Abstract

A primary-level comparator, with a reproducibility of 0.2 nm and intended for realization of a Systeme International length unit in the range of 1–100 mm, is reported. High-precision differential measurements of phase change on reflection from blocks and end plates are demonstrated. A set of experiments has been developed to measure systematic error associated with nonideal interferometer optics and deviations from flatness of an auxiliary plate. For specially selected high-grade 6-mm blocks, reproducible wringing has been achieved with a random uncertainty in length measurements of 0.1–0.2 nm. Subnanometer wear-off of the blocks as a result of the cleaning has been detected. Under the conditions of reproducible wringing, the accuracy of the length measurements is evaluated to be in the 2–3-nm range for 6-mm blocks.

© 1999 Optical Society of America

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References

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  1. “Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984).
  2. B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
    [CrossRef]
  3. N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
    [CrossRef]
  4. H. Darnedde, J. Helmcke, “European comparison of long gauge blocks,” Metrologia 33, 485–491 (1996).
    [CrossRef]
  5. H. Darnedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).
    [CrossRef]
  6. L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
    [CrossRef]
  7. E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. Circ.581, 1–20 (1957).
  8. In this paper we use the terms precision (repeatability of the results of the measurements), reproducibility, and accuracy, in this way defining the increasing hierarchy in the measurement results.
  9. If not specifically otherwise defined, the term “uncertainty” is used in the meaning of a random (A-type) uncertainty, or the error of the measurement result without application of any corrections for possible systematic effects.
  10. C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
    [CrossRef]
  11. S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).
  12. R. K. Leach, K. Jackson, A. Hart, “Measurement of gauge blocks by interferometry: measurement of the phase change at reflection,” (National Physical Laboratory, Teddington, UK, 1997).
  13. H. Matsumoto, L. Zeng, “Simple compensation method for wringing errors in the interferometric calibration of gauge blocks,” Metrologia 33, 1–4 (1996).
    [CrossRef]
  14. A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

1996 (4)

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

H. Darnedde, J. Helmcke, “European comparison of long gauge blocks,” Metrologia 33, 485–491 (1996).
[CrossRef]

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

H. Matsumoto, L. Zeng, “Simple compensation method for wringing errors in the interferometric calibration of gauge blocks,” Metrologia 33, 1–4 (1996).
[CrossRef]

1995 (1)

B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
[CrossRef]

1992 (2)

H. Darnedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).
[CrossRef]

S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).

1984 (1)

“Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984).

1955 (1)

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

Abramova, L.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Baechler, H.

B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
[CrossRef]

Baratov, V.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Belaidi, H.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Böhme, H.

S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).

Bönch, G.

S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).

Brown, N.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Bruce, C. F.

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

Darnedde, H.

H. Darnedde, J. Helmcke, “European comparison of long gauge blocks,” Metrologia 33, 485–491 (1996).
[CrossRef]

H. Darnedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).
[CrossRef]

Dutra, J. A.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Engelhard, E.

E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. Circ.581, 1–20 (1957).

Eom, T. B.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Fedorin, V.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

França, R. S.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Hart, A.

R. K. Leach, K. Jackson, A. Hart, “Measurement of gauge blocks by interferometry: measurement of the phase change at reflection,” (National Physical Laboratory, Teddington, UK, 1997).

Helmcke, J.

H. Darnedde, J. Helmcke, “European comparison of long gauge blocks,” Metrologia 33, 485–491 (1996).
[CrossRef]

Howick, E.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Ikonen, E.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Ishikawa, S.

S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).

Jackson, K.

R. K. Leach, K. Jackson, A. Hart, “Measurement of gauge blocks by interferometry: measurement of the phase change at reflection,” (National Physical Laboratory, Teddington, UK, 1997).

Khavinson, L.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Kruger, O.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Lan, Y.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Lassila, A.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Latigneva, E.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Leach, R. K.

R. K. Leach, K. Jackson, A. Hart, “Measurement of gauge blocks by interferometry: measurement of the phase change at reflection,” (National Physical Laboratory, Teddington, UK, 1997).

Ling-Tan, S. L.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Malinovsky, I.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Massone, C. A.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Matsumoto, H.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

H. Matsumoto, L. Zeng, “Simple compensation method for wringing errors in the interferometric calibration of gauge blocks,” Metrologia 33, 1–4 (1996).
[CrossRef]

Pusaka, J.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Riski, K.

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Singhal, R. P.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Thalmann, R.

B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
[CrossRef]

Titov, A.

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

Vaucher, B. G.

B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
[CrossRef]

Xu, Y.

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

Zeng, L.

H. Matsumoto, L. Zeng, “Simple compensation method for wringing errors in the interferometric calibration of gauge blocks,” Metrologia 33, 1–4 (1996).
[CrossRef]

Aust. J. Phys. (1)

C. F. Bruce, “The effects of collimation and oblique incidence in length interferometers,” Aust. J. Phys. 8, 224–240 (1955).
[CrossRef]

Metrologia (7)

H. Matsumoto, L. Zeng, “Simple compensation method for wringing errors in the interferometric calibration of gauge blocks,” Metrologia 33, 1–4 (1996).
[CrossRef]

“Documents concerning the new definition of the metre,” Metrologia 19, 163–177 (1984).

B. G. Vaucher, R. Thalmann, H. Baechler, “European comparison of short gauge block measurement by interferometry,” Metrologia 32, 79–86 (1995).
[CrossRef]

N. Brown, T. B. Eom, E. Howick, O. Kruger, Y. Lan, S. L. Ling-Tan, H. Matsumoto, J. Pusaka, R. P. Singhal, Y. Xu, “Asian-Pacific metrology programme of gauge blocks comparison,” Metrologia 33, 61–66 (1996).
[CrossRef]

H. Darnedde, J. Helmcke, “European comparison of long gauge blocks,” Metrologia 33, 485–491 (1996).
[CrossRef]

H. Darnedde, “High-precision calibration of long gauge blocks using the vacuum wavelength comparator,” Metrologia 29, 349–359 (1992).
[CrossRef]

L. Abramova, V. Baratov, V. Fedorin, L. Khavinson, E. Latigneva, K. Riski, E. Ikonen, A. Lassila, “Comparison of length standards between the CMA and the VNIIM,” Metrologia 33, 29–33 (1996).
[CrossRef]

Optik (Stuttgart) (1)

S. Ishikawa, G. Bönch, H. Böhme, “Phase-shifting interferometry with a coupled interferometer: application to optical roughness of gauge blocks,” Optik (Stuttgart) 91, 103–108 (1992).

Other (5)

R. K. Leach, K. Jackson, A. Hart, “Measurement of gauge blocks by interferometry: measurement of the phase change at reflection,” (National Physical Laboratory, Teddington, UK, 1997).

A. Titov, I. Malinovsky, H. Belaidi, R. S. França, J. A. Dutra, C. A. Massone, “Optical methods in length measurements and practical realization of the metre in the range of 1–1000 mm,” presented at the international seminar XVIII CBRAVIC de 21 a 24 de Julho de 1997-Petropolis, Rio de Janeiro, Brazil, Rev. Bras. Apl. Vacuo16, 38 (1997).

E. Engelhard, “Precise interferometric measurement of gauge blocks,” in Proceedings of the Symposium on Gauge Blocks, August 1955, Natl. Bur. Stand. Circ.581, 1–20 (1957).

In this paper we use the terms precision (repeatability of the results of the measurements), reproducibility, and accuracy, in this way defining the increasing hierarchy in the measurement results.

If not specifically otherwise defined, the term “uncertainty” is used in the meaning of a random (A-type) uncertainty, or the error of the measurement result without application of any corrections for possible systematic effects.

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Figures (9)

Fig. 1
Fig. 1

Example of data processing for central-length measurement: viewing of the block through the plate. The locations of channels (bands) are shown schematically. Circles, measured signal data; curves, the fits. The first approximation (parabolic) of the curvature of the block and the plate is shown as profiles. Inset, table listing the parameters of the fits (phases and deviations from flatness for each channel). The third row is the quality of the fit.

Fig. 2
Fig. 2

Stability of measurements for a 7-mm block (one wringing). Circles, a single measurement; squares, mean values for 1-day series. The deviation from the nominal length ΔL and the standard deviation (σ) are shown in the box.

Fig. 3
Fig. 3

Set of experiments for subnanometer-length measurements of gauge blocks. Experiment 1 is the measurement of the block wrung to a steel plate; experiment 2 is the correction measurement for interferometer optics and plate flatness; experiments 3 and 4 and 5 and 6 are the roughness and optical phase-change measurements for the block and the reference plate, respectively.

Fig. 4
Fig. 4

Examples of profile measurements for a 6-mm block: (a) length profile of the block without correction for the interferometer optics and the plate flatness, (b) measured correction for the interferometer optics and the base-plate flatness, (c) length profile of the block corrected for the interferometer optics and the plate flatness.

Fig. 5
Fig. 5

Reproducibility of the 6-mm block calibration. Data correspond to four independent wrings, taken as a series for each case. Mean values in the series are shown as squares; error bars correspond to standard deviations for individual measurements in the series. A triangle, a wedge, and two circles mark changes in the measurement conditions (details in the text).

Fig. 6
Fig. 6

Averaged data for two blocks measured on two steel plates. Measured (dark bars) and corrected (light bars) data are presented at the left. Small differences, obtained on different plates and associated with different roughnesses of the plates, are presented at the right (scaled ×10 for clarity).

Fig. 7
Fig. 7

Effect of inclination correction of the imaging interferometer measured by movement of the laser spot inside the input diaphragm. The curve is calculated for the beam of the Gaussian intensity distribution.

Fig. 8
Fig. 8

Schematic diagram of the scanning interferometer (see a description in the text). OI, optical isolator; B, beam splitter.

Fig. 9
Fig. 9

Inclination error of the interferometer versus the input angle of a highly collimated laser beam.

Equations (1)

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ΔL=La2+b2/24f2,

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