Comparative calculations of the volume of nearly perfect spheres using profilometer data

Three independently developed and conceptually different algorithms to calculate the volume of nearly perfect spheres with high precision have been applied and compared. Spherical harmonic decomposition, direct numerical integration and B-spline interpolation over radial data points have been applied to common data sets derived from sphericity measurements on 93 mm nominal diameter spheres manufactured from single crystals of silicon with maximum radial peak-to-valley errors ranging from 54 nm to 259 nm. Sphericity measurements are relative to an arbitrary datum sphere and for this comparison of calculated volume they have therefore been normalized using a nominal value for mean diameter. Five measurement sets on four different spheres were analysed and the range of calculated volumes for the three algorithms varied from 0,8 parts in 10 9 to 4 parts in 10 9 .