Shadows provide an important cue in computer graphics. In this thesis we focus on real-time soft shadow algorithms. Two new techniques are presented, both run entirely on modern graphics hardware. "Soft Shadows Using Precomputed Visibility Distance Functions" renders fake soft shadows in static scenes using precomputed visibility information. The technique handles dynamic local light sources and contains special computation steps to generate smooth shadows from hard visibility functions. The resulting images are not physically accurate, nevertheless the method renders plausible images that imitate global illumination. "Soft Projected Shadows" is a simple method for simulating natural shadow penumbra for projected grayscale shadow textures. Shadow blurring is performed entirely in image space and needs only a couple of special blurring passes on pixel shader 2.0 hardware. The technique treats shadow receivers as nearly planar surfaces and doesn’t handle self shadowing, but executes very fast and renders plausible soft shadows. Multiple overlapping shadow casters in a single shadow map are natively supported without any performance overhead.

The complex phenomenon of indentation deformation is studied using finite element analysis for both homogeneous and layered materials. For the homogeneous materials, the elastic-plastic deformation at large indentation depth is studied. The variation of the load-displacement curves as well as the variation of the energy ratio with the applied indentation depth for different strain hardening indices is presented. The power law relation between the indentation load and depth for shallow indentation becomes invalid for deep indentation. The ratio of plastic energy to total mechanical work is a linear function of the ratio of residual indentation depth and maximum indentation depth. For the layered materials (film-substrate systems), the elastic deformation under an indenter is studied. Various material parameters are investigated, including film thickness and modulus. A generalized power law equation is presented for characterizing the indentation load-displacement responses of film-substrate structures.

In order to improve the optical losses of spherical silicon solar cells, new fabrication designs were presented. The new device structures are fabricated based on integration of nanostructures into spherical silicon solar cells. These new device structures include: spherical silicon solar cells integrated with nanostructured antireflection coating layers, spherical silicon solar cells with hemispherical nanopit texturing, and cells integrated with colloidal quantum dots. Silicon spheres were characterized by means of transmission electron microscopy (TEM), single-crystal x-ray diffraction and x-ray powder diffraction to establish the crystallinity nature of the silicon spheres. Furthermore, the material properties of silicon spheres including surface morphology, microwave photoconductivity decay lifetime, and impurity elemental distributions were studied. Silicon nitride antireflection coating layers were developed and deposited onto the spherical silicon solar cells, using a PECVD system. A low temperature hydrogenation plasma technique was developed to improve the passivation quality of the spherical silicon solar cells. The spectral response of silicon spheres with and without a silicon nitride antireflection coating was studied. We have successfully developed and integrated a nanostructured antireflection coating layer into spherical silicon solar cells. The nanostructured porous layer consists of graded-size silicon nanocrystals and quantum-size Si nanoparticles embedded in an oxide matrix. This layer has been characterized by means of scanning electron microscopy (SEM), transmission electron microscopy (TEM), Scanning tunneling TEM, energy filtered TEM, transmission electron diffraction (TED), electron energy loss spectroscopy (EELS), energy dispersive x-ray (EDX), Raman spectroscopy and photoluminescence spectroscopy (PL). We developed a novel technique of electrochemical etching for silicon surface texturing using a liquid-phase deposition of oxide mask. Using a focus ion-beam (FIB) technique, cross-sectional TEM samples were prepared to investigate the nature of texturing and the composition of the deposited mask. The hemispherical nanopit texturing was successfully integrated into spherical silicon solar cells and the etching mechanisms and the chemical reactions were discussed. CdSe colloidal quantum dots with diameter of about 2.8nm were integrated into a graded-density nanoporous layer. This structure was implemented on the emitter of the spherical silicon solar cells and the spectral response with and without incorporation of QDs was studied.

The connectivity and structural integrity of the white matter of the brain is known to be implicated in a wide range of brain-related diseases and injuries. However, it is only since the advent of diffusion magnetic resonance imaging (dMRI) that researchers have been able to probe the miscrostructure of white matter in vivo. Presently, among a range of methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). It preserves the high angular resolution property of diffusion spectrum imaging (DSI) but requires less measurements. Meanwhile, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel. Unfortunately, the ability of HARDI to discriminate neural fibres that cross each other at acute angles is always limited. The limitation becomes the motivation to develop numerous post-processing tools, aiming at the improvement of the angular resolution of HARDI. Among such methods, spherical deconvolution (SD) is the one which attracts the most attentions. Due to its ill-posed nature, however, standard SD relies on a number of a priori assumptions needed to render its results unique and stable. In the present thesis, we introduce a novel approach to the problem of non-blind SD of HARDI signals, which does not only consider the existence of anisotropic diffusion component of HARDI signal but also explicitly take the isotropic diffusion component into account. As a result of that, in addition to reconstruction of fODFs, our algorithm can also yield a useful estimation of its related IDM, which quantifies a relative contribution of the isotropic diffusion component as well as its spatial pattern. Moreover, one of the principal contributions is to demonstrate the effectiveness of exploiting different prior models for regularization of the spatial-domain behaviours of the reconstructed fODFs and IDMs. Specifically, the fibre continuity model has been used to force the local maxima of the fODFs to vary consistently throughout the brain, whereas the bounded variation model has helped us to achieve piecewise smooth reconstruction of the IDMs. The proposed algorithm is formulated as a convex minimization problem, which admits a unique and stable minimizer. Moreover, using ADMM, we have been able to find the optimal solution via a sequence of simpler optimization problems, which are both computationally efficient and amenable to parallel computations. In a series of both in silico and in vivo experiments, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatial coherency of cerebral diffusion at moderate to severe noise levels. The performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach. Moreover, the results illustrate the power of applied spatial regularization terms.

There are emerging requirements for high accuracy multi-DOF actuators in numerous applications. As one of the novel motors capable of multi-DOF manipulation, permanent magnet spherical motors (PMSMs) that can provide continuous and dexterous motion in one joint have been widely studied for their advantages in structure and energy efficiency. The demands to bring forward the performance of PMSMs for precision applications have motivated this thesis to develop a closed-loop orientation control system with high accuracy and bandwidth. Unlike traditional control methods for PMSMs, which rely on explicit orientation feedback, a new control method (referred to here as direct field-feedback control or in short DFC) directly utilizing the magnetic fields for feedback have been developed in this thesis. Because magnetic field measurements are almost instantaneous and the need for real-time orientation estimation is eliminated in DFC, the system sampling time is greatly reduced. Meanwhile, several field-based methods have been developed for the major components in the DFC system and each component can be processed independently and concurrently with the magnetic field measurements. The parallel computation further improves the system bandwidth and also reduces accumulated error. The DFC system has been experimentally implemented and evaluated. The results show excellent control performances in terms of accuracy and bandwidth. To facilitate the design and analysis of the DFC system, several new algorithms have been developed, which include the modeling and computing of magnetic fields as well as forces and torques, an analysis of bijective relationship between orientation and magnetic fields, and a method for calibration and reconstruction of the rotor magnetic field in 3 dimensional space. These algorithms not only enable the implementation of the DFC system for a PMSM, but also benefit the PMSM studies in design, modeling and field-based sensing. While the immediate outcome of this research is a control system for PMSMs, this new control method can be applied to a broad spectrum of electromagnetic motion systems.

This thesis presents a practical approach to reduce the overall testing time in a spherical near-field (SNF) antenna measurement environment. The premise of this work is that the acquisition time is mostly dominated by the mechanical movement and the processing electronic. Moreover, it is assumed that the transformation time to go from the near-field domain to the far-field domain (NF-FF transform) is small compared to the acquisition time. Thus this operation can be done repeatedly while the acquisition is on-going without significantly affecting the overall test time. This situation allows to continuously evaluate the far-field (FF) of the antenna under test (AUT), so that certain decision functions based on the radiation pattern of the antenna can be monitored. Such decision functions are based on the antenna specification, such as the gain, the side lobe level, etc. We do not proceed with a complete scan of the measurement sphere but effectively allow the probe to follow a directed path under control of an acquisition rule, so that the sampled near-field (NF) datapoints constitute an acquisition map on the sphere. The acquisition can then be terminated based on decision function values, allowing the smallest amount of data needed to ensure accurate determination of the AUT performance measures.

Most current space robotics vehicles use solar energy as their prime energy source. In spherical robotic vehicles the use of solar cells is very restricted. Focusing on the particular problem, an improved method to generate electrical power will be developed; the innovation is the use of an internal pendulum-generator mechanism to generate electrical power while the ball is rolling. This concept will enable spherical robots on future long-duration planetary exploration missions. Through a developed proof-of-concept prototype, inspired by the Russian thistle plant, or tumbleweed, this thesis will demonstrate power generation capabilities of such a mechanism. Furthermore, it will also present and validate a parametric analytical model that can be used in future developments as a design tool to quantify power and define design parameters. The same model was used to define the design parameters and power generation capabilities of such a system in Martian environment.

Most current space robotics vehicles use solar energy as their prime energy source. In spherical robotic vehicles the use of solar cells is very restricted. Focusing on the particular problem, an improved method to generate electrical power will be developed; the innovation is the use of an internal pendulum-generator mechanism to generate electrical power while the ball is rolling. This concept will enable spherical robots on future long-duration planetary exploration missions. Through a developed proof-of-concept prototype, inspired by the Russian thistle plant, or tumbleweed, this thesis will demonstrate power generation capabilities of such a mechanism. Furthermore, it will also present and validate a parametric analytical model that can be used in future developments as a design tool to quantify power and define design parameters. The same model was used to define the design parameters and power generation capabilities of such a system in Martian environment.

Myopia is a major cause of vision loss throughout the world. High myopia is associated with severe eye diseases like maculopathy, retinal detachment and glaucoma. The prevalence of myopia is increasing, and varies by country and by ethnic group. In some Asian populations the prevalence is 70%-80%.  This thesis includes five experiments. In experiment I we investigated the effects of added positive and negative spherical aberration on accommodative response accuracy. We found that the accommodative response can be altered by modulating the spherical aberration of the eye with soft contact lenses. There was an improvement in the accommodative response slopes and a decrease in the lag of accommodation with the negative spherical aberration lenses compared to positive spherical aberration lenses.  In experiment II we investigated whether the negative spherical aberration in contact lenses could be tolerated visually in terms of wearability and comfort. We found that all the subjects were satisfied with the contact lens comfort, distance and near vision and the stability of the vision with the lenses. The accommodative response was stable through out the treatment period. In experiment III we investigated the efficacy of a novel dual treatment for the improvement of accommodative accuracy and dynamics in myopes. The spherical aberration of the eye was effectively altered to negative in the treatment group as predicted. In the control group as expected there was no significant change in the spherical aberration of the eye with and without contact lenses. The treatment lenses decreased the lag of accommodation and increased the accommodative response slope at 3 months. In the experiment IV we investigated the effect of the treatment lenses used in the previous experiment on high and low contrast visual acuities after a one year treatment period. The results showed a significant improvement in both high and low contrast visual acuities after the one year period in the treatment group compared to the control group, even though it was not clinically significant. In experiment V we investigated the intrasession repeatability of peripheral aberrations using COAS-HD VR aberrometer and also reported the distribution of higher order aberrations in a group of young emmetropes. There was no significant difference in the variance of total higher-order RMS between on- and off-axis measurements. There was a significant change in the horizontal coma, spherical aberration and higher-order RMS with off-axis angle along the horizontal visual field. We demonstrated that fast, repeatable and valid peripheral aberration measurements can be obtained with this instrument. This thesis contributes new results in this field of myopia, aberration and accommodation.

An expansion method for the stationary Schrodinger equation of a particle moving freely in an arbitrary axisymmeric three dimensional region defined by an analytic function is introduced. The region is transformed into the unit ball by means of coordinate substitution. As a result the Schrodinger equation is considerably changed. The wavefunction is expanded into a series of spherical harmonics, thus, reducing the transformed partial differential equation to an infinite system of coupled ordinary differential equations. A Fourier-Bessel expansion of the solution vector in terms of Bessel functions with real orders is employed, resulting in a generalized matrix eigenvalue problem. The method is applied to two particular examples. The first example is a prolate spheroidal billiard which is also treated by using an alternative method. The numerical results obtained by using both the methods are compared. The second exampleis a billiard family depending on a parameter. Numerical results concerning the second example include the statistical analysis of the eigenvalues.