3-99-00-000. Army Signal Corps Contract DA-SIG-36-039-61-G14.

The goal of this project is to obtain quantitative images of the lens and the ciliary body to validate EVAS-II (Second generation Ex Vivo Accommodation Simulator). To accomplish this goal it was necessary to develop methods, instrumentation and image processing techniques to acquire 3D images in EVAS-II, using UBM (Ultrasound Bio Microscope), and to apply these techniques to non-human primate eyes. The lens studies included measurement of speed of sound in the lens to reconstruct accurate images of the lens, development of instrumentation to measure the un-distorted lens shape and development of a mathematical model to quantify the whole lens shape. Speed measurements showed that the speed of sound exhibits a gradient profile in the equatorial plane, similar to refractive index and protein distributions in the lens. Lens shape measurements showed that the UBM can be used to accurately measure thickness, diameter, cross-sectional area, volume and surface area of the lens. The ciliary body studies included development of instrumentation and algorithms to obtain 3-D images of tissue in EVAS-II and development of methodology to quantify ciliary body movement during stretching. Studies showed that the accommodation process in young baboon eyes in EVAS-II is comparable to the in vivo process in rhesus monkeys. The UBM can be used to obtain reliable quantitative information about the lens and the ciliary body. 3-D UBM enables monitoring of ciliary body motion of the entire accommodative apparatus.

The main focus of this dissertation is to develop a multispectral imaging system with spectral zooming capability and also successfully demonstrate its promising medical applications through combining this technique with microscope system. The realization of the multispectral imaging method in this dissertation is based on the 4-f spatial filtering principle. When a collimated light is dispersed by the grating, there exists a clear linear distribution spectral line or spectrum at the Fourier plane of the Fourier transform lens group base on the Abbe imaging theory and optics Fourier Transform principle. The optical images, not the collimated light, are applied into this setup and the spectrum distribution still keeps linear relationship with the spatial positions at Fourier plane, even through there exists additional spectral crosstalk or overlap. The spatial filter or dynamic electrical filters used at the Fourier plane will facilitate randomly access the desired spectral waveband and agilely adjust the passband width. It offers the multispectral imaging functionality with spectral zooming capability. The system is flexible and efficiency. A dual-channel spectral imaging system based on the multispectral imaging method and acousto-optical tunable filter (AOTF) is proposed in the dissertation. The multispectral imaging method and the AOTF will form spate imaging channels and the two spectral channels work together to enhance the system efficiency. The AOTF retro reflection design is explored in the dissertation and experimental results demonstrate this design could effectively improve the spectral resolution of the passband. Moreover, a field lens is introduced into the multispectral imaging system to enhance the field of view of the system detection range. The application of field lens also improves the system spectral resolution, image quality and minimizes the system size. This spectral imaging system can be used for many applications. The compact prototype multispectral imaging system has been built and many outdoor remote spectral imaging tests have been performed. The spectral imaging design has also been successfully applied into microscope imaging. The prototype multispectral microscopy system shows excellent capability for normal optical detection of medical specimen and fluorescent emission imaging/diagnosis. Experiment results have demonstrated this design could realize both spectral zoom and optical zoom at the same time. This design facilitates fast spectral waveband adjustment as well as increasing speed, flexibility, and reduced cost.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

Carbon Monoxide (CO) was discovered in the stratosphere of Neptune from the detection of the J=3-2 and J=2-1 rotational transitions in emission at 345.8 and 230.5 GHz respectively. It was conventionally thought that all of the atmospheric carbon should be in its reduced form of methane (CH₄). Two sources of stratospheric CO have been postulated: CO transported from the interior by convection due to Neptune's strong internal heat source (internal source); or, CO produced through photochemical reactions from an external supply of water (external source). <p>In this research project the J=3-2 transition of CO was observed to find the CO profile in Neptune's atmosphere and determine the mechanism producing CO. Three instruments were used at the James Clerk Maxwell Telescope (JCMT) to measure the CO line: the heterodyne receiver B3; the University of Lethbridge Fourier Transform Spectrometer (FTS); and, the Submillimeter Common User Bolometer Array (SCUBA). <p>The high resolution (1.25 MHz) of the heterodyne observations over a large frequency range (~20 GHz) produced a very powerful result because the narrow emission core from the stratosphere and the broad absorption feature arising in the lower atmosphere were measured simultaneously. The CO abundance profile was determined using a model of the J=3-2 CO transition in Neptune's atmosphere developed for this project. Calculations indicate a CO abundance of 1.9^+0.5_-0.3x10^-6 in the upper stratosphere and (0.8±0.2)x10^-6 in the lower stratosphere and troposphere. <p>The moderate resolution of the FTS data allowed the broad absorption feature to be measured. Uranus was originally chosen as the calibration source, but the discovery of CO in Uranus by Encrenaz et al. (2004), while this project was in progress, prompted both Neptune and Uranus to be examined for CO absorption. Two data sets (1993 and 2002) were analyzed and it was found that the 1993 spectra produced superior results, giving a CO mole ratio in the lower atmosphere between 0.8x10^-6 and 2x10^-5; this agrees, within the uncertainty limit, with the lower atmosphere heterodyne result. A tentative detection of CO in Uranus was also obtained from the 1993 data, with a CO abundance profile constrained to pressures greater than 0.5 bar with an abundance between 5x10^-7 and 1x10^-5. The 2002 data were found to be inferior to the 1993 data because of imperfect cancellation of thermal emission from the terrestrial atmosphere. <p> The 850ìm SCUBA filter profile is well matched to the width of the CO feature. Photometric observations of Neptune and Uranus were used to determine if the reduction in integrated flux due to CO absorption could be detected using SCUBA. A CO mole ratio in the range (1.2-1.7) x10^-6 was found for Neptune, calibrated against Uranus and assuming no CO in Uranus. Calibration of the Neptune and Uranus SCUBA data against Mars to produce an independent estimate of the CO abundance in both planets did not produce a useful result because of large calibration errors. <p>Comparison of the results from the three techniques determined that the heterodyne measurement was superior and the derived CO profile was used to determine the source of neptunian CO. It was concluded that the source of CO in Neptune is both internal and external. The lower atmosphere result indicates an interior dominated by water ice. The most likely mechanism for the upper atmosphere CO involves meteoritic ablation, photolysis of H₂O, and chemical reaction with by-products of methane photochemistry. The required H₂O influx for this mechanism is at least two orders of magnitude higher than previously observed, indicating either that the observed H₂O abundance is too small or that CO is produced by a different mechanism.

The Fourier transform is one of the most useful tools in science and engineering and can be expanded to multi-dimensions and curvilinear coordinates. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. In this thesis, the development of a symbolic computer algebra toolbox to compute two dimensional Fourier transforms in polar coordinates is discussed. Among the many operations implemented in this toolbox are different types of convolutions and procedures that allow for managing the toolbox effectively. The implementation of the two dimensional Fourier transform in polar coordinates within the toolbox is shown to be a combination of two significantly simpler transforms. The toolbox is also tested throughout the thesis to verify its capabilities.

En este trabajo se han investigado diferentes técnicas para generar elementos ópticos difractivos que modifican el perfil de intensidad a lo largo del eje y las propiedades de apodización e hiperresolución transversales de un sistema óptico, y se han implementado experimentalmente mediante un modulador espacial de luz de cristal líquido (LCSLM).En primer lugar se han diseñado e implementado pupilas complejas de transmisión no uniforme, con el objeto de modificar el perfil de la intensidad a lo largo del eje en las proximidades del plano imagen de un sistema convergente y lograr perfiles arbitrarios con características de interés. Se ha propuesto un método para diseñar las pupilas de transmisión no uniforme basado en la relación de Transformada de Fourier que existe entre la función compleja radial de una pupila con simetría axial y la función del perfil de intensidad a lo largo del eje óptico. El método utiliza un algoritmo iterativo para obtener la función de pupila compleja a partir de un perfil de intensidad deseado, que tiene en cuenta las restricciones de resolución y de tamaño del modulador. Se ha comprobado numéricamente que el método iterativo propuesto para el diseño de las pupilas converge a funciones pupila que ofrecen respuestas en intensidad a lo largo del eje similares a los perfiles de intensidad deseados. Las pupilas se han implementado en un modulador espacial de luz en configuración sólo de fase. Se ha evaluado numérica y experimentalmente el resultado de estas pupilas comparando el perfil de intensidad deseado con el perfil obtenido a lo largo del eje, y se han analizado las respuestas para la imagen de un punto en los diferentes planos transversales.Se ha comprobado experimentalmente que la técnica modifica satisfactoriamente el perfil de intensidad a lo largo del eje para zonas cercanas al plano de mejor imagen, tanto para perfiles rectangulares de diferentes anchuras (diferentes profundidades de foco) como para un perfil triangular, un perfil consistente en dos rectángulos de la misma altura (doble foco) y un perfil asimétrico consistente en dos rectángulos de diferentes alturas. En la segunda parte de este trabajo se proponen diferentes métodos para multiplexar lentes de diferentes potencias en un mismo LCSLM, con el objeto de conseguir un incremento de la profundidad de foco mediante el solapamiento de los máximos de intensidad a lo largo del eje. Se han propuesto tres métodos: el multiplexado por anillos, el multiplexado por sectores y el multiplexado aleatorio. Se ha observado que el multiplexado aleatorio es el más satisfactorio para incrementar la DOF del sistema óptico. Esta opción de multiplexado proporciona un perfil de intensidad uniforme a lo largo de toda la DOF y una estructura de las PSF también uniforme a lo largo de ese intervalo, por lo que es muy adecuado para la formación de imágenes extensas.Se ha estudiado la respuesta del multiplexado aleatorio para la obtención de imágenes extensas con iluminación incoherente. Para ello, en primer lugar se ha evaluado numéricamente la MTF en el plano de mejor imagen y en planos desenfocados para diferentes opciones del multiplexado aleatorio. A continuación, se han obtenido los resultados experimentales para la imagen de objetos extensos a diferentes distancias de desenfoque y se han comparado con el resultado para una lente de Fresnel de una sola focal. Se ha observado que el multiplexado aleatorio ofrece resultados satisfactorios, en términos de resolución y de contraste, a lo largo de toda la profundidad de foco extendida. / In this work we have investigated different techniques for generating diffractive optical elements (DOEs) that modify the intensity profile along the axis and the transversal apodization and hiperresolution properties of an optical system. These DOEs have been experimentally implemented by means of a Liquid Crystal Spatial Light Modulator (LCSLM). Firstly, we have designed and implemented non uniform transmission complex pupils, with the aim of modifying the intensity profile along the axis near the image plane of a converging optical system, and obtaining arbitrary profiles with some interesting features. We have proposed a method for designing non uniform transmission pupils which is based on the Fourier Transform relation that exists among the radial complex function of a pupil with axial symmetry and the function that describes the intensity profile along the axis. The method uses an iterative algorithm to obtain the complex pupil function from a desired intensity profile, which have into account the limitations of resolution and size of the LCSLM. It has been tested by computer numerical calculations that the proposed iterative method for designing the complex pupils converges to pupil functions that bring along-the-axis intensity responses which are very similar to the desired intensity profiles. The pupils that have been obtained with the iterative method have been implemented on a phase only LCSLM in order to test their performance in a real optical system. The performance of these pupils has been evaluated by comparing the experimental intensity profile obtained with an optical system in the laboratory with the desired one. The Point Spread Function (PSF) at different transversal planes at different distances along the axis have also been analysed. The results show that the pupils satisfactorily modify the intensity profile along the axis for the tested desired profiles: rectangular profiles of different widths (different depths of focus); a triangular profile; a profile consisting of two rectangles of the same height (double focus); and an asymmetric profile comprising two rectangles of different heights. In the second part of this work, different methods for multiplexing lenses of different powers in the same LCSM are proposed. The intention of these proposals is to achieve a depth of focus increase by overlapping the intensity maxima through the axis. There have been proposed three methods: multiplexing by rings, multiplexing by sectors and random multiplexing.It has been observed that the random multiplexing technique is the most satisfactory for incrementing the DOF of the optical system. This option provides a uniform intensity profile along the whole DOF and a PSF structure which is also uniform along this interval; therefore it is very suitable for image formation of extended objects. It has been studied the random multiplexing performance for obtaining extended images with incoherent illumination. To this end, there have been numerically evaluated the MTF at the best image plane and in defocused planes for different options with the random multiplexing technique. Next, there have been obtained the experimental results for the images of extended objects at different defocused distances and the results have been compared with those for a Fresnel lens with a unique power. It has been observed that the random multiplexing provides satisfactory results, in terms of contrast and resolution, along the whole range of the extended depth of focus.

Nous étudions les poids de graphes (c'est-à-dire, les invariants de graphes) qui apparaissent naturellement dans la théorie de Mayer et la théorie de Ree-Hoover pour le développement du viriel dans le contexte d'un gaz imparfait. Nous portons une attention particulière au deuxième poids ωM(C) de Mayer et au poids ωRH(C) de Ree-Hoover d'un graphe 2-connexe c dans le cas d'un gaz à noyaux durs et à positions continues en une dimension. Ces poids sont calculés à partir de volumes signés de polytopes convexes associés au graphe c en utilisant la méthode des homomorphismes de graphes, que nous avons aussi adaptée au cas du poids de Ree-Hoover, ainsi que les transformées de Fourier. En faisant appel à l'inversion de Möbius, nous présentons des relations entre les poids de Mayer et de Ree-Hoover. Ces relations nous permettent de donner une définition simple explicite du concept du "star content" introduit par Ree-Hoover et d'analyser certaines de ses propriétés fondamentales. Parmi nos résultats, nous donnons des tables contenant les valeurs du poids de Mayer et du poids de Ree-Hoover pour tous les graphes 2-connexes de taille au plus 8 ainsi que d'autres paramètres descriptifs. Nous développons aussi des formules explicites pour les poids de Mayer et de Ree-Hoover pour certaines familles de graphes 2-connexes simplement, doublement et triplement infinies, incluant par exemple, le poids de Mayer des graphes bipartis complets K m,n. En analysant les tables précédentes à l'aide du logiciel Maple, nous montrons que les poids de Mayer et de Ree-Hoover ne sont pas exprimables comme des fonctions faisant seulement appel à certains paramètres classiques de la théorie des graphes. Finalement, nous présentons une méthode générale pour le calcul du poids de Mayer d'un graphe connexe quelconque basée sur les arborescences couvrantes en utilisant les transformées de Fourier. Nous illustrons cette méthode sur des cas particuliers incluant les particules dures en dimension quelconque d. Cette méthode donne aussi lieu à un algorithme de calcul basé sur les différences divisées pour le cas des particules dures en dimension d = 1. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Poids de Mayer, Poids de Ree-Hoover, Mécanique statistique, Méthode des homomorphismes de graphes, Transformées de Fourier, Gaz imparfaits.

In this thesis we study ideals in the Fourier algebra, A(G), of a locally compact group G. For a locally compact abelian group G, necessary conditions for a closed ideal in A(G) to be weakly complemented are given, and a complete characterization of the complemented ideals in A(G) is given when G is a discrete abelian group. The closed ideals in A(G) with bounded approximate identities are also characterized for any locally compact abelian group G. When G is an arbitrary locally compact group, we exploit the natural operator space structure that A(G) inherits as the predual of the group von Neumann algebra, VN(G), to study ideals in A(G). Using operator space techniques, necessary conditions for an ideal in A(G) to be weakly complemented by a completely bounded projection are given for amenable G, and the ideals in A(G) possessing bounded approximate identities are completely characterized for amenable G. Ideas from homological algebra are then used to study the biprojectivity of A(G) in the category of operator spaces. It is shown that A(G) is operator biprojective if and only if G is a discrete group. This result is then used to show that every completely complemented ideal in A(G) is invariantly completely complemented when G is discrete. We conclude by proving that for certain discrete groups G, there are complemented ideals in A(G) which fail to be complemented or weakly complemented by completely bounded projections.

Content-based image retrieval (CBIR) is still in its early stages, although several attempts have been made to solve or minimize challenges associated with it. CBIR techniques use such visual contents as color, texture, and shape to represent and index images. Of these, shapes contain richer information than color or texture. However, retrieval based on shape contents remains more difficult than that based on color or texture due to the diversity of shapes and the natural occurrence of shape transformations such as deformation, scaling and orientation. This thesis presents an approach for fusing several shape-based image retrieval techniques for the purpose of achieving reliable and accurate retrieval performance. An extensive investigation of notable existing shape descriptors is reported. Two new shape descriptors have been proposed as means to overcome limitations of current shape descriptors. The first descriptor is based on a novel shape signature that includes corner information in order to enhance the performance of shape retrieval techniques that use Fourier descriptors. The second descriptor is based on the curvature of the shape contour. This invariant descriptor takes an unconventional view of the curvature-scale-space map of a contour by treating it as a 2-D binary image. The descriptor is then derived from the 2-D Fourier transform of the 2-D binary image. This technique allows the descriptor to capture the detailed dynamics of the curvature of the shape and enhances the efficiency of the shape-matching process. Several experiments have been conducted in order to compare the proposed descriptors with several notable descriptors. The new descriptors not only speed up the online matching process, but also lead to improved retrieval accuracy. The complexity and variety of the content of real images make it impossible for a particular choice of descriptor to be effective for all types of images. Therefore, a data- fusion formulation based on a team consensus approach is proposed as a means of achieving high accuracy performance. In this approach a select set of retrieval techniques form a team. Members of the team exchange information so as to complement each other’s assessment of a database image candidate as a match to query images. Several experiments have been conducted based on the MPEG-7 contour-shape databases; the results demonstrate that the performance of the proposed fusion scheme is superior to that achieved by any technique individually.