Abstract

Theoretical considerations are presented on characteristics of the optical-alignment technique using dual gratings. The general formulation of the diffraction pattern is derived for superimposition of dual amplitude-phase gratings, as functions of aperture ratios for gratings and separation gaps between dual gratings. Numerical analyses reveal characteristics for precise positioning control or alignment technique, which utilize the detection of the minimum value of the first-order diffraction beam or the detection of the zero cross point of the difference in intensities between +1- and -1- order diffraction light for dual gratings. Alignment errors due to variations in an incident light angle, displacement in detector position, and fabrication errors for the gratings are also discussed.

© 1979 Optical Society of America

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  1. K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).
  2. K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).
  3. Y. Torii and Y. Mizushima, "Optical ultramicrometer technique utilizing a composite diffraction grating," Opt. Commun. 23, 135–138 (1977).
  4. D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).
  5. J. M. Cowley and A. F. Moodie, "Fourier images: I—the point source," Proc. Phys. Soc. B 70, 486–496 (1957).

1977

Y. Torii and Y. Mizushima, "Optical ultramicrometer technique utilizing a composite diffraction grating," Opt. Commun. 23, 135–138 (1977).

D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).

1975

K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).

1971

K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).

1957

J. M. Cowley and A. F. Moodie, "Fourier images: I—the point source," Proc. Phys. Soc. B 70, 486–496 (1957).

Austin, S.

D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).

Cowley, J. M.

J. M. Cowley and A. F. Moodie, "Fourier images: I—the point source," Proc. Phys. Soc. B 70, 486–496 (1957).

Flanders, D. C.

D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).

Kamiya, T.

K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).

K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).

Kamiyama, M.

K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).

Kodate, K.

K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).

K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).

Mizushima, Y.

Y. Torii and Y. Mizushima, "Optical ultramicrometer technique utilizing a composite diffraction grating," Opt. Commun. 23, 135–138 (1977).

Moodie, A. F.

J. M. Cowley and A. F. Moodie, "Fourier images: I—the point source," Proc. Phys. Soc. B 70, 486–496 (1957).

Smith, H. I.

D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).

Takenada, H.

K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).

Torii, Y.

Y. Torii and Y. Mizushima, "Optical ultramicrometer technique utilizing a composite diffraction grating," Opt. Commun. 23, 135–138 (1977).

Appl. Phys. Lett.

D. C. Flanders, H. I. Smith, and S. Austin, "A new interferometric alignment technique," Appl. Phys. Lett., 31, 426–428 (1977).

Jpn. J. Appl. Phys.

K. Kodate, T. Kamiya, and M. Kamiyama, "Double diffraction in the Fresnel region," Jpn. J. Appl. Phys. 10, 1040–1045 (1971).

K. Kodate, T. Kamiya, and H. Takenada, "Double diffraction of phase gratings in the Fresnel region," Jpn. J. Appl. Phys. 14, 1323–1334 (1975).

Opt. Commun.

Y. Torii and Y. Mizushima, "Optical ultramicrometer technique utilizing a composite diffraction grating," Opt. Commun. 23, 135–138 (1977).

Proc. Phys. Soc. B

J. M. Cowley and A. F. Moodie, "Fourier images: I—the point source," Proc. Phys. Soc. B 70, 486–496 (1957).

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