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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 13 — May. 1, 2009
  • pp: 2536–2541

Method for absolute flatness measurement of optical surfaces

Chen Xu, Lei Chen, and Jiayi Yin  »View Author Affiliations

Applied Optics, Vol. 48, Issue 13, pp. 2536-2541 (2009)

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To determine the absolute flatness deviations of optical surfaces, a novel method using two optical plates to achieve the absolute flatness test is presented. Absolute deviations of three surfaces, the rear surface of plate I and the front and rear surfaces of plate II, are obtained by four measurements. Wavefront error due to the inhomogeneity of plate II is measured beforehand and is then subtracted from the test results. Vertical profiles of the three surfaces are compared with the measurement results obtained by Zygo’s three-flat application. Good agreement validates our method. The advantage of our method is that only one transmission flat is needed during the absolute test, which is especially useful for large-aperture interferometer calibration.

© 2009 Optical Society of America

OCIS Codes
(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: January 5, 2009
Revised Manuscript: April 12, 2009
Manuscript Accepted: April 13, 2009
Published: April 27, 2009

Chen Xu, Lei Chen, and Jiayi Yin, "Method for absolute flatness measurement of optical surfaces," Appl. Opt. 48, 2536-2541 (2009)

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  1. Lord Rayleigh, “Interference bands and their application,” Nature 48, 212-214 (1893). [CrossRef]
  2. 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]
  3. I. Powell and E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579-2588 (1998). [CrossRef]
  4. M. Vannoni and G. Molesini, “Validation of absolute planarity reference plates with a liquid mirror,” Metrologia 42, 389-393(2005). [CrossRef]
  5. G. Schulz and J. Schwider, “Precise measurement of planeness,” Appl. Opt. 6, 1077-1084 (1967). [CrossRef] [PubMed]
  6. G. Schulz and J. Schwider, “Establishing an optical flatness,” Appl. Opt. 10, 929-934 (1971). [CrossRef] [PubMed]
  7. B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23, 379-383 (1984).
  8. J. Grzanna and G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107-112 (1990). [CrossRef]
  9. 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]
  10. G. Schulz, “Absolute flatness testing by an extended rotation method using two angles of rotation,” Appl. Opt. 32, 1055-1059 (1993). [CrossRef] [PubMed]
  11. C.Ai and J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32, 4698-4705 (1993). [CrossRef] [PubMed]
  12. C.Ai, J. C. Wyant, L.-Z. Shao, and R. E. Parks, “Method and apparatus for absolute measurement of entire surfaces of flats,” U.S. patent 5,502,566 (26 March 1996).
  13. 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]
  14. K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437-2446 (1994). [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. C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996). [CrossRef] [PubMed]
  17. V. Greco and G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341-1346(1998). [CrossRef]
  18. 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]
  19. 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]
  20. K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40, 1637-1648(2001). [CrossRef]
  21. M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
  22. U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45, 5856-5865 (2006). [CrossRef] [PubMed]
  23. F. Morin and S. Bouillet, “Absolute interferometric measurement of flatness: application of different methods to test a 600 mm diameter reference flat,” Proc. SPIE 6616, 1-11(2007).
  24. U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46, 1(2007). [CrossRef]
  25. M. Vannoni and G. Molesini, “Absolute planarity with three-flat test: an iterative approach with Zernike polynomials,” Opt. Express 16, 340-354 (2008). [CrossRef] [PubMed]
  26. M. Vannoni and G. Molesini, “Three-flat test with plates in horizonatal posture,” Appl. Opt. 47, 2133-2145 (2008). [CrossRef] [PubMed]
  27. J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. 24, 3059-3061 (1985). [CrossRef] [PubMed]
  28. V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147-148 (1990).

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