Abstract

We achieved displacement metrology with a high-amplitude signal by using a rectangular phase grating as the pupil in a grating imaging system. The imaging phenomenon with a pupil transmission grating that has a bilevel profile with a 50% duty ratio is discussed on the basis of the optical transfer function. By optimizing the imaging condition, we obtained high-contrast images with high light power under a magnified or demagnified imaging system. The amplitude of the signal in the displacement measurement was four times higher than that of the conventional grating imaging system with amplitude gratings.

© 2006 Optical Society of America

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  1. R. M. Pettigrew, "Analysis of grating imaging and its application to displacement metrology," Proc. SPIE 136, 325-332 (1977).
  2. J. Jahns and A. W. Lohman, "The Lau effect: a diffraction experiment with incoherent illumination," Opt. Commun. 28, 263-267 (1979).
    [CrossRef]
  3. F. Gori, "Lau effect and coherence theory," Opt. Commun. 31, 4-8 (1979).
    [CrossRef]
  4. R. Sudol and B. J. Thompson, "Lau effect: theory and experiment," Appl. Opt. 20, 1107-1116 (1981).
  5. K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
    [CrossRef]
  6. D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, "Optical encoder based on the Lau effect," Opt. Eng. 39, 817-824 (2000).
    [CrossRef]
  7. G. J. Swanson and E. N. Leith, "Lau effect and grating imaging," J. Opt. Soc. Am. 72, 552-555 (1982).
  8. G. J. Swanson and E. N. Leith, "Analysis of the Lau effect and generalized grating imaging," J. Opt. Soc. Am. A 2, 789-793 (1985).
  9. D. Crespo, J. Alonso, and E. Bernabeu, "Generalized grating imaging using an extended monochromatic light source," J. Opt. Soc. Am. A 17, 1231-1240 (2000).
  10. D. Crespo, J. Alonso, and E. Bernabeu, "Experimental measurement of generalized grating images," Appl. Opt. 41, 1223-1228 (2002).
  11. K. Hane and C. P. Grover, "Imaging with rectangular transmission gratings," J. Opt. Soc. Am. A 4, 706-711 (1987).
  12. K. Hane and C. P. Grover, "Magnified grating images used in displacement sensing," Appl. Opt. 26, 2355-2359 (1987).
  13. Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

2002 (1)

2000 (2)

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, "Optical encoder based on the Lau effect," Opt. Eng. 39, 817-824 (2000).
[CrossRef]

D. Crespo, J. Alonso, and E. Bernabeu, "Generalized grating imaging using an extended monochromatic light source," J. Opt. Soc. Am. A 17, 1231-1240 (2000).

1987 (2)

1985 (1)

1983 (1)

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
[CrossRef]

1982 (1)

1981 (1)

1979 (2)

J. Jahns and A. W. Lohman, "The Lau effect: a diffraction experiment with incoherent illumination," Opt. Commun. 28, 263-267 (1979).
[CrossRef]

F. Gori, "Lau effect and coherence theory," Opt. Commun. 31, 4-8 (1979).
[CrossRef]

1977 (1)

R. M. Pettigrew, "Analysis of grating imaging and its application to displacement metrology," Proc. SPIE 136, 325-332 (1977).

Alonso, J.

Bernabeu, E.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
[CrossRef]

Crespo, D.

Gori, F.

F. Gori, "Lau effect and coherence theory," Opt. Commun. 31, 4-8 (1979).
[CrossRef]

Grover, C. P.

Hane, K.

K. Hane and C. P. Grover, "Magnified grating images used in displacement sensing," Appl. Opt. 26, 2355-2359 (1987).

K. Hane and C. P. Grover, "Imaging with rectangular transmission gratings," J. Opt. Soc. Am. A 4, 706-711 (1987).

Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

Jahns, J.

J. Jahns and A. W. Lohman, "The Lau effect: a diffraction experiment with incoherent illumination," Opt. Commun. 28, 263-267 (1979).
[CrossRef]

Leith, E. N.

Lohman, A. W.

J. Jahns and A. W. Lohman, "The Lau effect: a diffraction experiment with incoherent illumination," Opt. Commun. 28, 263-267 (1979).
[CrossRef]

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
[CrossRef]

Morlanes, T.

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, "Optical encoder based on the Lau effect," Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Nakashima, T.

Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

Ohmura, Y.

Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

Ojeda-Castaneda, J.

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
[CrossRef]

Oka, T.

Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

Pettigrew, R. M.

R. M. Pettigrew, "Analysis of grating imaging and its application to displacement metrology," Proc. SPIE 136, 325-332 (1977).

Sudol, R.

Swanson, G. J.

Thompson, B. J.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

J. Jahns and A. W. Lohman, "The Lau effect: a diffraction experiment with incoherent illumination," Opt. Commun. 28, 263-267 (1979).
[CrossRef]

F. Gori, "Lau effect and coherence theory," Opt. Commun. 31, 4-8 (1979).
[CrossRef]

K. H. Brenner, A. W. Lohmann, and J. Ojeda-Castaneda, "Lau effect: OTF theory," Opt. Commun. 46, 14-17 (1983).
[CrossRef]

Opt. Eng. (1)

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, "Optical encoder based on the Lau effect," Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Proc. SPIE (1)

R. M. Pettigrew, "Analysis of grating imaging and its application to displacement metrology," Proc. SPIE 136, 325-332 (1977).

Other (1)

Y. Ohmura, T. Oka, T. Nakashima, and K. Hane, "Imaging by a phase grating used in displacement measurement," in Proceedings of American Society for Precision Engineering 2004 Annual Meeting (American Society for Precision Engineering, 2004), Vol. 34, pp. 518-521.

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