Abstract

Absolute testing of spherical surfaces is a technological necessity because of increased accuracy requirements. In a Fizeau setup, the main part of the interferometer deviations thereby comes from the reference surface. We demonstrate the validity of an absolute testing procedure for the reference surface that has been proposed earlier. The procedure relies on the decomposition of the surface deviations into odd and even parts and could be used in partially coherent illumination. The odd deviations are obtained from a basic and a 180°-rotated position of an auxiliary sphere, and the even deviations can be measured with the help of a cat’s eye position in double pass using an opaque half screen in the interferometer aperture.

© 2008 Optical Society of America

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References

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  1. G. Schulz and J. Schwider, “Interferometric testing of smooth surfaces,” Progress in Optics, Vol. XIII, E.Wolf, ed. (Elsevier, 1976), pp. 93-167.
    [Crossref]
  2. R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56-63 (1978).
  3. B. S. Fritz, “Absolute calibration of an optical flat” Opt. Eng. 23, 379-383 (1984).
  4. C. Ai and J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32, 4698-4705 (1993).
    [Crossref] [PubMed]
  5. C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996).
    [Crossref] [PubMed]
  6. C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
    [Crossref]
  7. R. E. Parks, Lianzhen Shao, and C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37, 5951-5956 (1998).
    [Crossref]
  8. M. Vannoni and G. Molesini, “Three-flat test with plates in horizontal posture,” Appl. Opt. 47, 2133-2145 (2008).
    [Crossref] [PubMed]
  9. M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
    [Crossref]
  10. U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45, 5856-5864 (2006).
    [Crossref] [PubMed]
  11. J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
    [Crossref]
  12. J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
    [Crossref]
  13. G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409-415 (1966).
    [Crossref] [PubMed]
  14. G. Schulz, “Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte,” Opt. Acta 14, 375-388 (1967).
    [Crossref]
  15. G. Schulz, J. Schwider, C. Hiller, and B. Kicker, “Establishing an optical flatness standard,” Appl. Opt. 10, 929-934(1971).
    [Crossref] [PubMed]
  16. G. Schulz, “Absolute flatness testing by an extended rotation method using two angles of rotation,” Appl. Opt. 32, 1055-1059 (1993).
    [Crossref] [PubMed]
  17. K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437-2446 (1994).
    [Crossref] [PubMed]
  18. J. Grzanna, “Absolute testing of optical flats at points on a square grid: error propagation,” Appl. Opt. 33, 6654-6661(1994).
    [Crossref] [PubMed]
  19. K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40, 1637-1648(2001).
    [Crossref]
  20. G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699-706 (1973).
    [Crossref]
  21. K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
    [Crossref]
  22. H. H. Hopkins, “Applied optics at Reading,” Opt. Laser Technol. 2, 158 (1970).
  23. J. Harris, “The universal Fizeau interferometer,” Ph.D.dissertation (Reading University, 1971).
  24. G. Overton, “Near-field polishing yields ultraflat silica surface,” Laser Focus (July 2008) p. 20.
  25. G. Seitz, “Alternatives Verfahren zur Absolutkalibrierung von interferometrischen Anordnungen,” DGaO meeting, Kloster Banz, Germany, 21-24 May 1997, Poster 1, abstract p. 92.
  26. Neil W. Gardner and Angela D. Davies, “Self-calibration for micro-refractive lens measurements,” Opt. Eng. 45, 033603(2006).
    [Crossref]
  27. U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).
  28. C. J. Evans, M. Küchel, and C. A. Zanoni, “Apparatus and method for calibrating an interferometer using a selectively rotatable sphere,” U.S. patent 6,816,267 (2004).
  29. A. E. Jensen, “Absolute calibration method for laser Twyman-Green wave front testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).
  30. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693-2703 (1974).
    [Crossref] [PubMed]
  31. K.-E. Elssner, R. Burow, J. Grzanna, and R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649-4661 (1989).
    [Crossref] [PubMed]
  32. J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.
  33. K. Creath and J. C. Wyant, “Testing spherical surfaces: a fast, quasi-absolute technique” Appl. Opt. 31, 4350-4355 (1992).
    [Crossref] [PubMed]
  34. J. Schwider, “Absolute sphericity tests,” paper presented at the Second Internationale Tagung Laser und ihre Anwendungen, Dresden, Germany (1973).
  35. J. Schwider, “Advanced evaluation techniques in interferometry,” Progress in Optics Vol. XXVIII, E.Wolf, ed. (Elsevier, 1990), pp. 271-359.
    [Crossref]
  36. M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” US patent 6,804,011 B2 (2004).

2008 (1)

2006 (2)

U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45, 5856-5864 (2006).
[Crossref] [PubMed]

Neil W. Gardner and Angela D. Davies, “Self-calibration for micro-refractive lens measurements,” Opt. Eng. 45, 033603(2006).
[Crossref]

2005 (1)

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

2001 (2)

K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40, 1637-1648(2001).
[Crossref]

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[Crossref]

1998 (1)

1996 (2)

C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996).
[Crossref] [PubMed]

C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
[Crossref]

1994 (2)

1993 (2)

1992 (1)

1989 (1)

1984 (1)

B. S. Fritz, “Absolute calibration of an optical flat” Opt. Eng. 23, 379-383 (1984).

1980 (1)

K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
[Crossref]

1978 (1)

R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56-63 (1978).

1974 (1)

1973 (2)

A. E. Jensen, “Absolute calibration method for laser Twyman-Green wave front testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699-706 (1973).
[Crossref]

1971 (1)

1970 (1)

H. H. Hopkins, “Applied optics at Reading,” Opt. Laser Technol. 2, 158 (1970).

1967 (2)

G. Schulz, “Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte,” Opt. Acta 14, 375-388 (1967).
[Crossref]

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[Crossref]

1966 (2)

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409-415 (1966).
[Crossref] [PubMed]

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

Ai, C.

Brangaccio, D. J.

Bruning, J. H.

Burow, R.

Carakos, R.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

Creath, K.

Davies, Angela D.

Neil W. Gardner and Angela D. Davies, “Self-calibration for micro-refractive lens measurements,” Opt. Eng. 45, 033603(2006).
[Crossref]

Dew, G. D.

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409-415 (1966).
[Crossref] [PubMed]

Elssner, K.-E.

Elßner, K.-E.

K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
[Crossref]

Elssner, K.-E.

J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.

Estler, W. T.

C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
[Crossref]

Evans, C. J.

R. E. Parks, Lianzhen Shao, and C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37, 5951-5956 (1998).
[Crossref]

C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
[Crossref]

C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996).
[Crossref] [PubMed]

C. J. Evans, M. Küchel, and C. A. Zanoni, “Apparatus and method for calibrating an interferometer using a selectively rotatable sphere,” U.S. patent 6,816,267 (2004).

Freischlad, K. R.

Fritz, B. S.

B. S. Fritz, “Absolute calibration of an optical flat” Opt. Eng. 23, 379-383 (1984).

Gallagher, J. E.

Gardner, Neil W.

Neil W. Gardner and Angela D. Davies, “Self-calibration for micro-refractive lens measurements,” Opt. Eng. 45, 033603(2006).
[Crossref]

Griesmann, U.

U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45, 5856-5864 (2006).
[Crossref] [PubMed]

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

Grzanna, J.

J. Grzanna, “Absolute testing of optical flats at points on a square grid: error propagation,” Appl. Opt. 33, 6654-6661(1994).
[Crossref] [PubMed]

K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437-2446 (1994).
[Crossref] [PubMed]

K.-E. Elssner, R. Burow, J. Grzanna, and R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649-4661 (1989).
[Crossref] [PubMed]

K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
[Crossref]

J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.

Harris, J.

J. Harris, “The universal Fizeau interferometer,” Ph.D.dissertation (Reading University, 1971).

Herriott, D. R.

Hiller, C.

Hocken, R. J.

C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
[Crossref]

Hopkins, H. H.

H. H. Hopkins, “Applied optics at Reading,” Opt. Laser Technol. 2, 158 (1970).

Jensen, A. E.

A. E. Jensen, “Absolute calibration method for laser Twyman-Green wave front testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

Kestner, R. N.

C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996).
[Crossref] [PubMed]

Kicker, B.

Küchel, M.

C. J. Evans, M. Küchel, and C. A. Zanoni, “Apparatus and method for calibrating an interferometer using a selectively rotatable sphere,” U.S. patent 6,816,267 (2004).

Küchel, M. F.

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[Crossref]

M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” US patent 6,804,011 B2 (2004).

Minkwitz, G.

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

Molesini, G.

Overton, G.

G. Overton, “Near-field polishing yields ultraflat silica surface,” Laser Focus (July 2008) p. 20.

Parks, R. E.

Riekher, R.

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

Rosenfeld, D. P.

Schulz, G.

K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437-2446 (1994).
[Crossref] [PubMed]

G. Schulz, “Absolute flatness testing by an extended rotation method using two angles of rotation,” Appl. Opt. 32, 1055-1059 (1993).
[Crossref] [PubMed]

K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
[Crossref]

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699-706 (1973).
[Crossref]

G. Schulz, J. Schwider, C. Hiller, and B. Kicker, “Establishing an optical flatness standard,” Appl. Opt. 10, 929-934(1971).
[Crossref] [PubMed]

G. Schulz, “Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte,” Opt. Acta 14, 375-388 (1967).
[Crossref]

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

G. Schulz and J. Schwider, “Interferometric testing of smooth surfaces,” Progress in Optics, Vol. XIII, E.Wolf, ed. (Elsevier, 1976), pp. 93-167.
[Crossref]

Schwider, J.

G. Schulz, J. Schwider, C. Hiller, and B. Kicker, “Establishing an optical flatness standard,” Appl. Opt. 10, 929-934(1971).
[Crossref] [PubMed]

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[Crossref]

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

G. Schulz and J. Schwider, “Interferometric testing of smooth surfaces,” Progress in Optics, Vol. XIII, E.Wolf, ed. (Elsevier, 1976), pp. 93-167.
[Crossref]

J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.

J. Schwider, “Absolute sphericity tests,” paper presented at the Second Internationale Tagung Laser und ihre Anwendungen, Dresden, Germany (1973).

J. Schwider, “Advanced evaluation techniques in interferometry,” Progress in Optics Vol. XXVIII, E.Wolf, ed. (Elsevier, 1990), pp. 271-359.
[Crossref]

Seitz, G.

G. Seitz, “Alternatives Verfahren zur Absolutkalibrierung von interferometrischen Anordnungen,” DGaO meeting, Kloster Banz, Germany, 21-24 May 1997, Poster 1, abstract p. 92.

Shao, Lianzhen

Soons, J.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

Spolaczyk, R.

K.-E. Elssner, R. Burow, J. Grzanna, and R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649-4661 (1989).
[Crossref] [PubMed]

J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.

Vannoni, M.

Vogel, A.

Wang, Q.

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

White, A. D.

Wyant, J. C.

Zanoni, C. A.

C. J. Evans, M. Küchel, and C. A. Zanoni, “Apparatus and method for calibrating an interferometer using a selectively rotatable sphere,” U.S. patent 6,816,267 (2004).

Appl. Opt. (13)

C. Ai and J. C. Wyant, “Absolute testing of flats by using even and odd functions,” Appl. Opt. 32, 4698-4705 (1993).
[Crossref] [PubMed]

C. J. Evans and R. N. Kestner, “Test optics error removal,” Appl. Opt. 35, 1015-1021 (1996).
[Crossref] [PubMed]

R. E. Parks, Lianzhen Shao, and C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37, 5951-5956 (1998).
[Crossref]

M. Vannoni and G. Molesini, “Three-flat test with plates in horizontal posture,” Appl. Opt. 47, 2133-2145 (2008).
[Crossref] [PubMed]

U. Griesmann, “Three-flat test solutions based on simple mirror symmetry,” Appl. Opt. 45, 5856-5864 (2006).
[Crossref] [PubMed]

G. Schulz, J. Schwider, C. Hiller, and B. Kicker, “Establishing an optical flatness standard,” Appl. Opt. 10, 929-934(1971).
[Crossref] [PubMed]

G. Schulz, “Absolute flatness testing by an extended rotation method using two angles of rotation,” Appl. Opt. 32, 1055-1059 (1993).
[Crossref] [PubMed]

K.-E. Elssner, A. Vogel, J. Grzanna, and G. Schulz, “Establishing a flatness standard,” Appl. Opt. 33, 2437-2446 (1994).
[Crossref] [PubMed]

J. Grzanna, “Absolute testing of optical flats at points on a square grid: error propagation,” Appl. Opt. 33, 6654-6661(1994).
[Crossref] [PubMed]

K. R. Freischlad, “Absolute interferometric testing based on reconstruction of rotational shear,” Appl. Opt. 40, 1637-1648(2001).
[Crossref]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693-2703 (1974).
[Crossref] [PubMed]

K.-E. Elssner, R. Burow, J. Grzanna, and R. Spolaczyk, “Absolute sphericity measurement,” Appl. Opt. 28, 4649-4661 (1989).
[Crossref] [PubMed]

K. Creath and J. C. Wyant, “Testing spherical surfaces: a fast, quasi-absolute technique” Appl. Opt. 31, 4350-4355 (1992).
[Crossref] [PubMed]

CIRP Annals (1)

C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and 'absolute testing',” CIRP Annals 45, 617-634,(1996).
[Crossref]

J. Opt. Soc. Am. (1)

A. E. Jensen, “Absolute calibration method for laser Twyman-Green wave front testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

J. Sci. Instrum. (1)

G. D. Dew, “The measurement of optical flatness,” J. Sci. Instrum. 43, 409-415 (1966).
[Crossref] [PubMed]

Opt. Acta (5)

G. Schulz, “Ein Interferenzverfahren zur absoluten Ebenheitsprüfung längs beliebiger Zentralschnitte,” Opt. Acta 14, 375-388 (1967).
[Crossref]

J. Schwider, G. Schulz, R. Riekher, and G. Minkwitz, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen I,” Opt. Acta 13, 103-119 (1966).
[Crossref]

J. Schwider, “Ein Interferenzverfahren zur Absolutprüfung von Planflächennormalen II,” Opt. Acta 14, 389-400 (1967).
[Crossref]

G. Schulz, “Interferentielle Absolutprüfung zweier Flächen,” Opt. Acta 20, 699-706 (1973).
[Crossref]

K.-E. Elßner, J. Grzanna, and G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563-580 (1980).
[Crossref]

Opt. Eng. (2)

Neil W. Gardner and Angela D. Davies, “Self-calibration for micro-refractive lens measurements,” Opt. Eng. 45, 033603(2006).
[Crossref]

B. S. Fritz, “Absolute calibration of an optical flat” Opt. Eng. 23, 379-383 (1984).

Opt. Laser Technol. (1)

H. H. Hopkins, “Applied optics at Reading,” Opt. Laser Technol. 2, 158 (1970).

Optik (Jena) (1)

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Jena) 112, 381-391 (2001).
[Crossref]

Proc. SPIE (2)

R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56-63 (1978).

U. Griesmann, Q. Wang, J. Soons, and R. Carakos, “A simple ball averager for reference sphere calibrations,” Proc. SPIE 5869, S1-S8 (2005).

Other (9)

C. J. Evans, M. Küchel, and C. A. Zanoni, “Apparatus and method for calibrating an interferometer using a selectively rotatable sphere,” U.S. patent 6,816,267 (2004).

J. Schwider, K.-E. Elssner, J. Grzanna, and R. Spolaczyk, “Results and error sources in absolute sphericity measurement,” Proceedings 1st Symposium Budapest, T. Kemény and K. Havrilla, eds., IMEKO TC Series No. 14 (Nova Science, 1987), pp. 93-103.

J. Schwider, “Absolute sphericity tests,” paper presented at the Second Internationale Tagung Laser und ihre Anwendungen, Dresden, Germany (1973).

J. Schwider, “Advanced evaluation techniques in interferometry,” Progress in Optics Vol. XXVIII, E.Wolf, ed. (Elsevier, 1990), pp. 271-359.
[Crossref]

M. F. Küchel, “Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometer,” US patent 6,804,011 B2 (2004).

G. Schulz and J. Schwider, “Interferometric testing of smooth surfaces,” Progress in Optics, Vol. XIII, E.Wolf, ed. (Elsevier, 1976), pp. 93-167.
[Crossref]

J. Harris, “The universal Fizeau interferometer,” Ph.D.dissertation (Reading University, 1971).

G. Overton, “Near-field polishing yields ultraflat silica surface,” Laser Focus (July 2008) p. 20.

G. Seitz, “Alternatives Verfahren zur Absolutkalibrierung von interferometrischen Anordnungen,” DGaO meeting, Kloster Banz, Germany, 21-24 May 1997, Poster 1, abstract p. 92.

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Figures (11)

Fig. 1
Fig. 1

Three plate test for spherical surfaces. Upper left: The optical ray path for a spherical Fizeau interferometer is given under the assumption that the last lens component of the transmission sphere is an aplanatic meniscus whose exit surface is used as a reference surface A in the Fizeau test of another spherical surface B. Upper right: Two surface combinations ( A B ) and ( C B ) are shown that are necessary for the three-plate test. The third combination ( A C ) is shown below on the left. On the right below, the third position with a plane mirror in the focal region for providing a test on the whole surface together with the combinations ( A B ) and ( C B ) shown above.

Fig. 2
Fig. 2

Spherical Fizeau interferometer with the realization of the three positions for the even/odd test where a second spherical surface serves only as an intermediate for the determination of the odd deviations of the concave reference surface.

Fig. 3
Fig. 3

Odd deviations of the reference surface (“Dist” denotes the contour line distance; all values in waves).

Fig. 4
Fig. 4

Even deviations of the reference surface measured with two orthogonal screen positions (“Dist” denotes the contour line distance; all values in waves).

Fig. 5
Fig. 5

Absolute deviations of the reference surface obtained by combining the data of Figs. 3, 4a (“Dist” denotes the contour line distance; all values in waves).

Fig. 6
Fig. 6

Repeatability test for the reference surface representing the difference of the absolute deviations of two consecutive runs. The repeatability is 0.0017 wave rms (“Dist” denotes the contour line distance).

Fig. 7
Fig. 7

Deviation picture of the reference surface using a high-quality reference normal (“Dist” denotes the contour line distance; all values in waves).

Fig. 8
Fig. 8

Difference of two absolute results with complementary screen orientations. The rms value is slightly better than the repeatability value of Fig. 6. The symmetry of the residual aberrations is due to the mathematical completion of the cat’s eye position (“Dist” denotes the contour line distance; all values in waves).

Fig. 9
Fig. 9

Difference of two absolute results with orthogonal screen orientations. The rms value is again slightly better than the repeatability value of Fig. 6. The symmetry of the residual aberrations is due to the mathematical completion of the cat’s eye position (“Dist” denotes the contour line distance; all values in waves).

Fig. 10
Fig. 10

Absolute deviations of the spherical proof glass used for the test (“Dist” denotes the contour line distance; all values in waves).

Fig. 11
Fig. 11

Optical setup for the measurement of the even part of the absolute deviations due the method given by Jensen.

Equations (7)

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W 1 ( x , y ) = S ( x , y ) + P ( x , y ) , W 2 ( x , y ) = S ( x , y ) + P ( x , y ) , W 3 ( x , y ) = S ( x , y ) + S ( x , y ) ,
2 S ( x , y ) = [ W 1 ( x , y ) W 2 ( x , y ) ] + W 3 ( x , y ) .
O P D ( x , y ) = n A B ¯ + B C ¯ + C D ¯ + n E D ¯ 2 n E D ¯ .
B C ¯ + C D ¯ = 2 R { A B ¯ + E D ¯ } .
A B ¯ = S ( x , y ) ; E D ¯ = S ( x , y ) .
O P D ( x , y ) = n E D ¯ + B C ¯ + C D ¯ + n A B ¯ 2 n A B ¯ .
O P D ( x , y ) + O P D ( x , y ) = 4 R 2 { A B ¯ + E D ¯ } = 4 R 2 { S ( x , y ) + S ( x , y ) } .

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