Numerical methods for the manufacture of optics using sub-aperture tools

Moore’s law, predicting a doubling of transistor count per microprocessor every two years, remains valid, demonstrating exponential growth of computing power. This thesis examines the application of numerical methods to aid optical manufacturing for a number of case-studies related to the use of sub-aperture tools. One class of sub-aperture tools consists of rigid tools which are well suited to smooth surfaces. Their rigidity leads to mismatch between the surfaces of tool and aspheric workpieces. A novel, numerical method is introduced to analyse the mismatch qualitatively and quantitatively, with the advantage that it can readily be applied to aspheric or free-form surfaces for which an analytical approach is difficult or impossible. Furthermore, rigid tools exhibit an edge-effect due to the change in pressure between tool and workpiece when the tool hangs over the edge. An FEA model is introduced that simulates the tool and workpiece as separate entities, and models the contact between them; in contrast to the non-contact, single entity model reported in literature. This model is compared to experimental results. Another class of sub-aperture processes does not use physical tools to press abrasives onto the surface. A numerical analysis of one such process, Fluid Jet Polishing, is presented - work in collaboration with Chubu University. Numerical design of surfaces, required for generating tool-paths, is investigated, along with validation techniques for two test-cases, E-ELT mirror segments and IXO mirror segment slumping moulds. Conformal tools are not well suited to correct surface-errors with dimensions smaller than the contact area between tool and workpiece. A method with considerable potential is developed to analyse spatial-frequency error-content, and used to change the size of the contact area during a process run, as opposed to the constant-sized contact area that is state-of-the-art. These numerical methods reduce dependence on empirical data and operator experience, constituting important steps towards the ultimate and ambitious goal of fully-integrated process-automation

Advances in Vibration Analysis Research

Vibrations are extremely important in all areas of human activities, for all sciences, technologies and industrial applications. Sometimes these Vibrations are useful but other times they are undesirable. In any case, understanding and analysis of vibrations are crucial. This book reports on the state of the art research and development findings on this very broad matter through 22 original and innovative research studies exhibiting various investigation directions. The present book is a result of contributions of experts from international scientific community working in different aspects of vibration analysis. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement