Orthokeratology (OK) is the reduction, modification or elimination of myopia through application of contact lenses. With the development of high Dk/t lens materials, overnight therapy has become the modality of choice for OK. Overnight OK lens wear has been previously investigated in terms of its efficacy to reduce myopia. However, the underlying effects of overnight OK lens wear on the human cornea have received less attention. As well as the clinical efficacy of overnight OK, this study investigated the effects of overnight OK on topographical corneal thickness and the overnight corneal edema response, and corneal tissue changes with overnight OK. Eighteen subjects participated as the OK lens-wearing group, wearing BE lenses (UltraVision, Brisbane, Queensland) in both eyes. A further ten subjects participated as control subjects, wearing conventional rigid lenses (J-Contour, UltraVision) in the right eye (RE) only. The left eye (LE) acted as a non-lens-wearing control. Both groups wore lenses overnight only, with no lens wear during the day. Measurements were conducted at baseline then on day 1, 4, 10, 30, 60, and 90 for the OK lens-wearing eyes; and up to day 30 for the control group, in the morning (after overnight lens wear) and in the evening (after 8-10 hours of lens removal). Variables measured included best vision sphere (BVS), unaided logMAR visual acuity (VA), refractive astigmatism, apical corneal power (ACP), simulated K readings (Medmont E300 corneal topographer), topographical corneal thickness (Holden-Payor optical pachometer), and keratocyte and endothelial cell densities (ConfoScan2 confocal microscope). Approximately 75% of myopia was corrected after the first night of OK lens wear and the changes in refractive error stabilised by day 10. By day 90, myopia reduction averaged 2.54 ?? 0.63 D. This was associated with significant improvement in unaided VA of about 82% after the first night of lens wear. There was no change in refractive astigmatism over the 3-month period. There was significant reduction in ACP in the OK lens-wearing eyes after the first night of lens wear, which accounted for more than 70% of the total ACP change over the 3-month period (RE: -2.16 ?? 0.53 D; LE: -2.11 ?? 0.86 D). There was significant central epithelial thinning (about 30%) and significant thickening (about 3%) in the mid-peripheral stroma in the OK lens-wearing eyes. Significant central epithelial thinning was found after the first night of lens wear while thickening in the mid-peripheral stroma reached statistical significance by day 4. Further analysis suggests that topographical corneal thickness changes account for the refractive error changes with overnight OK lens wear, rather than corneal bending. The central overnight stromal edema response was significantly reduced in the OK lens-wearing eyes (1.2 ?? 0.5%) to a level lower than in the conventional RGP (6.2 ?? 1.2%) and non-lens-wearing eyes (2.5 ?? 0.9%) in the control group. Mid-peripheral and peripheral stromal edema responses showed similar levels to those predicted based on lens Dk/t. A single overnight wear of BE and Paragon Corneal Refractive Therapy (CRT) lenses showed that the edema response to BE lens wear is significantly less than in the CRT lens-wearing eyes (BE: 2.5 ?? 0.7%; CRT 3.5 ?? 1.3%) immediately on eye opening. No significant changes were found in either central stromal keratocyte or endothelial cell densities in either OK or control groups over the study period. In conclusion, overnight OK lens wear induces significant reductions in myopia after the first night of lens wear associated with improvement in unaided VA. Overnight OK lens wear causes significant thinning in the central epithelium and significant mid-peripheral stromal thickening which results in flattening of the central cornea and steepening in the mid-periphery. Although there were no significant changes in central stromal keratocyte and endothelial cell densities, thinning of the central epithelial layer raises concerns regarding the safety of the procedure, especially with the alarming number of corneal infections reported recently in the literature.

This work is an investigation into the curvature related potential for flux to flow in the radial direction in the back-iron of laminated axial flux machine cores. Analytical and numerical models are presented. Analysis based on these models has shown that, in practical axial flux machines, the radial component of the flux density can be neglected with respect to the flux density distribution in the core back-iron. It has also been found that if the core permeability, core conductivity and number of poles are sufficiently high then power loss due to curvature related cross-lamination flux is negligible compared to normal eddy current losses. A closed form expression to predict losses due to curvature related radial flux is also presented. This expression allows axial flux machine designers to make quick assessment of the need to consider these losses when designing axial flux machines.

The Hartmann screen test (HST) is a well-known technique that has been used for many years in optical metrology. This thesis describes how the technique has been adapted to create a system for continuous in situ monitoring of the internal stress in thin films during plasma deposition. Stress is almost always present in thin films. Stress can affect the physical properties of film, and also influence phenomena which are important in the technology of thin film manufacture such as adhesion and crystallographic defects. For these reasons, it is very important to control and manage the film stress during manufacture of devices based on thin films. The commonest way to infer stress is to measure the change in substrate curvature that it produces. This is often done by comparison of substrate curvatures before and after deposition with surface profilometry, or interferometry. However, these methods are unsuitable for implementing during film deposition in the vacuum chamber. A novel method for measuring changes in curvature of the thin film substrate in situ has been developed, making use of the HST. An expanded laser beam is passed through a screen containing a number of small apertures, which breaks it up into several rays. After reflecting from the surface of the thin film wafer, the rays are received on an array detector as a spot pattern. Image processing is performed on the recorded spot images to determine the positions of spots accurately. Spot centre positions are recorded at start of deposition as a reference, then their displacement is tracked with time during deposition. The spot deflections are fitted to a theoretical model, in which the change in sample profile is described by a second-order surface. The principal axes of curvature of this surface and their orientation are obtained by a least-squares fitting procedure. From this, the thin film stress can be inferred and monitored in real time. Equipment using this technique has been designed and developed in prototype form for eventual use in the RMIT cathodic arc deposition facility. First experiments with a classic Hartmann screen configuration proved that the technique gave good results, but precision was limited by diffraction and interference effects in the recorded image which made determination of spot centres more difficult. A modified configuration was developed, in which a camera is focused on the Hartmann screen, giving much sharper spot patterns and improved resolution. Tests on the prototype system and comparison with other techniques have shown that it is possible to determine changes in sample curvature with a precision of approximately 0.01 m-1. This corresponds to stress changes of around 0.5 GPa for typical wafer and film thicknesses used in practice. The Hartmann screen test is straightforward to use and to interpret. Image processing and analysis of the recorded spot patterns can be automated and performed continuously in real time during thin film deposition. The system promises to be very useful for monitoring stress and thus controlling the deposition process for improved quality of thin film manufacture.

This paper discusses the relationship between the shape of the shading, the surface whose depth at each point equals the brightness in the image, and the shape of the original surface. I suggest the shading as an initial local approximation to shape, and discuss the scope of this approximation and what it may be good for. In particular, qualitative surface features, such as the sign of the Gaussian curvature, can be computed in some cases directly from the shading. Finally, a method to compute the direction of the illuminant (assuming a single point light source) from shading on occluding contours is shown.

A simulation scheme is proposed to analyze the effects of elliptic-conical lensed fiber parameters on the coupling efficiency between a 980nm laser diode and single-mode fiber(SMF). The variation of fiber tip shapes with different melting zone volumes was investigated in this thesis. The heat-transfer finite element model in MARC package is employed to simulate the temperature distribution during the melting process. The free convection is considered in predicting the melting zone. Due to the surface tension, a round tip may be solidificated. In this study an elliptical tip lens is expected to improve the coupling efficiency. The microlens shapes with different radius of curvature is simulated with the software of Surface Evolver. The coupling efficiency of 980nm laser source and different elliptic-conical lensed fiber is calculated by utilizing the ZEMAX optical analysis software. The Taguchi method is employed to evaluate the effect of tip shape parameters on the coupling efficiency. The optimal elliptic-conical lensed fiber parameters has also been proposed. The efficiency loss introduced from the misalignments in laser module packaging has also been discussed in this study.

Intraocular pressure (IOP) measurement is a routine procedure and a fundament in glaucoma care. Elevated IOP is the main risk factor for glaucoma, and to date, reduction of IOP is the only possible treatment. In a retrospective clinical material, the prevalence of open angle glaucoma was estimated on the west coast of Iceland. IOP measurement and optic nerve head examination were used to capture glaucoma suspects, within the compulsory ophthalmological examination for the prescription of eye glasses. The results were mainly in agreement with a recent prospective study in the same region. This indicated that retrospective data, under certain conditions, may contribute with useful information on the prevalence of glaucoma. However, normal tension glaucoma is underestimated if perimetry and/or fundus photography are not included in the examination. Three studies focused on the measurement of IOP. Goldmann applanation tonometry (GAT) is the standard method. GAT is affected by corneal properties, e.g. central corneal thickness (CCT) and corneal curvature (CC). Refractive surgery changes these properties. This has put focus on how corneal biomechanics translate into tonometric errors and stimulated the development of new methods. As a result, Pascal ® Dynamic Contour Tonometry (PDCT) and Icare® rebound tonometry have been introduced. A method under development by our research group is Applanation Resonance Tonometry (ART). It is based on resonance technology and estimates IOP from continuous measurement of force and contact area. Comparison of PDCT, Icare and GAT in a prospective study showed that the concordance to GAT was close to the limits set by the International Standard Organization (ISO) for PDCT, while Icare was outside the limits. To investigate if laser-assisted subepithelial keratectomy (LASEK) affects tonometry, a study was performed where measurements with GAT, PDCT and ART were obtained before, three and six months after LASEK. The hypothesis was that PDCT and ART would be less affected by LASEK than GAT. The results showed a statistically significant reduction of measured IOP three and six months after LASEK for all tonometry methods. Change in visual acuity and IOP between three and six months suggested a prolonged postoperative process. A servo-controlled prototype (ART servo) was developed. A study was undertaken to assess the agreement of ARTservo and a further developed v manual prototype (ART manual) with GAT. The study design was in accordance with the requirements of the ISO standard for tonometers. ARTmanual fulfilled the precision requirements of the ISO standard. ARTservo did not meet all the requirements of the standard at the highest pressure levels. Four tonometry methods, GAT, PDCT, Icare and ART, were investigated. None of them was independent of both CCT and CC. The inconsistencies in the results emphasize the importance of study design. A meta-analysis comprising healthy eyes (IOP ≤ 21 mmHg) in the three papers, revealed age as an important confounder. In summary, glaucoma prevalence in Iceland was investigated and the results indicated that a retrospective approach can contribute with meaningful information. ART and PDCT had a similar agreement to GAT. ART manual fulfilled the precision requirements set by the ISO-standard, ARTservo and PDCT were close, while Icare was distinctly outside the limits. All tonometry methods were affected by LASEK and no method was completely independent of corneal properties.

In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.

The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.

<p>In general relativity, the Riemannian Penrose inequality (RPI) provides a lower bound for the ADM mass of an asymptotically flat manifold of nonnegative scalar curvature in terms of the area of the outermost minimal surface, if one exists. In physical terms, an equivalent statement is that the total mass of an asymptotically flat spacetime admitting a time-symmetric spacelike slice is at least the mass of any black holes that are present, assuming nonnegative energy density. The main goal of this thesis is to deduce geometric lower bounds for the ADM mass of manifolds to which neither the RPI nor the famous positive mass theorem (PMT) apply. This is the case, for instance, for manifolds that contain metric singularities or have boundary components that are not minimal surfaces.</p> <p>The fundamental technique is the use of conformal deformations of a given Riemannian metric to arrive at a new Riemannian manifold to which either the PMT or RPI applies. Along the way we are led to consider the geometry of certain types non-smooth metrics. We prove a result regarding the local structure of area-minimizing hypersurfaces with respect such metrics using geometric measure theory.</p> <p>One application is to the theory of ``zero area singularities,'' a type of singularity that generalizes the degenerate behavior of the Schwarzschild metric of negative mass. Another application deals with constructing and understanding some new invariants of the harmonic conformal class of an asymptotically flat metric.</p> / Dissertation