OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 10 — Apr. 1, 1999
  • pp: 2018–2027

Absolute measurement of planarity with Fritz’s method: uncertainty evaluation

Vincenzo Greco, Riccardo Tronconi, Ciro Del Vecchio, Marcelo Trivi, and Giuseppe Molesini  »View Author Affiliations


Applied Optics, Vol. 38, Issue 10, pp. 2018-2027 (1999)
http://dx.doi.org/10.1364/AO.38.002018


View Full Text Article

Enhanced HTML    Acrobat PDF (3013 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Fritz’s method [Opt. Eng. 23, 379 (1984)] of using Zernike polynomials to assess the absolute planarity of test plates is revisited. A refinement is described that takes into account the data decorrelation that appears in experiments. An uncertainty balance is defined by propagation of error contributions through the steps of the method. The resultant measuring procedure is demonstrated on a data set from experiments, and a nanometer level of uncertainty is achieved.

© 1999 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

History
Original Manuscript: October 5, 1998
Revised Manuscript: December 22, 1998
Published: April 1, 1999

Citation
Vincenzo Greco, Riccardo Tronconi, Ciro Del Vecchio, Marcelo Trivi, and Giuseppe Molesini, "Absolute measurement of planarity with Fritz’s method: uncertainty evaluation," Appl. Opt. 38, 2018-2027 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-10-2018


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893). [CrossRef]
  2. C. Ai, J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32, 4698–4705 (1993). [CrossRef] [PubMed]
  3. K.-E. Elssner, A. Vogel, J. Grzanna, G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437–2446 (1994). [CrossRef] [PubMed]
  4. C. J. Evans, R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996). [CrossRef] [PubMed]
  5. J. Chen, D. Song, R. Zhu, Q. Wang, L. Chen, “Large-aperture high-accuracy phase-shifting digital flat interferometer,” Opt. Eng. 35, 1936–1942 (1996). [CrossRef]
  6. P. Hariharan, “Interferometric testing of optical surfaces: absolute measurement of flatness,” Opt. Eng. 36, 2478–2481 (1997). [CrossRef]
  7. C. J. Evans, “Comment on the paper ‘Interferometric testing of optical surfaces: absolute measurement of flatness,’” Opt. Eng. 37, 1880–1882 (1998). [CrossRef]
  8. I. Powell, E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579–2588 (1998). [CrossRef]
  9. R. E. Parks, C. J. Evans, P. O. Sullivan, L.-Z. Shao, B. Loucks, “Measurement of the LIGO pathfinder optics,” in Optical Manufacturing and Testing II, H. P. Stahl, ed., Proc. SPIE3134, 95–111 (1997). [CrossRef]
  10. R. E. Parks, L.-Z. Shao, C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37, 5951–5956 (1998). [CrossRef]
  11. G. Schulz, J. Schwider, “Precise measurement of planeness,” Appl. Opt. 6, 1077–1084 (1967). [CrossRef] [PubMed]
  12. R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978). [CrossRef]
  13. B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23, 379–383 (1984). [CrossRef]
  14. C. J. Evans, R. E. Parks, P. J. Sullivan, G. S. Taylor, “Visualization of surface figure by the use of Zernike polynomials,” Appl. Opt. 34, 7815–7819 (1995). [CrossRef] [PubMed]
  15. E.g., code v (Optical Research Associates, Pasadena, Calif.)
  16. J. S. Loomis, fringe User’s Manual—Version 2 (University of Arizona, Tucson, Ariz., November1976).
  17. C.-J. Kim, R. R. Shannon, “Catalog of Zernike polynomials,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, New York, 1987), Vol. 10, pp. 193–221.
  18. V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998). [CrossRef]
  19. V. B. Gubin, 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).
  20. S. Brandt, Statistical and Computational Methods in Data Analysis, 2nd ed. (North-Holland, Amsterdam, 1970), p. 216.
  21. Bureau International des Poids et MesuresInternational Electrotechnical CommissionInternational Federation of Clinical ChemistryInternational Organization for StandardizationInternational Union of Pure and Applied PhysicsInternational Union of Pure and Applied ChemistryInternational Organization of Legal Metrology, Guide to the Expression of Uncertainty in Measurements (International Organization for Standardization, Geneva, 1993).
  22. Mark IVxp (Zygo Corporation, Middlefield, Conn.).
  23. R. Tronconi, “Misura assoluta di planarità con metodi interferometrici,” laurea dissertation (University of Florence, Florence, Italy, April1997).
  24. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983). [CrossRef] [PubMed]
  25. W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).
  26. V. B. Gubin, V. N. Sharonov, “Absolute calibration of spherical surfaces,” Sov. J. Opt. Technol. 57, 554–555 (1990).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited