SPHERICITY ANALYSIS OF SOLID DENSITY STANDARDS

An analysis of dimensional sphericity measurement data is presented, a pplied to near-perfect single-crystal silicon spheres used as solid de nsity standards and for the precise determination of the Avogadro cons tant. Using the formal correspondence of the expansion of the three-di mensional measurement data set in terms of spherical harmonics with th e theory of angular momentum in quantum mechanics, invariant quantitie s are determined, allowing objective assessment of fabrication and mea surement process variables. Two methods for sphericity analysis are pr esented and applications to solid density standards are given. Within the limitations of the quantity and quality of the measurement data te sted, our results are consistent with qualitative assessments of spher e topography and have revealed a structure in the spectral distributio n of spherical harmonic amplitudes. (C) 1998 American Institute of Phy sics. [S0034-6748(98)04602-4].