Characterizing the New Sphere Interferometer for the Diameter Determination of the Avogadro Spheres

Abstract:

For the aimed redefinition of the SI-unit kilogram the international Avogadro group is to measure the amount of substance of a silicon sphere with a relative uncertainty of better than 2 x 10^-8. Up to now 3.0 x 10^-8 is reached, mainly caused by the 2.7 x 10^-8 uncertainty of the volume determination. Which itself is essentially affected by the uncertainty of wave front distortion caused by optical fabrication errors and possible misalignment. To gain more information on how the wave front distortion influences the result a new interferometer with improved optics and rather large changes in the etalon is built up. A comparison of the measurements of one sphere taken with two different interferometers gives direct access to this information. Additionally a ray tracing software is being developed to simulate the alignment and measurement processes. Following the alignment steps the resulting positioning uncertainties of each element can be simulated and elements which contribute mainly to the uncertainty can be identified. This gives evidence where an improvement of the alignment techniques is most effective and necessary. With the additional use of Monte Carlo method based calculations the influence on the measurement results can be determined.

• Periodical: Key Engineering Materials (Volume 613)
• Pages: 11-16
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.613.11
• Online since: May 2014
• Authors: Torsten Mai*, Guido Bartl, Arnold Nicolaus, Andreas Peter
• Keywords: Avogadro Constant, Interferometry, Metrology, Silicon Sphere

References

[1] G. Girard, The third periodic verification of Nation Prototypes of the kilogram (1988-1992), Metrologia, 31(4) (1994) 317-336.

DOI: 10.1088/0026-1394/31/4/007

[2] P. Becker et al., Counting atoms in a 28Si crystal for a new kilogram definition, Metrologia, 48(2) (2011) S1-S13.

[3] B. P. Kibble and G. J. Hunt, A Measurement of the Gyromagnetic Ratio of the Proton in a Strong Magnetic Field, Metrologia, 15(4) (1979) 5-30.

DOI: 10.1088/0026-1394/15/1/002

[4] BIPM 2010 CCM Report of the 12th meeting (2010) to the CIPM, Recommendation G1, published on http: /www. bipm. org.

[5] G. Bartl, H. Bettin, M. Krystek, T. Mai, R. A. Nicolaus and A. Peter, A Volume determination of the Avogadro spheres of highly enriched 28Si with aspherical Fizeau interferometer, Metrologia, 48(2) (2011) S96-S103.

DOI: 10.1088/0026-1394/48/2/s12

[6] R. A. Nicolaus, Precise method of determining systematic errors in phase-shifting interferometry on Fizeau interferences, Appl. Opt., 32 (1993) 6380-6386.

DOI: 10.1364/ao.32.006380

[7] M. A. Heráez, D. A. Lalor and M. A. Gdeisat, Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path, Appl. Opt., 41 (2002) 7437-7444.

DOI: 10.1364/ao.41.007437