Interferometric determination of the topographies of absolute sphere radii using the sphere interferometer of PTB

This paper presents a method to reconstruct the absolute shape of a sphere—i.e. a topography of radii—using the sphere interferometer of PTB in combination with a stitching approach. The method allows for the reconstruction of absolute radii instead of the relative shape deviations which result from conventional sphericity measurements. The sphere interferometer was developed for the volume determination of spherical material measures—in particular the spheres of the Avogadro project—by precise diameter measurements with an uncertainty of 1 nm or less. In the scope of the present work a procedure has been implemented that extends the applicability of the interferometer to fields where not the volume or diameter but the direction-dependent radii are of interest. The results of the reconstruction were compared quantitatively to the independent results of sphericity measurements from CSIRO.