An investigation into the surface characteristics of three-dimensional objects
This thesis presents three-dimensional surface metrology techniques suitable for the appraisal 'of curved surfaces. Instrument requirements for measuring 3-D curved surfaces are discussed and four instruments selected which meet these requirements. These instruments are a Laser Radius-scope, Fizeau Interferometer, Laser Ranging Probe and a Stylus Profilometer. Numerical algorithms for assessing the data from these instruments are then considered, with particular emphasis being placed on the evaluation of the radius of curvature of the surface, removal of this best-fit sphere from the data and visualisation of the resulting errors of form. New circle and sphere-fitting algorithms are presented for radius of curvature analysis. These numerical methods, together with a number of standard, well documented routines (least-squares circle and sphere) are then tested for their sensitivity to a number of sample parameters on ideal, computer generated data sets. The parameters tested are sample length/area, radius of curvature, centre offset and surface roughness. The new techniques show a considerable improvement in estimating the radius of the test data; in the presence of + I0.00/*m peak-to-valley surface roughness, the new circle-fit routine produced a radius error of 0.32/xm as opposed to -0.85/*m for the least-squares circle routine, whilst the new sphere-fit had a radius error of 2.29jum compared to the least-squares sphere's error of -3.64/xm. The new sphere-fit also reduces the computation times on a 66MHz. 486DX2 Personal Computer from 14.89 seconds for least-squares sphere to 0.66 seconds. Four studies are then carried out on nominally spherical samples of varying dimensions, radius of curvature and surface finish. The studies assess the radius of curvature of the samples, either directly for the Laser Radius-scope and Fizeau Interferometer or, in the case of the Laser Ranging Probe and the Stylus Profilometer, by the application of the numerical routines previously tested. The advantages, limitations and faults of each instrument are discussed and it is concluded that despite the stylus profiler's instrumentational flaws, it offers the most flexible method of measuring the three-dimensional surface profiles of curved surfaces.