Abstract

A method for measuring profiles along a circle on a flat surface with no standard is described. For the measurement, two unknown surfaces are placed almost parallel, and the distance between them is measured many times along a circle by rotation of one of the surfaces. Profiles of the two surfaces can be determined from the distance data. In this study the measuring method is explained: The space between two surfaces measured with a Fizeau interferometer. Four measuring experiments are carried out for determining the profile of a precision-grade half-mirror; in each experiment a different ordinary mirror with unknown profile is used as the second mirror. Profiles of the precise mirrors obtained by these experiments agree closely, with deviations of ∼2 nm. A similar experiment with many concentric circles was carried out with a precise half-mirror and another precise mirror. Although the profiles of many concentric circles were independent of one another, the result shows that the high-frequency component of a whole plane can be estimated.

© 2003 Optical Society of America

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References

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  1. J. Grzanna, G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107–112 (1990).
    [CrossRef]
  2. G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
    [CrossRef] [PubMed]
  3. K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
    [CrossRef]
  4. S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on flat surfaces with no standard,” in Proceedings of IMEKO-14 World Congress, (IMEKO, Budapest, 1997), Vol. 8, pp. 147–152.
  5. S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on a flat surface using a Fizeau-interferometer with no standard,” in Proceedings of IMEKO-15 World Congress, (IMEKO, Budapest, 1999), Vol. 9, pp. 49–54.
  6. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer based topography and interferometory,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]

1992 (1)

1990 (1)

J. Grzanna, G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107–112 (1990).
[CrossRef]

1982 (1)

1980 (1)

K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Elssner, K. E.

K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Grzanna, J.

G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
[CrossRef] [PubMed]

J. Grzanna, G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107–112 (1990).
[CrossRef]

K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Ina, H.

Iwahashi, Y.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on flat surfaces with no standard,” in Proceedings of IMEKO-14 World Congress, (IMEKO, Budapest, 1997), Vol. 8, pp. 147–152.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on a flat surface using a Fizeau-interferometer with no standard,” in Proceedings of IMEKO-15 World Congress, (IMEKO, Budapest, 1999), Vol. 9, pp. 49–54.

Iwata, K.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on a flat surface using a Fizeau-interferometer with no standard,” in Proceedings of IMEKO-15 World Congress, (IMEKO, Budapest, 1999), Vol. 9, pp. 49–54.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on flat surfaces with no standard,” in Proceedings of IMEKO-14 World Congress, (IMEKO, Budapest, 1997), Vol. 8, pp. 147–152.

Kobayashi, S.

Schulz, G.

G. Schulz, J. Grzanna, “Absolute flatness testing by the rotation method with optimal measuring-error compensation,” Appl. Opt. 31, 3767–3780 (1992).
[CrossRef] [PubMed]

J. Grzanna, G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107–112 (1990).
[CrossRef]

K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Sonozaki, S.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on a flat surface using a Fizeau-interferometer with no standard,” in Proceedings of IMEKO-15 World Congress, (IMEKO, Budapest, 1999), Vol. 9, pp. 49–54.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on flat surfaces with no standard,” in Proceedings of IMEKO-14 World Congress, (IMEKO, Budapest, 1997), Vol. 8, pp. 147–152.

Takeda, M.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

K. E. Elssner, J. Grzanna, G. Schulz, “Interferentielle Absolutprüfung von Sphärizitätsnormalen,” Opt. Acta 27, 563–580 (1980).
[CrossRef]

Opt. Commun. (1)

J. Grzanna, G. Schulz, “Absolute testing of flatness standards at square-grid points,” Opt. Commun. 77, 107–112 (1990).
[CrossRef]

Other (2)

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on flat surfaces with no standard,” in Proceedings of IMEKO-14 World Congress, (IMEKO, Budapest, 1997), Vol. 8, pp. 147–152.

S. Sonozaki, K. Iwata, Y. Iwahashi, “Measurement of profile along a circle on a flat surface using a Fizeau-interferometer with no standard,” in Proceedings of IMEKO-15 World Congress, (IMEKO, Budapest, 1999), Vol. 9, pp. 49–54.

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