A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

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Screening of breast cancer patients for their tumour's prognostic marker status is necessary in determining the most suitable course of treatment. This is particularly important in the assessment of HER-2 expression status in identifying candidates who may respond to trastuzumab therapy. Current methods are limited in their effectiveness in accurately determining actual marker status.Discussed herein is an investigation into the development of a titanium dioxide nanoparticle system which may be applied as a medical imaging methodology through the use of positron emission tomography to gauge accurately a patient's HER-2 expression status in identifying candidates for trastuzumab therapy. The initial synthesis of organically coated ultra-small titanium dioxide nanoparticles is discussed in depth with respect to a range of coating molecules and further functionalisation. Additionally, methodology to elicit an exchange of these coat molecules is explored in detail resulting in the generation of TiO2 nanoparticles capable of forming long-term stable suspensions in water. An exploration of the synthesis of fluoride accepting groups for use in generating radiolabelled compounds is explored both successfully and unsuccessfully leading to the development of conditions suitable for radiolabelling aryltrifluoroborate compounds. Attempts to then combine these radionuclide accepting groups with biologically compatible TiO2 nanoparticles are discussed as an initial step toward the generation of a potential PET tracer. However, while this conjugation was achieved, a successful demonstration of the radiolabelling was not achieved requiring further focus on modulating the nanoparticle to easily allow its recovery from such reactions. Finally, an investigation into the effects of trastuzumab and cetuximab on FDG uptake by cells in vitro is discussed with respect to the potential of monitoring disease response to these drugs with conventional FDG-PET.

Thesis (M.Sc.)--University of the Witwatersrand, Faculty of Science, School of Geosciences, 2017. / The costs of acid mine drainage (AMD) monitoring result in the quest for alternative noninvasive method that can provide qualitative data on the progression of the pollution plume and ground geophysics was the ideal solution. However, the monitoring of AMD plume progression by ground geophysics (time-lapse electrical resistance) proves to be noninvasive but also time consuming. This study focuses on the modeling of different geophysical anomalies (mainly geoelectrical resistivity response) of the karstic aquifers. The models are generated from field parameters such as the electrical resistivity of the host rock and the target rock, depth to the target, noise level and electrode configuration in order to ensure that the model outcomes represent the actual field data. This process uses Complex Resistivity Model (CRMod) and Complex Resistivity Tomography (CRTomo) to generate geoelectric subsurface models. Different resistivity values are applied to targets in order to assess the difference against the baseline model for each target scenario. The resistivity difference is reduced to smallest possible value between the reference and new models in order to gauge the lowest percentage change in the model at which the background noises start to have impact on the results. The study shows that the behavior of targets (aquifer) could be clearly detected through resistivity difference tomography rather than inversion tomography. The electrode array plays a significant part in the detection of target areas and their differences in resistance because of its sensitivity. This therefore indicates that the electrode array should be chosen according to study requirements. Furthermore, this study shows that the modelling of different target sizes, alignments and shapes plays huge role in the final results. Future studies that can provide a correlation between the field quantitative data from sampling and the model outcomes have the ability to add to the knowledge of geophysical modeling, thus reducing costs associated with field based plume AMD monitoring. Key words: Acid mine drainage, geophysics, karst aquifer, complex resistance, modelling, tomography / XL2018

Single-frequency Global Positioning System (GPS) receivers do not accurately compensate for the ionospheric delays imposed upon GPS signals. This can lead to significant errors and single-frequency systems rely upon models to compensate. This investigation applies 4D (four-dimensional) ionospheric tomography to GPS timing for the first time. The tomographic algorithm, MIDAS (Multi-Instrument Data Analysis System), is used to correct for the ionospheric delay and the results are compared to existing single and dual-frequency techniques. Days during the solar maximum years 2002, 2003 and 2004 have been chosen to display results when the ionospheric delays are large and variable. Maps of the ionospheric electron density, across Europe, are produced by using data collected from a fixed network of dual-frequency GPS receivers. Results that improve upon the use of existing ionospheric models are achieved for fixed (static) and mobile (moving) GPS receiver scenarios. The effects of excluding all of the GPS satellites below various elevation masks, ranging from 5° to 40°, on timing solutions for fixed and mobile situations are also presented. The greatest timing accuracies when using the fixed GPS receiver technique are obtained by using the highest mask. The mobile GPS timing solutions are most accurate when satellites at lower elevations continue to be included. Furthermore, timing comparisons are made across baselines up to ~4000 km and the ionospheric errors are shown to increase with increasing baseline. GPS time transfer is then investigated and MIDAS is shown to improve the time transfer stabilities of a single-frequency GPS system. The results are comparable to the dual-frequency time transfer after ~2 hours averaging time. Overall, the MIDAS technique provides the most accurate and most stable results (comparable to dual-frequency) for a single-frequency based GPS system. Ionospheric corrections (via MIDAS) may be broadcast to users nationally or via the internet for example, opening up the possibility of improving the accuracy and stability of single-frequency GPS systems in real-time.

This research demonstrates the potential of novel technology for space-based remote sensing of the topside ionosphere-plasmasphere, supported by ionospheric imaging, which can augment and enhance our current understanding of the Earth’s plasmasphere. The research was conducted in two phases. The first was the development of a technology demonstrator ‘TOPCAT’ that installed a dual-frequency GPS receiver dedicated for topside ionosphere-plasmasphere imaging into a Low Earth Orbit (LEO). The novelties of TOPCAT were that it was designed from commercial-off-the-shelf (COTS) components and was installed on-board the CubeSat ‘UKube-1’, greatly reducing development and launch costs of the instrument. The successful launch of TOPCAT for space-borne remote sensing of the topside ionosphere and plasmasphere could provide the necessary proof of concept for the installation of a constellation of CubeSats – a possible next phase that may be implemented in the future. Thus, in its first stage, the thesis discusses the development of TOPCAT, together with design challenges encountered from constraints imposed by CubeSat technology. The discussion also includes the series of qualification tests performed to successfully qualify TOPCAT as a space-worthy payload design that can remotely image regions beyond the ionosphere. The second phase of research was the validation of the Multi-Instrument Data Analysis System (MIDAS) for the topside ionosphere and plasmasphere. A tomography algorithm originally developed for the ionosphere, MIDAS uses total electron content (TEC) measurements from differential phase of GPS signals, and inverts them to derive the electron density of the region. The thesis investigates the extension of MIDAS to image regions beyond the ionosphere by validating the algorithm for the topside ionosphere and plasmasphere. The process was carried out by first reconstructing a simulation by Gallagher et al. [1988] to verify the quality of the images. This was followed by the use of real GPS phase data from the COSMIC constellation to reconstruct the topside ionosphere-plasmasphere, and the qualitative comparison of the images with previous independent observations obtained through COSMIC and Jason-1 missions. Results showed that MIDAS can successfully reconstruct the undisturbed (quiet) topside ionosphere-plasmasphere using COSMIC data. However, imaging the storm-time topside ionosphere-plasmasphere requires better data coverage (i.e. more receivers) as the resolution offered by COSMIC was not sufficient to reconstruct fast-evolving structures – thereby emphasising the need for more data sources providing high resolution global coverage, such as a constellation of CubeSats with LEO-based GPS receivers.

Located at the southernmost sector of the Western Branch of the East African Rift System, the Malawi Rift exemplifies an active, magma-poor, weakly extended continental rift. This work focuses on the northern portion of the Malawi Rift, which is flanked by long (>100 km) basin-bounding border faults and crosses several significant remnant structures. This combination of characteristics makes the Malawi Rift the ideal location to investigate the controlling processes governing present-day extension throughout the lithosphere. To investigate these processes I image shallow basin- to uppermost-mantle structure beneath the region using a combination of passive- and active-source seismic datasets. I conduct passive-source imaging of the crust and upper mantle using ambient-noise and teleseismic Rayleigh-wave phase velocities between 9 and 100 s period. This study includes six lake-bottom seismometers located in Lake Malawi (Nyasa), the first time seismometers have been deployed in any of the African rift lakes. I utilize the resulting phase-velocity maps to invert for a shear velocity model of the Malawi Rift discussed below. I utilize active-source tomographic imaging to obtain new constraints on rift basin structure in the Malawi Rift from a 3-D compressional velocity (Vp) model. The velocity model uses observations from the first wide-angle refraction study conducted using lake-bottom seismometers in one of the great lakes of East Africa. The 3-D velocity model reveals up to ~5 km of synrift sediments, which smoothly transition from eastward thickening against the Livingstone Border Fault in the North Basin to westward thickening against the Usisya Border Fault in the Central Basin. I use new constraints on synrift sediment thickness to construct displacement profiles for both faults. Both faults accommodate large throws (> 7 km) but the Livingstone Fault is ~30 km longer. The dimensions of these faults suggest they are nearing their maximum size. The presence of >4 km of sediment within the accommodation zone suggests fault length was established early pointing the "constant length" model of fault growth. The presence of an intermediate velocity unit with velocities of 3.75-4.5 km/s is interpreted to represent prior rifting (Permo-Triassic and/or Cretaceous) sedimentary deposits beneath Lake Malawi. These thick (up to 4.6 km) packages of preexisting sedimentary strata improve the understanding of the Tanganyika-Rukwa-Malawi rift system and the role of earlier stretching phases on synrift basin development. I use the previously obtained local-scale measurements of Rayleigh wave phase velocities between 9 and 100 s combined with constraints on basin structure and crustal thickness to robustly invert for shear velocity from the surface to 135 km for the Malawi Rift. We compare our resulting 3-D model to a 3-D model of shear velocity obtained for the mature Main Ethiopian Rift and Afar Depression using commensurate datasets and identical methodologies. Comparing the Vs models for the two regions reveals markedly different seismic velocities particularly pronounced in the upper mantle (average velocities in the Malawi Rift are ~9% faster than the Main Ethiopian Rift). Our 3-D Vs model of the Malawi Rift reveals a strong, localized low velocity anomaly associated with the Rungwe Volcanic Province within the crust and upper mantle that can be explained without requiring the presence of partial melt. Away from the Rungwe Volcanic Province, velocities within the plateau regions are fast (> 4.6 km/s) and representative of depleted lithospheric mantle to depths of 100 and >135 km to the west and east of the rift, respectively. Thinned lithosphere, represented by the absence of similarly high velocities, is centered directly beneath the rift axis and footwall escarpments of the rift basins. The correlation between the localization of lithospheric thinning, the boundaries between abutting Proterozoic mobile belts, and the positions of the basin-bounding border faults may point to the controlling role of preexisting large-scale structures in localizing strain and allowing extension to occur here.

Catalyst is a key component in the chemical industry, with more than 90% of total chemical products reliant on their use. However, the working mechanisms are in many cases still not fully understood. For heterogeneous catalysts, in which the reactions normally occur on solid phase materials, a better understanding of the catalytic surfaces, and how they evolve under reactive environments is recognised as the next step forward in the field. This work presents a study utilising atom probe tomography (APT), combined with an in-situ reaction cell, to understand the initial oxidation processes of catalytic NiFe and NiCo model alloy systems. In order to improve reliability of results, a protocol was developed to clean the sample surfaces by field ion evaporation, eliminate sample surface contamination before in-situ oxidation was then performed. APT was successfully applied to these alloys to characterise oxide development as a function of exposure time and temperature. APT also demonstrated surface enrichment induced by oxide formation remained after reduction of the alloy. The successful application of APT on the model alloys led to the next goal which was to associate the data to real catalytic particles. To achieve this, work was extended into the field of nanoparticle catalysts. Nanoparticles with similar compositions to the model alloys were fabricated by chemical synthesis and were examined initially by transmission electron microscopy (TEM). The main goal of this phase was to investigate the surface segregation behaviour of the particles, identifying common behaviours with the model alloys. However, the presence of residual complex chemical environments around the particles following synthesis made APT analysis difficult. Therefore, an alternative method of particle fabrication was explored to better control the resulting materials for easier application of atom probe for nanoparticle analyses. Metallic nanoparticles of Ag, AuCu, AuNi, and AuNiMo were made by an inert gas condensation method, deposited on suitable support materials and were subsequently analysed by APT, facilitated by an improved sample preparation method. Surface segregation on individual nanoparticles was detected. Together with other complementary surface-probing techniques, a complete understanding of these particles from micrometre down to the level of individual particles was achieved. The potential for APT is highlighted to play a key role in this approach to realise a complete understanding of the chemical order, microstructure in multimetallic nanoparticles designed for catalysis.

When one takes an x-ray, one learns how much material is along the line between the x-ray source and the x-ray sensor. The goal of tomography is to learn what one can about an object, by knowing how much material is on a collection of lines or rays passing through that object. Mathematically, this is a collection of line integrals of density function of the object. In this paper, we provide and prove reconstructions for a class of convex objects of uniform density using x-rays from three point sources.

High harmonic generation (HHG) in solids has two main applications. First, HHG is an all-solid-state source of coherent attosecond very ultraviolet (VUV) radiation. As such, it presents a promising source for attosecond science. The ultimate goal of attosecond science is to make spatially and temporally resolved movies of microscopic processes, such as the making and breaking of molecular bonds. Second, the HHG process itself can be used to spatially and temporally resolve fast processes in the condensed matter phase, such as charge shielding, multi-electron interactions, and the dynamics and decay of collective excitations. The main obstacles to realize these goals are: the very low efficiency of HHG in solids and incomplete understanding of the ultrafast dynamics of the complex many-body processes occurring in the condensed matter phase. The theoretical analysis developed in this thesis promises progress along both directions. First, it is demonstrated that nanoengineering by using lower-dimensional solids can drastically enhance the efficiency of HHG. The effect of quantum confinement on HHG in semiconductor materials is studied by systematically varying the confinement width along one and two directions transverse to the laser polarization. Our analysis shows growth in high harmonic efficiency concurrent with a reduction of ionization. This decrease in ionization comes as a consequence of an increased band gap resulting from the confinement. The increase in harmonic efficiency results from a restriction of wave packet spreading, leading to greater re-collision probability. Consequently, nanoengineering of one and two-dimensional nanosystems may prove to be a viable means to increase harmonic yield and photon energy in semiconductor materials driven by intense laser fields. Thus, it will contribute towards the development of reliable, all-solid-state, small-scale, and laboratory attosecond pulse sources. Second, it is shown that HHG from impurities can be used to tomographically reconstruct impurity orbitals. A quasi-classical three-step model is developed that builds a basis for impurity tomography. HHG from impurities is found to be similar to the high harmonic generation in atomic and molecular gases with the main difference coming from the non-parabolic nature of the bands. This opens a new avenue for strong field atomic and molecular physics in the condensed matter phase and allows many of the processes developed for gas-phase attosecond science to be applied to the condensed matter phase. As a first application, my conceptual study demonstrates the feasibility of tomographic measurement of impurity orbitals. Ultimately, this could result in temporally and spatially resolved measurements of electronic processes in impurities with potential relevance to quantum information sciences, where impurities are prime candidates for realizing qubits and single photon sources. Although scanning tunneling microscope (STMs) can measure electron charge distributions in impurities, measurements are limited to the first few surface layers and ultrafast time resolution is not possible yet. As a result, HHG tomography can add complementary capacities to the study of impurities.