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

A study of double-variable-curvature microlenses (DVCM) for promoting coupling efficiency between the high-power 980-nm laser diodes and the single-mode fibers has been proposed. The purpose of the fiber microlens fabrication was to make the mode field match between the laser beam and the fiber as the beam propagating through the fiber microlens. To make the mode match, the shapes of the fiber microlens demanded nothing else but the offset and the curvature radii in minor and major axes. The double-variable-curvature fiber endface (DVCFE) was manufactured through a single-step fully automation grinding process and had less average offset of 0.3£gm, consequently. The radii of curvature in minor and major axis were controlled as an average of 1.2£gm and 33.6£gm, respectively. In the fusing procedure, the slight arc fusion was mainly applied for fine polishing merely instead of reshaping for the reason that the fabricated DVCFE was very close to the ideal shape. Hence, the fabrication time was reduced and the yield was promoted due to the withdrawn step of tip elimination. Furthermore, while the fusion parameters were set to be: fusing distance: 10£gm, arc intensity: 3bits, and fusing time: 200ms in the slight fusion process, the offset was reduced to 0.2£gm due to the shape constraint and surface tension of the DVCFE. And the radii of curvature increased 1.7£gm to 2.9£gm in the minor axis and increased 4.5£gm to 38.1£gm in the major axis, respectively. Owing to the controls of the fully automated grinding procedure and the omission of the tip elimination, the coupling efficiency and yield were improved. As a result, in the experiment, the average and maximum coupling efficiency of 83% and 88% were demonstrated, respectively. And the coupling efficiencies of the 20 samples were higher than 80%. In other words, the proposed DVCM structure of this study was a high coupling efficiency, a high yield output, and reproducible and fully automated single-step grinding process.

This study is to improve the coupling efficiency between 980nm high-power pump laser diode and single-mode fiber. In this study, we use the third generation of fiber grinding machine which is designed by Cheng Shiu University, professor Ying-Chien Tsai. This machine is fully automatic. we use it to fabricate the hyperbola microlenses. The advantages about hyperbola microlenses structure are a single-step fabrication, grinding steps to simplify, reduce the grinding time and will greatly reduce the offset of fiber. In the fusing procedure, the slight arc fusion was mainly applied for fine polishing merely instead of reshaping for the reason that the fabricated hyperbola fiber endface was very close to the ideal shape. The fabrication reproducibility and yield increase, and can reduce the cost of grinding. The fiber end shape is similar to the math on the hyperboloid, and the length of the axis of the hyperboloid profile shows a hyperbola. By mathematical properties of hyperbola, we derivation the parameter of radius of curvature for hyperbola microlenses. The definition of the radius of curvature of the hyperbolic vertex and the mode field diameter (the MFD) = 4.2£gm point of intersection with the hyperbola, the characteristics of the formation of this three o'clock round the curvature is the radius of curvature we have said. The radius of curvature (R) is a semi-consistent axial length (a) and two progressive line angle (£c) function, it means we can through the control of ¡§a¡¨ and £c to control the R, but £c is fixed after grinding process. So we choose control parameter ¡§a¡¨ by fusing process, via control ¡§a¡¨ to achieve the purpose of the control R. By various fusing parameters to adjust the gain of ¡§a¡¨, we can control the R in an ideal 2.6-2.8£gm. This process indeed improves the coupling efficiency. This method gives a low offset of the fiber it easier for more than 80%. And larger offset of the fiber by this method can achieve to 70% even 80%.