Influence of the distribution of measuring points on the mean diameter determination of the Avogadro project's silicon spheres

Abstract

The members of the International Avogadro Project are aiming at the redetermination of Avogadro's constant with a relative uncertainty of less than 2×10−8 in order to be qualified for the redefinition of the kilogram. Therefore, among other quantities, the volume of a sphere made of a silicon single crystal has to be determined very precisely with a diameter uncertainty of 0.3 nm. A special Fizeau interferometer with spherical reference faces has been developed at PTB providing the required precision in absolute interferometry and a generous coverage of the surface of the sphere at the same time. Due to the intrinsic imbalanced distribution of measurement positions given by the setup, an equalization has to be performed without introducing a numerical error. In this paper an appropriate procedure using point distributions on a sphere is described and characterized with regard to the number of points involved.