Simulative determination of the wavefront uncertainty of PTB’s Sphere Interferometer II

For redefining the SI-unit kilogram preconditions have to be fulfilled by the contributing experiments. At the moment the most challenging of these is the need of relative measurement uncertainties below 2 x 10^-8. For the X-Ray-Crystal-Density-Method this uncertainty is currently already exhausted by the volume measurement of the silicon spheres because of the conservative estimation of the influence of alignment deviations and surface and material errors. For improving the knowledge of this uncertainty source an optical ray tracing simulation and analysis software were developed. The sequential ray tracing calculates the ray paths from the multimode fiber to the camera surface and considers multiple reflections in the Fizeau-etalon and the measured topographies of the silicon spheres. The analysis software then calculates the interferograms on the camera regarding the coherence properties of the simulated raypaths. Additionally a Monte-Carlo-module for simulating the alignment process is implemented. The results show that the uncertainty from deviations of the real wavefronts from the optical design can be reduced from currently around 2 x 10^-8 to 7.5 x 10^-9 in the future.