Jung, Markus Manfred
(1999)
Assessment of curved, rotationally symmetric surfaces in three dimensions.
*University of Southampton, School of Engineering Sciences, Doctoral Thesis*, 131pp.

## Abstract

Methods for the assessment of curved, rotationally symmetric surfaces in three dimensions are developed and outlined in this thesis. The assessment of electrical switching contacts, contact lens moulds and aspherical leps surfaces is demonstrated. Discrete data for surface assessment is obtained by surface measurement with a profilometer. Hence, surface measurement refers to simultaneous measurement of surface form and surface irregularity. The data is defined in a Cartesian co-ordinate system, and a data set consists of up to 27,000 discrete points on an uniform grid. The grid spacing in x and y is typically between 25um and 125um. The resolution of the data in the vertical axis is lOnm (Inm = 10"9 metre). The key aspects of the research are as follows:

A method for data interpretation is proposed. The method is primarily intended to simplify surface assessment of aspherical surfaces. It consists of three key elements: pre-processing, form characterisation and data decomposition into error types. Pre-processing detects the position and orientation of a surface. The surface is then aligned and a separation of surface geometry from position and orientation is achieved. For pre-processing four algorithms are developed, outlined and compared. Form characterisation of rotationally symmetric, aspherical surfaces is then considered. A least squares method is used to fit discrete data to a general solution function in explicit notation. Various problems related to form characterisation with explicit functions are addressed and solutions are presented. Finally, methods for data decomposition into error types are presented. A standardised decomposition method (BS-ISO 10110-5) is compared with an alternative method that is developed in this research. General recommendations for the measurement and the assessment of aspherical surfaces are given.

A method for the selection of a form characterisation algorithm for the assessment of nominally spherical surfaces is proposed. Many different sphere fitting algorithms are reported in literature and the best-fit parameters, centre co-ordinates and radius, vary on the same set of discrete data with the algorithm that is used for form characterisation. Five sphere fitting algorithms are investigated in this research: linear and non-linear least squares sphere fit, minimum zone sphere fit, four-point sphere fit and sphere fit by error curve analysis. In conclusion to the investigation it is proposed to use the surface irregularity distribution as a criteria for the selection of a sphere fitting algorithm. The data sampling strategy, distribution of discrete points within a segment and size and location of a segment on a surface, is also investigated. General recommendations for the measurement and the assessment of nominally spherical surfaces are given.

The idea of computer aided surface assessment (CASA) is evolved. In CASA, data visualisation and data interpretation are combined for processing of discrete data from the measurement of a surface. Software for computer aided surface assessment is developed and outlined in this thesis.

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