Abstract

We propose one- and two-wavelength methods of absolute measurement of diffraction-grating spacings based on the Littman configuration for autocollimation. The one-wavelength method has been applied to measure the spacing of a grating with a nominal value of 2160 grooves/mm. The grating spacing was measured to be 463.16  nm, with an experimental standard deviation of 0.24  nm. It has been demonstrated that the both methods can provide direct traceability in the submicrometer region in terms of wavelength standards for applications in the field of nanometrology.

© 1999 Optical Society of America

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References

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  1. V. I. Korotkov, S. A. Pulkin, A. L. Vitushkin, and L. F. Vitushkin, Appl. Opt. 35, 4782 (1996).
    [CrossRef] [PubMed]
  2. L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).
  3. W. Demtröder, Laserspektroskopie (Springer-Verlag, Berlin, 1991), Chap. 4.1.3.
    [CrossRef]
  4. S. S. H. Naqvi, S. Gaspar, K. Hickman, K. Bishop, and J. R. McNeil, Appl. Opt. 31, 13771992; H. P. Kleinknecht and H. Meier, Appl. Opt. 19, 525 (1980).
  5. T. J. Quinn, Metrologia 30, 523 (1994).
    [CrossRef]
  6. K. C. Harvey and C. J. Mayatt, Opt. Lett. 16, 910 (1991).
    [CrossRef] [PubMed]

1996 (1)

1994 (2)

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

T. J. Quinn, Metrologia 30, 523 (1994).
[CrossRef]

1992 (1)

1991 (1)

Bishop, K.

Demtröder, W.

W. Demtröder, Laserspektroskopie (Springer-Verlag, Berlin, 1991), Chap. 4.1.3.
[CrossRef]

Gaspar, S.

Harvey, K. C.

Hickman, K.

Korotkov, V. I.

V. I. Korotkov, S. A. Pulkin, A. L. Vitushkin, and L. F. Vitushkin, Appl. Opt. 35, 4782 (1996).
[CrossRef] [PubMed]

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

Mayatt, C. J.

McNeil, J. R.

Naqvi, S. S. H.

Pulkin, S. A.

V. I. Korotkov, S. A. Pulkin, A. L. Vitushkin, and L. F. Vitushkin, Appl. Opt. 35, 4782 (1996).
[CrossRef] [PubMed]

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

Quinn, T. J.

T. J. Quinn, Metrologia 30, 523 (1994).
[CrossRef]

Vitushkin, A. L.

Vitushkin, L. F.

V. I. Korotkov, S. A. Pulkin, A. L. Vitushkin, and L. F. Vitushkin, Appl. Opt. 35, 4782 (1996).
[CrossRef] [PubMed]

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

Zeilikovich, L. S.

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

Appl. Opt. (2)

Metrologia (1)

T. J. Quinn, Metrologia 30, 523 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

L. F. Vitushkin, L. S. Zeilikovich, V. I. Korotkov, and S. A. Pulkin, Opt. Spectrosc. 77, 129 (1994).

Other (1)

W. Demtröder, Laserspektroskopie (Springer-Verlag, Berlin, 1991), Chap. 4.1.3.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Schematic of the optical layout of the proposed methods to measure grating spacing: CL, collimation lens; OI, optical isolator; BE, beam expander; FL, focusing lens; BS, beam splitter; PBS, polarizing beam splitter; M, mirror, HWP, half-wave plate; QWP, quarter-wave plate; 1st, first-order diffracted beam; 0th, zeroth-order diffracted beam.

Fig. 2
Fig. 2

Principle of autocollimation for two diffracted beams by a Littman-mounted grating using a PRE. The solid and dotted lines correspond to the optical layout for the zeroth- and the first-order diffracted beams, respectively. GN, direction of grating normal. See text for other definitions.

Equations (5)

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sinα±sinβm=mλD
D=λsinΦ1cosα1+1-cosΦ1sinα1
tanα1=sinΦ1+sinΔα-sinΔα+Φ2cosΦ1+cosΔα-1+cosΔα+Φ2
D=λ1sinΘ1cosβλ1-1-cosΘ1sinβλ1
tanβλ1=Δλλ1sinΘ1+sinΘ2Δλλ11-cosΘ1-1-cosΘ2

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