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Applied Optics

Applied Optics


  • Vol. 37, Iss. 25 — Sep. 1, 1998
  • pp: 5951–5956

Pixel-based absolute topography test for three flats

Robert E. Parks, Lianzhen Shao, and Chris J. Evans  »View Author Affiliations

Applied Optics, Vol. 37, Issue 25, pp. 5951-5956 (1998)

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We demonstrate a method of performing the absolute three-flat test by using reflection symmetries of the surfaces and an algorithm for generating the rotation of arrays of pixel data. Most of the operations involve left/right and top/bottom flips of data arrays, operations that are very fast on most frame grabbers and are available on most commercial phase-measuring interferometers. We demonstrate the method with simulated data as well as with actual data from 150-mm-diameter surfaces that are flat to less than 25 nm peak to valley.

© 1998 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4630) Instrumentation, measurement, and metrology : Optical inspection

Original Manuscript: April 30, 1998
Revised Manuscript: November 26, 1998
Published: September 1, 1998

Robert E. Parks, Lianzhen Shao, and Chris J. Evans, "Pixel-based absolute topography test for three flats," Appl. Opt. 37, 5951-5956 (1998)

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  1. F. H. Rolt, Gauges and Fine Measurement (Macmillan, London, 1928).
  2. G. Schulz, J. Schwider, “Precise measurement of planeness,” Appl. Opt. 6, 1077–1084 (1967). [CrossRef] [PubMed]
  3. B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23, 379–383 (1984). [CrossRef]
  4. C. Ai, J. C. Wyant, “Absolute testing of flats decomposed into even and odd functions,” in Interferometry Surface Characterization and Testing, K. Creath, E. Grievenkamp, eds., Proc. SPIE1776, 73–83 (1992). [CrossRef]
  5. C. J. Evans, R. E. Parks, “Absolute calibration of spherical surfaces,” in Optical Fabrication and Testing, Vol. 13 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 185–187.
  6. Lord Raleigh, “Interference bands and their application,” Nature (London) 48, 212–214 (1893);“The interferometer,” Nature (London) 59, 533 (1899). [CrossRef]
  7. R. Bunnagel, H. Oehring, K. Steiner, “Fizeau interferometer for measuring the flatness of optical surfaces,” Appl. Opt. 7, 331–335 (1968). [CrossRef] [PubMed]
  8. H. Barrell, R. Marriner, “Liquid surface interferometry,” Nature (London) 162, 529–530 (1948). [CrossRef]
  9. G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409–415 (1966). [CrossRef] [PubMed]
  10. R. W. Porter, Amateur Telescope Making (Scientific American, New York, 1933), Vol. 3, p. 234.
  11. W. B. Emerson, “Determination of planeness and bending of optical flats,” J. Res. Natl. Bur. Stand. 49, 241 (1952). [CrossRef]
  12. J. B. Saunders, Precision Measurements, A. C. S. Van Heel, ed. (North-Holland, Amsterdam, 1967), pp. 8–11.
  13. B. E. Truax, “Absolute calibration method for laser Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313–1316 (1973).
  14. K-E. Elssner, R. Burow, J. Grzanna, R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649–4661 (1989). [CrossRef] [PubMed]
  15. R. Cobleigh, Handy Farm Devices and How to Make Them (1909; reprinted by Lyons and Burford, New York, 1996).
  16. L. Tschirf, “Pruefung von Abricht-Linealen,” Arch. Technisch. Messen 8224-1 (1941).
  17. C. J. Evans, R. J. Hocken, W. T. Estler, “Self-calibration: reversal, redundancy, error separation and ‘absolute testing,’” CIRP Ann. 45/2, 617–634 (1996). [CrossRef]
  18. G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring error compensation,” Appl. Opt. 31, 3767–3780 (1992). [CrossRef] [PubMed]
  19. See, for example, J. E. Greivenkamp, J. H. Bruning, “Phase shifting interferometry,” in Optical Workshop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  20. C. Ai, J. C. Wyant, “Absolute testing of flats using even and odd functions,” Appl. Opt. 32, 4698–4705 (1993). [CrossRef] [PubMed]
  21. C. Ai, J. C. Wyant, “Modified three-flat method using even and odd functions,” in Optical Fabrication and Testing, Vol. 24 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 71–74.
  22. C. J. Evans, R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015–1021 (1996). [CrossRef] [PubMed]
  23. 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]
  24. R. E. Spero, S. E. Whitcomb, “The Laser Interferometer Gravitational-wave Observatory (LIGO),” Opt. Photon. News35–39 (July1995).
  25. W. T. Estler, C. J. Evans, L. Shao, “Uncertainty estimation for multiposition form error metrology,” Precis. Eng. 21, 72–82 (1997). [CrossRef]

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