From object tracking to 3D reconstruction, RGB-Depth (RGB-D) camera networks play an increasingly important role in many vision and graphics applications. With the recent explosive growth of Augmented Reality (AR) and Virtual Reality (VR) platforms, utilizing camera RGB-D camera networks to capture and render dynamic physical space can enhance immersive experiences for users. To maximize coverage and minimize costs, practical applications often use a small number of RGB-D cameras and sparsely place them around the environment for data capturing. While sparse color camera networks have been studied for decades, the problems of extrinsic calibration of and rendering with sparse RGB-D camera networks are less well understood. Extrinsic calibration is difficult because of inappropriate RGB-D camera models and lack of shared scene features. Due to the significant camera noise and sparse coverage of the scene, the quality of rendering 3D point clouds is much lower compared with synthetic models. Adding virtual objects whose rendering depend on the physical environment such as those with reflective surfaces further complicate the rendering pipeline. In this dissertation, I propose novel solutions to tackle these challenges faced by RGB-D camera systems. First, I propose a novel extrinsic calibration algorithm that can accurately and rapidly calibrate the geometric relationships across an arbitrary number of RGB-D cameras on a network. Second, I propose a novel rendering pipeline that can capture and render, in real-time, dynamic scenes in the presence of arbitrary-shaped reflective virtual objects. Third, I have demonstrated a teleportation application that uses the proposed system to merge two geographically separated 3D captured scenes into the same reconstructed environment. To provide a fast and robust calibration for a sparse RGB-D camera network, first, the correspondences between different camera views are established by using a spherical calibration object. We show that this approach outperforms other techniques based on planar calibration objects. Second, instead of modeling camera extrinsic using rigid transformation that is optimal only for pinhole cameras, different view transformation functions including rigid transformation, polynomial transformation, and manifold regression are systematically tested to determine the most robust mapping that generalizes well to unseen data. Third, the celebrated bundle adjustment procedure is reformulated to minimize the global 3D projection error so as to fine-tune the initial estimates. To achieve a realistic mirror rendering, a robust eye detector is used to identify the viewer's 3D location and render the reflective scene accordingly. The limited field of view obtained from a single camera is overcome by our calibrated RGB-D camera network system that is scalable to capture an arbitrarily large environment. The rendering is accomplished by raytracing light rays from the viewpoint to the scene reflected by the virtual curved surface. To the best of our knowledge, the proposed system is the first to render reflective dynamic scenes from real 3D data in large environments. Our scalable client-server architecture is computationally efficient - the calibration of a camera network system, including data capture, can be done in minutes using only commodity PCs.

This research investigates the strength behavior of horizontally curved composite I-girder bridge structural systems, and the representation of this behavior by the AASHTO (2004b) LRFD provisions. The primary focus is on the design of a representative curved composite I-girder bridge tested at the FHWA Turner-Fairbank Highway Research Center, interpretation of the results from the testing of this bridge, including correlation with extensive linear and nonlinear finite element analysis solutions, and parametric extension of the test results using finite element models similar to those validated against the physical tests. These studies support the potential liberalization of the AASHTO (2004b) provisions by the use of a plastic moment based resistance, reduced by flange lateral bending effects, for composite I-girders in positive bending.

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This research work has been conducted to introduce a novel class of Fabry-Perot (FP) resonators : curved FP cavity based on coating-free Bragg mirrors of cylindrical shape, obtained by silicon micromachining. Another specificity is the rather large cavity lengths (L>200 µm) combined with high quality factor Q (up to 104), for the purpose of applications requiring cavity enhanced absorption spectroscopy, in which the product Q.L is a figure of merit. In this contest, the basic architecture has been modeled analytically to know the high order transverse modes supported by such cavities. Hence, the experimental conditions which lead to preferential excitation (or rejection) of these modes have been tested experimentally leading to the validation of our theoretical model and to a better understanding of the cavity behaviour. A second architecture, based on the curved FP together with a fiber rod lens has been developed for the purpose of providing stable designs. It was also modeled, fabricated and characterized leading to the expected performance improvements. On another side, a highlight on one of the potential applications that we identified for the curved cavities is presented by inserting the cavity into an electro-mechanical system. It consists of exciting and measuring tiny vibration through opto-mechanical coupling in a MEMS mechanical resonator embedding an FP cavity.Finally, as a complement to our study on resonators, we started exploring applications of optical interferometers based on similar micromachined silicon Bragg mirrors. For this purpose, an optical measurement microsystem was designed, fabricated and characterized ; it consists of an optical probe for surface profilometry in confined environments, based on an all-silicon Michelson interferometer

Die Nanooptik beschäftigt sich mit der Wechselwirkung von Licht mit Materie, deren charakteristische Dimension im Nanometer Bereich liegt. Insbesondere wenn die Materie aus Metall besteht, zeigen sich interessante, wellenlängenabhängige Unterschiede in der Stärke der Wechselwirkung. Die Ursache dafür sind die kollektiven Moden der quasifreien Ladungsträger, die Plasmonen. Obgleich sich experimentelle Methoden in den letzten Jahren stetig verbessert haben, ist es nach wie vor nur mit erheblichem Aufwand möglich, sich Einblicke in die mikroskopischen Zusammenhänge zu verschaffen. Eine Ergänzung zu den Experimenten bieten theoretische Modelle. Auf Grund der sich mit der Zeit stetig verbesserten Leistung der Rechentechnik, kommen dabei zunehmend numerische Verfahren zum Einsatz. Eines dieser Verfahren ist das Unstetige Galerkin Verfahren, welches in dieser Arbeit auf folgende Fragestellungen der plasmonischen Nanooptik angewandt wurde: • Bei dem unstetigen Galerkin Verfahren werden die zu simulierenden Körper üblicherweise mittels Dreiecke und Tetraeder approximiert. Da die Geometrie der metallischen Systeme einen entscheidenden Einfluss auf die Wechselwirkung hat, wurde untersucht, inwieweit sich durch Einsatz von Elementen mit gekrümmten Flächen die Genauigkeit oder die Geschwindigkeit der Simulation steigern lässt. Es konnte gezeigt werden, dass runde Elemente die Genauigkeit bei gleicher Diskretisierung um bis zu zwei Größenordnungen steigern oder die Rechenzeit bei gleicher Genauigkeit auf ein Sechstel verkürzen können. • Bestrahlt man Metallnanopartikel mit intensiven Laserpulsen, so strahlen diese nicht nur bei der Frequenz des eingestrahlten Lichtes, sondern auch bei der doppelten Frequenz ab. Dieses Phänomen der Frequenzverdopplung (SHG, engl.: „Second-Harmonic-Generation“) ist unter anderem von der Form der Partikel und der Wellenlänge des Pulses abhängig. Da durchstimmbare gepulste Laser sehr teuer sind, wurde untersucht, ob sich mit Hilfe der linearen Partikelspektren Vorhersagen über die Stärke der Frequenzverdopplung machen lassen. Dabei wurde festgestellt, dass die Effizienz der Frequenzverdopplung zunimmt, wenn man die linearen Resonanzen der Partikel auf die SHG- oder Anregungswellenlänge abstimmt. Schafft man es, das plasmonische System so einzustellen, dass sowohl die Anregungswellenlänge, wie auch die SHG- Wellenlänge auf einer linearen Resonanz liegen, so kann die Effizienz der SHG weiter gesteigert werden. / Nanooptics is a discipline dealing with the interaction of light with matter where its characteristic dimensions are defined to be in the range of nanometers. In particular, if the matter consists of metal, i.e. conductive material, interesting wavelength dependent phenomena can be observed, which scale with the strength of the interaction. These phenomena are caused by the formation of collective modes between quasi-free charge carriers resulting in so called plasmons. Although improved experimental methods have evolved over the last few years, insight into the microscopic relationship between light and matter is only achievable with high effort. Supplemental information to experimental findings can be drawn from theoretical models. Due to the constantly improving computational power, numerical methods are progressively more employed. One of these methods is the discontinuous Galerkin method, which was applied to the following problems in plasmonic nanooptics: • Within the discontinuous Galerkin method the simulated objects are usually approximated by triangles or tetrahedrons. Since the geometry of conductive systems has a major impact on the interaction between light and matter, the usability of elements with curved surfaces for the discretisation of the space has been investigated with respect to accuracy and speed of the simulation. In this work, it could be shown that curved elements improve the simulations precision up to two orders of magnitude with the same amount of discretisation compared to linear elements. Related to speed, it has been found that the computational time is reduced by a factor of 6 with a comparable simulation accuracy. • By irradiating metallic nanoparticles with high power laser pulses these particles do not only emit light of the same frequency as the incident electromagnetic wave, but also with the doubled frequency (SHG, second harmonic generation). Among other things, this phenomenon of frequency doubling mainly depends on the geometry of the particle and the wavelength of the pulse. Since tunable pulsed laser sources are very expensive, it has been theoretically investigated if the strength of the frequency doubling can be deduced from the particles linear spectra. By this, it has been discovered that the efficiency of frequency doubling can be improved by adjusting the linear resonances of the particle to the SHG or excitation wavelength. The SHG efficiency can be increased even further, if the plasmonic system is tuned to a point where both the excitation and the SHG wavelength correspond to a linear resonance of the nanoparticle.

The Vlasov-Poisson system is most commonly used to model the movement of charged particles in a plasma or of stars in a galaxy. It consists of a kinetic equation known as the Vlasov equation coupled with a force determined by the Poisson equation. The system in Euclidean space is well-known and has been extensively studied under various assumptions. In this paper, we derive the Vlasov-Poisson equations assuming the particles exist only on the 2-sphere, then take an in-depth look at particles which initially lie along a great circle of the sphere. We show that any great circle is an invariant set of the equations of motion and prove that the total energy, number of particles, and entropy of the system are conserved for circular initial distributions. / Graduate

Doppelt gekrümmte Schalen und Gitterschalen sind Tragsysteme, die, obwohl in Ihrer Wirkungsweise grundsätzlich verschieden, besonders für den Einsatz von Textilbeton geeignet sind. Aufgrund ihrer doppelten Krümmung weisen derartige Tragsysteme zahlreiche Besonderheiten hinsichtlich Formfindung, Lastabtrag und Herstellung auf. Anhand eines Ausführungsbeispiels von monolithischen Schirmschalen und Konstruktionsstudien zu Gitterschalen werden die Strukturkonzepte und ihre Auswirkungen auf das Tragverhalten, das Bewehrungskonzept und die Auswirkungen auf die Herstellung sowie die Bauteilfügung erläutert. / Structural systems based on double curved monolithic shells or gridshells are both characterised by their good load bearing behaviour depending on the chosen geometry. Although both systems are different regarding their functionality they are suitable applications for TRC while taking advantage of the main constructive and design characteristics of the material. In describing an execution example of an umbrella-shaped shell-structure and design studies on gridshells the relation between structural concept and load bearing behaviour and the relation between the reinforcement concept and production as well as joining are discussed.

Magnetic Resonance Imaging (MRI) is considered as a slow imaging technique. Various approaches to accelerate MRI imaging have been explored by researchers in the past decades. Earlier gradient based methods have reached the safety limit. Parallel receiving techniques achieve accelerations by reducing phase encoding steps. Among these methods, SEA Imaging achieved the highest possible acceleration by completely eliminating phase encoding. However, SEA imaging is limited to thin planar slices above the array due to the correction needed for the inherent phase cancellation caused by voxel-sized coils. A phase compensation gradient pulse is used for this correction in SEA imaging. This phase compensation is dependent on slice position and thickness as well as the orientation of the array elements, placing stringent restrictions on SEA imaging, limiting its applications. Converting the SEA system into Transmit / Receive (T/R) mode, which is the main purpose of this study, eliminates the requirement for phase compensation gradient because phase departed during transmit is refocused during receiving. Independent amplitude and phase control of RF pulse for each coil of a SEA array is achieved using a low cost scalable parallel transmit system design. The first 64-channel parallel transmitter for MRI in the world is constructed and tested. Software is also developed to control the phase and amplitude of all the 64 channels of RF excitation pulses independently through National Instruments DAQ system. The system consists of vector modulators controlled by digital controlled potentiometers, two-stage amplifiers and T/R switches on the transmit side. All these are combined with newly designed and constructed preamplifiers and the existing 64-channel parallel receivers on the receive side, leading to the only 64-channel parallel T/R system available for MRI. As a bonus, the system can be easily updated to full Transmit SENSE capability. Furthermore, simulations and images are done to synthesize transmit patterns thanks to the large channel count. Testing results show that the system is capable of 100W per channel simultaneous transmission. Using this system, transmit field can be synthesized by varying the phase and amplitude across channel without traditionally required complicated pulse sequences involving simultaneous RF and gradient fields. Curved slice excitation has conventionally been considered a difficult task for MRI, achievable only through complicated pulses sequences. Using this system and flexible array wrapped around the subject to be imaged, the system is able to excite curved slice using one shot. TR images indicate that the system is capable of high speed surface imaging at 200 frames per second following the surface of a flexible SEA array coil which has not been achieved using other methods in MRI.

A dual-axis fluidic thrust vectoring (FTV) system is proposed where the supersonic propulsive jet of an aircraft is exhausted over a scarfed (swept), curved surface to produce flight control moments in both the pitch and yaw axes. This work contributes towards practical dual-axis FTV through expansion of fundamental curved-wall jet (CWJ) understanding, development of the novel Superimposed Characteristics technique for supersonic nozzle design, and performance evaluation of an experimental scarfed curved wall FTV configuration. Previous work has suggested that the use of a sheared exhaust velocity profile improves the attachment of supersonic jets to curved surfaces; however, evidence to support this is limited. To address this, an inviscid numerical CWJ model was developed using the two-dimensional method of characteristics. A major outcome is improved understanding of the effect of exhaust velocity profile on CWJ wave structure and subsequent jet attachment. A sheared velocity exhaust is shown to generate a wave structure that diminishes adverse streamwise pressure gradients within a supersonic curved-wall jet. This reduces the likelihood of boundary layer separation and as a result, a sheared exhaust velocity CWJ is expected to be less readily separated compared to other exhaust velocity profiles. A novel method termed Superimposed Characteristics was developed for the low-order design of supersonic nozzles with rectangular exits. The technique is capable of generating 3D nozzle geometries based on independent exit plane orientation and exhaust velocity distribution requirements. The Superimposed Characteristics method was used to design scarfed rectangular exit nozzles with sheared velocity exhaust profiles. These nozzles were then evaluated using finite volume computational methods and experimental methods. From the analysis, the Superimposed Characteristics method is shown to be valid for preliminary nozzle design. Experimental methods were used to study the on- and off-design attachment qualities of uniform and sheared velocity exhaust jets for a FTV configuration with an external curved wall termination angle of 90 degrees and scarf angle of 30 degrees. Experiments at the on-design nozzle pressure ratio (NPR) of 3.3 demonstrated pitch and yaw jet deflection angles of 78 degrees and 23 degrees respectively for the uniform exhaust velocity CWJ. The sheared exhaust velocity CWJ achieved lower pitch and yaw deflection angles of 34 degrees and 14 degrees respectively at the same on-design NPR. The lower jet deflection angles observed for sheared exhaust velocity jets is inconsistent with the CWJ model prediction of reduced adverse streamwise pressure gradients; however, there was insufficient experimental instrumentation to identify the cause. In the off-design experiments, the uniform exhaust velocity CWJ was observed to detach at an NPR of 3.6, whilst the sheared exhaust velocity CWJ remained attached at NPRs in excess of 4. The capability of sheared exhaust velocity CWJs to remain attached at higher NPRs is consistent with the analytical theory and the CWJ model predictions. An actuation study was carried out to achieve controlled jet detachment using secondary blowing injected normal to the curved wall. Full separation of the wall jets was achieved downstream of the injection point. This provided vectoring angles of more than 20 degrees in pitch and 10 degrees in yaw, exceeding expected vectoring requirements for practical aircraft control. At the on-design NPR, the uniform and sheared exhaust velocity jets required secondary blowing mass flow rates of 2.1% and 3.8% of the primary mass flow respectively to achieve full separation.