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

Measurement Science and Technology

Volumn 21, Issue 11, 2010, Pages

  Bartl, Guido ^a   Krystek, Michael ^a   Nicolaus, Arnold ^a   Giardini, Walter ^b  

^a PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

^b NATIONAL MEASUREMENT INSTITUTE   (Australia)

Author keywords

Absolute radius; Avogadro constant; Diameter; Interferometry; Roundness; Silicon sphere; Sphere interferometer; Sphericity; Stitching; Sub aperture

Indexed keywords

INTERFEROMETERS; INTERFEROMETRY; STITCHING (METAL JOINING); UNCERTAINTY ANALYSIS; VOLUME MEASUREMENT;

ABSOLUTE RADIUS; AVOGADRO CONSTANT; DIAMETER; ROUNDNESS; SPHERICITY; SUB-APERTURES;

SPHERES;

EID: 78149435665     PISSN: 09570233     EISSN: 13616501     Source Type: Journal    
DOI: 10.1088/0957-0233/21/11/115101     Document Type: Article

References (26)

1. Becker P, Friedrich H, Fujii K, Giardini W, Mana G, Picard A, Pohl H-J, Riemann H and Valkiers S 2009 The Avogadro constant determination via enriched silicon-28 Meas. Sci. Technol. 20 092002
2. Leistner A J and Giardini W J 1994 Fabrication and sphericity measurements of single-crystal silicon spheres Metrologia 31 231-43
3. Nicolaus R A and Elster C 2005 Diameter determination of Avogadro spheres #1 and #2 IEEE Trans. Instrum. Meas. 54 872-6
4. Elßner K-E, Grzanna J and Schulz G 1980 Interferentielle Absolutprüfung von Sphärizitätsnormalen J. Mod. Opt. 27 563-80
5. Selberg L A 1992 Radius measurement by interferometry Opt. Eng. 31 1961-6
6. Otsubo M, Okada K and Tsujiuchi J 1994 Measurement of large plane surface shapes by connecting small-aperture interferograms Opt. Eng. 33 608-13
7. Murphy P, Forbes G, Fleig J, Dumas P and Tricard M 2003 Stitching interferometry: a flexible solution for surface metrology Optics Photon. News 14 38-43
8. Sjödahl M and Oreb B F 2002 Stitching interferometric measurement data for inspection of large optical components Opt. Eng. 41 403-8
9. Jansen M, te Voert M and Haitjema H 2010 Calibration of CMM reference spheres using stitching interferometry Proc. 10th Int. EuSPEN Conference (Delft) vol 1, pp 79-82
10. Griesmann U, Soons J and Wang Q 2004 Measuring form and radius of spheres with interferometry Ann. CIRP 53 451-4
11. Schmitz T L, Evans C J, Davies A and Estler W T 2002 Displacement uncertainty in interferometric radius measurements Ann. CIRP 51 451-4
12. Giardini W, Manson P, Wouters M, Warrington B, Ward B, Bignell N, Walsh C, Jaatinen E and Kenny M 2009 Density of a single-crystal natural silicon sphere IEEE Trans. Instrum. Meas. 58 908-14
13. Borys M, Gläser M and Mecke M 2007 Mass determination of silicon spheres used for the Avogadro project Measurement 40 785-90
14. Bettin H and Toth H 2006 Solid density determination by the pressure-of-flotation method Meas. Sci. Technol. 17 2567-73
15. Bartl G and Nicolaus R A 2009 Investigations on diameter measurements of the Avogadro silicon sphere dependent on the position in the field of view of the interferometer optics IEEE Trans. Instrum. Meas. 58 919-23
16. Bartl G and Nicolaus A 2009 Influence of the distribution of measuring points on the mean diameter determination of the Avogadro project's silicon spheres Meas. Sci. Technol. 20 065104
17. Cohen-Tannoudji C, Diu B and Laloë F 1977 Quantum Mechanics: Part 1 (New York: Wiley)
18. Wyant J C and Creath K 1992 Basic Wavefront Aberration Theory for Optical Metrology (Applied Optics and Optical Engineering Series vol XI) (New York: Academic) chapter 1
19. Born M and Wolf E 1989 Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light 6th edn (New York: Pergamon)
20. Noll R J 1976 Zernike polynomials and atmospheric turbulence J. Opt. Soc. Am. 66 207-11
21. Golub G 1965 Numerical methods for solving linear least squares problems Numer. Math. 7 206-16
22. Golub G H and Van Loan C F 1966 Orthogonalization and least squares Matrix Computations 3rd edn (Baltimore, MD: Johns Hopkins University Press) p 206 ff.
23. Nelder J A and Mead R 1965 A simplex method for function minimization Comput. J. 7 308-13
24. Sacconi A and Pasin W 1994 An intercomparison of roundness measurements between ten European national standards laboratories Measurement 13 119-28
25. Haitjema H, Bosse H, Frennberg M, Sacconi A and Thalmann R 1996 International comparison of roundness profiles with nanometric accuracy Metrologia 33 67-73
26. Neugebauer M 2001 Uncertainty analysis for roundness measurements by the example of measurements on a glass hemisphere Meas. Sci. Technol. 12 68-76