Algorithms for Surface Texture Profiles and Parameters

This thesis is concerned with the development of algorithms for the reliable calculation of surface texture profile parameters published by the International Organisation for Standardisation (ISO). Some of these parameters are impossible to compute exactly given a discrete set of measured profile points. A need to represent the profile as a continuous function therefore arises, a need that occurs in many metrological applications. By reconstructing surface profiles accurately, with elements of numerical safety, we can provide a mathematically sound basis on which to compute surface texture profile parameters. As an important direct benefit, parameters involving the integrals of profiles can be calculated exactly from the interpolant introduced. Another advantage of a continuous representation is that it allows measured surface profile data, that is shown to be inherently non-uniform in the x-axis spacing, to be re-sampled at uniform intervals as it has been discovered that standard filtering
techniques are apparently ineffective with non-uniform spacing. A novel method for data fitting discretely sampled surface profiles is presented with the advantages clearly stated. This provides a solid basis for profile parameters to be calculated upon and also intelligent functions for the evaluation of measurement uncertainty to be appended, which is equally important for the evolution of algorithms designed to be the complete evaluation of a parameter with a traceable measure of uncertainty.