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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 11 — May. 28, 2007
  • pp: 6809–6816

Iterative algorithm for three flat test

Maurizio Vannoni and Giuseppe Molesini  »View Author Affiliations

Optics Express, Vol. 15, Issue 11, pp. 6809-6816 (2007)

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Absolute planarity measurements by interferometry are classically made using three flats, compared two by two in the course of four or more tests. Data reduction is performed with various analytical methods. Here we present instead a data processing algorithm that converges to solution numerically by iteration. Examples are presented both on synthetic interferograms and on experimental data. High accuracy and versatility of the approach are demonstrated.

© 2007 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4800) Instrumentation, measurement, and metrology : Optical standards and testing
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 16, 2006
Revised Manuscript: March 19, 2007
Manuscript Accepted: March 20, 2007
Published: May 18, 2007

Maurizio Vannoni and Giuseppe Molesini, "Iterative algorithm for three flat test," Opt. Express 15, 6809-6816 (2007)

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  1. Lord Rayleigh, "Interference bands and their application," Nature (London) 48, 212-214 (1893). [CrossRef]
  2. H. Barrell and R. Marriner, "Liquid surface interferometry," Nature (London) 162, 529-530 (1948). [CrossRef]
  3. G. D. Dew, "The measurement of optical flatness," J. Sci. Instrum. 43, 409-415 (1966). [CrossRef] [PubMed]
  4. R. Brünnagel, H. -A. Oehring, and K. Steiner, "Fizeau interferometer for measuring the flatness of optical surfaces," Appl. Opt. 7, 331-335 (1967). [CrossRef]
  5. J. P. Marioge, B. Bonino, and M. Mullot, "Standard of flatness: its application to Fabry-Perot interferometers," Appl. Opt. 14, 2283-2285 (1975). [CrossRef] [PubMed]
  6. K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, "Establishing a flatness standard," Appl. Opt. 33, 2437-2446 (1994). [CrossRef] [PubMed]
  7. J. Chen, D. Song, R. Zhu, Q. Wang, and L. Chen, "Large-aperture high-accuracy phase-shifting digital flat interferometer," Opt. Eng. 35, 1936-1942 (1996). [CrossRef]
  8. I. Powell and E. Goulet, "Absolute figure measurements with a liquid-flat reference," Appl. Opt. 37, 2579-2588 (1998). [CrossRef]
  9. M. Vannoni and G. Molesini, "Validation of absolute planarity reference plates with a liquid mirror," Metrologia 42, 389-393 (2005). [CrossRef]
  10. G. Schulz and J. Schwider, "Precise measurement of planeness," Appl. Opt. 6,1077-1084 (1967). [CrossRef] [PubMed]
  11. G. Schulz, J. Schwider, C. Hiller, and B. Kicker, "Establishing an optical flatness standard," Appl. Opt. 10, 929-934 (1971). [CrossRef] [PubMed]
  12. J. Grzanna and G. Schulz, "Absolute testing of flatness standards at square-grid points," Opt. Commun. 77, 107-112 (1990). [CrossRef]
  13. G. Schulz and J. Grzanna, "Absolute flatness testing by the rotation method with optimal measuring error compensation," Appl. Opt. 31, 3767-3780 (1992). [CrossRef] [PubMed]
  14. G. Schulz, "Absolute flatness testing by an extended rotation method using two angles of rotation," Appl. Opt. 32, 1055-1059 (1993). [CrossRef] [PubMed]
  15. J. Grzanna, "Absolute testing of optical flats at points on a square grid: error propagation," Appl. Opt. 33, 6654-6661 (1994). [CrossRef] [PubMed]
  16. B. (B). F. Oreb, D. I. Farrant, C. J. Walsh, G. Forbes, and P. S. Fairman, "Calibration of a 300-mm-Aperture Phase-Shifting Fizeau Interferometer," Appl. Opt. 39, 5161-5171 (2000). [CrossRef]
  17. S. Sonozaki, K. Iwata, and Y. Iwahashi, "Measurement of profiles along a circle on two flat surfaces by use of a Fizeau interferometer with no standard," Appl. Opt. 42, 6853-6858 (2003). [CrossRef] [PubMed]
  18. B. S. Fritz, "Absolute calibration of an optical flat," Opt. Eng. 33, 379-383 (1984).
  19. C. Ai and J. C. Wyant, "Absolute testing of flats by using even and odd functions," Appl. Opt. 32, 4698-4705 (1993). [CrossRef] [PubMed]
  20. C. J. Evans and R. N. Kestner, "Test optics error removal," Appl. Opt. 35,1015-1021 (1996). [CrossRef] [PubMed]
  21. P. Hariharan, "Interferometric testing of optical surfaces: absolute measurement of flatness," Opt. Eng. 36, 2478-2481 (1997). [CrossRef]
  22. C. J. Evans, "Comment on the paper ‘Interferometric testing of optical surfaces: absolute measurement of flatness," Opt. Eng. 37, 1880-1882 (1998). [CrossRef]
  23. R. E. Parks, L.-Z. Shao, and C. J. Evans, "Pixel-based absolute topography test for three flats," Appl. Opt. 37, 5951-5956 (1998). [CrossRef]
  24. V. Greco, R. Tronconi, C. Del Vecchio, M. Trivi, and G. Molesini, "Absolute measurement of planarity with Fritz’s method: uncertainty evaluation," Appl. Opt. 38, 2018-2027 (1999). [CrossRef]
  25. K. R. Freischlad, "Absolute interferometric testing based on reconstruction of rotational shear," Appl. Opt. 40, 1637-1648 (2001). [CrossRef]
  26. M. F. Küchel, "A new approach to solve the three flat problem," Optik 112, 381-391 (2001). [CrossRef]
  27. U. Griesmann, "Three-flat test solutions based on simple mirror symmetry," Appl. Opt. 45, 5856-5865 (2006). [CrossRef] [PubMed]
  28. W. Gao, P.S. Huang, T. Yamada, S. Kiyono, "A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers," Precision Engineering 26, 396-404 (2002). [CrossRef]
  29. M. Schulz and C. Elster, "Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution," Opt. Eng. 45, 060503 (2006). [CrossRef]
  30. V. Greco and G. Molesini, "Micro-temperature effects on absolute flatness test plates," Pure Appl. Opt. 7, 1341-1346 (1998). [CrossRef]
  31. V. B. Gubin and V. N. Sharonov, "Absolute calibration of spherical surfaces," Sov. J. Opt. Technol. 57, 554-555 (1990).
  32. .International Bureau of Weights and Measures, International Electrotechnical Commission, International Federation of Clinical Chemistry, International Organization for Standardization, International Union of Pure and Applied Chemistry, International Union of Pure and Applied Physics, and International Organization of Legal Metrology, Guide to the Expression of Uncertainty in Measurements (International Organization for Standardization, Geneva, 1993).

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