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Optical simulation of the new PTB sphere interferometer

For the redefinition of the SI-unit kilogram the Avogadro constant needs to be determined with lowest possible uncertainty. The approach which is followed by an international group including the PTB is the XRCD-method (Azuma et al 2015 Metrologia 52 360). Currently the uncertainty of the silicon sphere volume determination is the main contribution to the uncertainty of the Avogadro constant and therefore critical for reaching the self-set goal of underrunning a relative uncertainty of 1.5×10−8. The volume uncertainty itself is dominated by the wave-front deformation uncertainty which occurs due to optical imperfections in the measurement system. Up to now this type of uncertainty was only roughly estimated. This paper presents results from a self developed optical raytracing software which allows the main deviations of the real optical system from the ideal optical design to be investigated. With this software a complete sphere measurement can be simulated which helps to determine the influence of the system imperfections. In result the relative uncertainty contribution of the wave-front uncertainties to the volume measurement can be reduced to 4.5×10−9.