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

PDF Article

References

  • View by:
  • |
  • |
  • |

  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).
  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).
  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).

1998 (4)

C. J. Evans, “Comment on the paper ‘Interferometric testing of optical surfaces: absolute measurement of flatness,’” Opt. Eng. 37, 1880–1882 (1998).
[CrossRef]

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[CrossRef]

I. Powell, E. Goulet, “Absolute figure measurements with a liquid-flat reference,” Appl. Opt. 37, 2579–2588 (1998).
[CrossRef]

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

1997 (1)

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurement of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

1996 (2)

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

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]

1995 (1)

1994 (1)

1993 (1)

1990 (2)

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).

V. B. Gubin, V. N. Sharonov, “Absolute calibration of spherical surfaces,” Sov. J. Opt. Technol. 57, 554–555 (1990).

1984 (1)

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

1983 (1)

1967 (1)

1893 (1)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Ai, C.

Brandt, S.

S. Brandt, Statistical and Computational Methods in Data Analysis, 2nd ed. (North-Holland, Amsterdam, 1970), p. 216.

Burow, R.

Chen, J.

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]

Chen, L.

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]

Elssner, K.-E.

Evans, C. J.

C. J. Evans, “Comment on the paper ‘Interferometric testing of optical surfaces: absolute measurement of flatness,’” Opt. Eng. 37, 1880–1882 (1998).
[CrossRef]

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

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

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]

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).

Flannery, B. P.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).

Fritz, B. S.

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

Goulet, E.

Greco, V.

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[CrossRef]

Grzanna, J.

Gubin, V. B.

V. B. Gubin, V. N. Sharonov, “Absolute calibration of spherical surfaces,” Sov. J. Opt. Technol. 57, 554–555 (1990).

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).

Hariharan, P.

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurement of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

Kestner, R. N.

Kim, C.-J.

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.

Loomis, J. S.

J. S. Loomis, fringe User’s Manual—Version 2 (University of Arizona, Tucson, Ariz., November1976).

Loucks, B.

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).

Merkel, K.

Molesini, G.

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[CrossRef]

Parks, R. E.

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

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]

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).

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978).

Powell, I.

Press, W. H.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).

Rayleigh, Lord

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Schulz, G.

Schwider, J.

Shannon, R. R.

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.

Shao, L.-Z.

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

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).

Sharonov, V. N.

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).

V. B. Gubin, V. N. Sharonov, “Absolute calibration of spherical surfaces,” Sov. J. Opt. Technol. 57, 554–555 (1990).

Song, D.

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]

Spolaczyk, R.

Sullivan, P. J.

Sullivan, P. O.

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).

Taylor, G. S.

Teukolsky, A. A.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).

Tronconi, R.

R. Tronconi, “Misura assoluta di planarità con metodi interferometrici,” laurea dissertation (University of Florence, Florence, Italy, April1997).

Vetterling, W. T.

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).

Vogel, A.

Wang, Q.

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]

Wyant, J. C.

Zhu, R.

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]

Appl. Opt. (8)

Nature (London) (1)

Lord Rayleigh, “Interference bands and their applications,” Nature (London) 48, 212–214 (1893).
[CrossRef]

Opt. Eng. (4)

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]

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurement of flatness,” Opt. Eng. 36, 2478–2481 (1997).
[CrossRef]

C. J. Evans, “Comment on the paper ‘Interferometric testing of optical surfaces: absolute measurement of flatness,’” Opt. Eng. 37, 1880–1882 (1998).
[CrossRef]

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

Pure Appl. Opt. (1)

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7, 1341–1346 (1998).
[CrossRef]

Sov. J. Opt. Technol. (2)

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).

V. B. Gubin, V. N. Sharonov, “Absolute calibration of spherical surfaces,” Sov. J. Opt. Technol. 57, 554–555 (1990).

Other (10)

W. H. Press, A. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in fortran, 2nd ed. (Cambridge, U. Press, Cambridge, 1992).

E.g., code v (Optical Research Associates, Pasadena, Calif.)

J. S. Loomis, fringe User’s Manual—Version 2 (University of Arizona, Tucson, Ariz., November1976).

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.

S. Brandt, Statistical and Computational Methods in Data Analysis, 2nd ed. (North-Holland, Amsterdam, 1970), p. 216.

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).

Mark IVxp (Zygo Corporation, Middlefield, Conn.).

R. Tronconi, “Misura assoluta di planarità con metodi interferometrici,” laurea dissertation (University of Florence, Florence, Italy, April1997).

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).

R. E. Parks, “Removal of test optics errors,” in Advances in Optical Metrology, N. Balasubramanian, J. C. Wyant, eds., Proc. SPIE153, 56–63 (1978).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics