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OpenPET was developed to be a scalable and flexible design for data acquisition and signal processing in Positron Emission Tomography (PET) systems. The OpenPET hardware design is mature, but the control software and firmware need further development. In this thesis we developed a software application to connect a host PC with an OpenPET system. We also developed data acquisition firmware that allows data transfer to the host PC. A novel design for an OpenPET coincidence detection processor was proposed, with its basic functionality implemented and validated. A novel method to process PET events in real time was also introduced and validated using simulated data. The feasibility of implementation of this method using Field Programmable Gate Arrays (FPGAs) was demonstrated for our OpenPET system.

Metal nanostructures, with their extraordinary optical properties, have attracted great attention in recent years. Subwavelength-scaled metal elements, without involving array effects, have the unique ability to confine or route light at the nano-scale. In this thesis, we provide three topics relating to the manipulation of light using metal nanostructures. We first present a theory to solve the end-face reflection of a subwavelength metal stripe, which is beneficial to the design of optical resonator antennas. Subsequently, we take the advantage of the destructive interference among triple nano-slits to sharpen the focus beam in the near-field at near-infrared wavelengths, which is of interest to the study of near-field optical phase imaging and lithography. Lastly, we demonstrate a rectangular subwavelength aperture quad to convert linearly polarized radiation to a radially polarized beam, which is useful to create a deep-subwavelength focus and for optical trapping. / Graduate

Vacuum microelectronic (VME) devices are of interest for the development of flat-screen displays and microwave devices. In many cases, their operation depends on the field emission of electrons from micron-sized cathodes (semiconductor or metal), into a vacuum. Major challenges to be met before these devices can be fully exploited include obtaining - low operating voltages, high maximum emission currents, uniform emission characteristics, and long-term emission stability. The research in this thesis concerns the production of silicon field emitters and the improvement of their emission properties by the process of anodisation. Anodisation was carried out for short times, in order to form a very thin layer of porous silicon (PS) at the surface of both p and p⁺-type silicon emitters. The aim in doing this was to form a high density of asperities over the surface of the emitters. It was the intention that these asperities, rather than the "macroscopic" apex of the emitter, would control emission. This was the first work of its kind to be carried out. Transmission electron microscopy was used to characterise the morphology of p and p⁺-type silicon emitters before and after anodisation. Both the structure and arrangement of the surface fibrils, the thickness of the PS layers at the apex and nature of PS cross-sections were studied. The morphology was correlated to subsequent field emission measurements. Field emission characteristics, before and after anodisation, were obtained using a scanning electron microscope adapted for field emission measurements, and a field emission microscope. Extensive measurements showed that, following anodisation, there was substantial improvement in emission behaviour. After anodisation, the following was found to be true: i) The starting voltage was reduced by up to 50% (with p<sup>+</sup -type PS emitters exhibiting a greater reduction in starting voltage than p-type PS emitters). ii) Number of emitting tips per array was increased. iii) Higher maximum currents (up to 3 times higher) were obtained before tips underwent destruction. iv) The resistive effect of the PS layer at the apex was important in determining the maximum current obtained from a tip. In addition, both field emission and field ion microscopy were used to identify the emission source following anodisation. It was shown that individual fibrils on the emission surface caused an increase in field enhancement over a flat plane, leading to emission at lower voltage. Overall, porous silicon appears to be a very promising material for field emission displays.

In this thesis we investigate the role played by fundamental properties of QED in determining the non-perturbative fermion-boson vertex. These key features are gauge invariance and multiplicative renormalisability. We use the Schwinger-Dyson equations as the non- perturbative tool to study the general structure of the fermion-boson vertex in QED. These equations, being an infinite set, have to be truncated if they are to be solved. Such a truncation is made possible by choosing a suitable non-perturbative ansatz for the fermion-boson vertex. This choice must satisfy these key properties of gauge invariance and multiplicative renormalisability. In this thesis we develop the constraints, in the case of massless unquenched QED, that have to be fulfilled to ensure that both the fermion and photon propagators are multiplicatively renormalisable-at least as far as leading and subleading logarithms are concerned. To this end, the Schwinger-Dyson equations are solved perturbatively for the fermion and photon wave-function renormalisations. We then deduce the conditions imposed by multiplicative renormalisability for these renormalisation functions. As a last step we compare the two results coming from the solution of the Schwinger-Dyson equations and multiplicative renormalisability in order to derive the necessary constraints on the vertex function. These constitute the main results of this part of the thesis. In the weak coupling limit the solution of the Schwinger-Dyson equations must agree with perturbation theory. Consequently, we can find additional constraints on the 3- point vertex by perturbative calculation. Hence, the one loop vertex in QED is then calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in any covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the O(a) vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes. These are the new results of the second part of this thesis.

The Rowden Moor experimental site (A.F.R.C. I.G.E.R., North Wyke) provided an opportunity to characterise discharge regimes, elucidate runoff generation mechanisms and to consider implications for solute movement under natural and drained conditions. Research was conducted on a heavy clay grassland soil in an area of high rainfall (1053 mm a ˉ¹) in South West England. A combined hydrometric and tensiometric study was undertaken within a nested experimental design (1 m² to 1 ha) on one undrained and one drained site throughout a drainage season (October to March). Results at the hectare scale demonstrated that drainage did not substantially alter the volume of field runoff ( ~ 400 mm) but did change the dominant flowpaths. Drainage diverted water from surface/near surface routes to depth so that drain storm runoff was lagged by some 30 minutes over undrained site discharge. The drained site also exhibited a more peaky regime, with a maximum daily discharge of 45 mm being almost twice that for the undrained field. At the field and plot scale, the significance of macropore flow was noted. To investigate this in more detail, a tracer experiment was performed on an isolated soil block which had been mole drained and so had enhanced macroporosity. Macropore flow was generated under unsaturated conditions (little matric potential response and no water table was identified). Stable oxygen concentrations were δ18O +3.5 and -5.8 in tracer and background water respectively. Drainflow indicated that there was rapid interaction between applied tracer and soil water (peak flow δ18O -1.1). Thus, the matrix-macropore interface was not a boundary between two separate domains of old and new water, high and low conductivity but a site of rapid interchange and mixing. Temporal variability of soil status and malric water composition, also indicated that limited areas of the matrix were capable of transmitting rapid flow. It became clear that even in a heavy clay soil such as that found at Rowden, where macropore flow was promoted by drainage operations, the matrix still had an important role to play. On the basis of potential, soil moisture and observation of tracers, it is proposed that discrete (finger-like) volumes of the matrix are capable of rapid water transmission. Although it was frequently impossible to relate moisture content and soil water potential because instrumentation monitored different volumes of soil, hysteretic soil moisture behaviour over the drainage season was evident in both data sets. This study confirmed the importance of rapid subsurface runoff generation mechanisms on drained soils, but noted that discontinuous translatory flow in the matrix and macropore flow occurred and that the two ‘domains’ were inextricably linked. Further work should be undertaken at the detailed scale to elucidate the soil characteristics which promote rapid runoff mechanisms and the consequences for water quality, especially where the soil subsurface represents a major reservoir (e.g. nitrates).

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