Abstract

The absolute accuracy of laser interferometers employed in displacement metrology is limited by two dominant factors: uncertainties in the source vacuum wavelength and the refractive index of the ambient air. In this paper we describe an interferometer system designed to minimize these uncertainties. Based on a commercial interferometer, the new system features direct measurement of the vacuum wavelength by frequency comparison with a portable iodine-stabilized He–Ne laser. The refractive index of air is computed from accurately measured values of pressure, temperature, and relative humidity. Combined with a desktop computer, the interferometer system permits the automated field measurement of displacement errors (such as those associated with precision machine tools) with an absolute accuracy of 8.5 parts in 108. Performance of the interferometer in field metrology is illustrated by the results of recent validation testing of the large optics diamond turning machine (LODTM) at Lawrence Livermore National Laboratory. These results highlight the need for new measurements of the absolute refractive index of standard air in order to reduce a limiting uncertainty on such measurements of ±5 parts in 108.

© 1985 Optical Society of America

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References

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  1. N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).
  2. R. R. Donaldson, “Technology of Machine Tools,” Vol. 5, UCRL-53960-5 (1980), Sec. 9.14.
  3. The identification of commercial instruments is given only for the sake of clarity. In no instance does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the particular equipment described is necessarily the best available for the described purpose.
  4. Hewlett-Packard model 5528A laser measurement system;see Hewlett-Packard J. 34, No. 4 (Apr.1983).
  5. R. J. Hocken, H. P. Layer, “Lasers For Dimensional Measurement,” Ann. CIRP 28/1, 303 (1979).
  6. J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
    [CrossRef]
  7. D. A. Jennings et al., “Direct Frequency Measurement of the I2-Stabilized He–Ne 473-THz (633-nm) Laser,” Opt. Lett. 8, 136 (1983).
    [CrossRef] [PubMed]
  8. H. P. Layer, “A Portable Iodine Stabilized Helium-Neon Laser,” IEEE Trans. Instrum. Meas. IM-29, 358 (1980).
    [CrossRef]
  9. B. Edlen, “The Refractive Index of Air,” Metrologia 2, 71 (1966).
    [CrossRef]
  10. F. Jones, “The Refractivity of Air,” J. Res. Natl. Bur. Stand. 86, 27 (1981).
    [CrossRef]
  11. S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
    [CrossRef]
  12. T. J. Edwards, “Observations on the Stability of Thermistors,” Rev. Sci. Instrum. 54, 613 (1983).
    [CrossRef]
  13. R. Revelle, “Carbon Dioxide and World Climate,” Sci. Am. 247, No. 2, 35 (Aug.1982).
    [CrossRef]

1983 (4)

N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).

Hewlett-Packard model 5528A laser measurement system;see Hewlett-Packard J. 34, No. 4 (Apr.1983).

T. J. Edwards, “Observations on the Stability of Thermistors,” Rev. Sci. Instrum. 54, 613 (1983).
[CrossRef]

D. A. Jennings et al., “Direct Frequency Measurement of the I2-Stabilized He–Ne 473-THz (633-nm) Laser,” Opt. Lett. 8, 136 (1983).
[CrossRef] [PubMed]

1982 (1)

R. Revelle, “Carbon Dioxide and World Climate,” Sci. Am. 247, No. 2, 35 (Aug.1982).
[CrossRef]

1981 (1)

F. Jones, “The Refractivity of Air,” J. Res. Natl. Bur. Stand. 86, 27 (1981).
[CrossRef]

1980 (2)

H. P. Layer, “A Portable Iodine Stabilized Helium-Neon Laser,” IEEE Trans. Instrum. Meas. IM-29, 358 (1980).
[CrossRef]

R. R. Donaldson, “Technology of Machine Tools,” Vol. 5, UCRL-53960-5 (1980), Sec. 9.14.

1979 (1)

R. J. Hocken, H. P. Layer, “Lasers For Dimensional Measurement,” Ann. CIRP 28/1, 303 (1979).

1978 (1)

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

1976 (1)

J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
[CrossRef]

1966 (1)

B. Edlen, “The Refractive Index of Air,” Metrologia 2, 71 (1966).
[CrossRef]

Brown, N. J.

N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).

Chartier, J. M.

J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
[CrossRef]

Donaldson, R. R.

N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).

R. R. Donaldson, “Technology of Machine Tools,” Vol. 5, UCRL-53960-5 (1980), Sec. 9.14.

Edlen, B.

B. Edlen, “The Refractive Index of Air,” Metrologia 2, 71 (1966).
[CrossRef]

Edwards, T. J.

T. J. Edwards, “Observations on the Stability of Thermistors,” Rev. Sci. Instrum. 54, 613 (1983).
[CrossRef]

Filliben, J. J.

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

Helmcke, J.

J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
[CrossRef]

Hocken, R. J.

R. J. Hocken, H. P. Layer, “Lasers For Dimensional Measurement,” Ann. CIRP 28/1, 303 (1979).

Jennings, D. A.

Jones, F.

F. Jones, “The Refractivity of Air,” J. Res. Natl. Bur. Stand. 86, 27 (1981).
[CrossRef]

Layer, H. P.

H. P. Layer, “A Portable Iodine Stabilized Helium-Neon Laser,” IEEE Trans. Instrum. Meas. IM-29, 358 (1980).
[CrossRef]

R. J. Hocken, H. P. Layer, “Lasers For Dimensional Measurement,” Ann. CIRP 28/1, 303 (1979).

Mangum, B. W.

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

Revelle, R.

R. Revelle, “Carbon Dioxide and World Climate,” Sci. Am. 247, No. 2, 35 (Aug.1982).
[CrossRef]

Thompson, D. C.

N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).

Tillet, S. D.

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

Wallard, A. J.

J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
[CrossRef]

Wood, S. W.

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

Ann. CIRP (1)

R. J. Hocken, H. P. Layer, “Lasers For Dimensional Measurement,” Ann. CIRP 28/1, 303 (1979).

Hewlett-Packard J. (1)

Hewlett-Packard model 5528A laser measurement system;see Hewlett-Packard J. 34, No. 4 (Apr.1983).

IEEE Trans. Instrum. Meas. (2)

J. M. Chartier, J. Helmcke, A. J. Wallard, “International Intercomparison of the Wavelength of Iodine-Stabilized Lasers,” IEEE Trans. Instrum. Meas. IM-25, 450 (1976).
[CrossRef]

H. P. Layer, “A Portable Iodine Stabilized Helium-Neon Laser,” IEEE Trans. Instrum. Meas. IM-29, 358 (1980).
[CrossRef]

J. Res. Natl. Bur. Stand. (2)

F. Jones, “The Refractivity of Air,” J. Res. Natl. Bur. Stand. 86, 27 (1981).
[CrossRef]

S. W. Wood, B. W. Mangum, J. J. Filliben, S. D. Tillet, “An Investigation of the Stability of Thermistors,” J. Res. Natl. Bur. Stand. 83, 247 (1978).
[CrossRef]

Metrologia (1)

B. Edlen, “The Refractive Index of Air,” Metrologia 2, 71 (1966).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

N. J. Brown, R. R. Donaldson, D. C. Thompson, “Fabrication of Machined Optics for Precision Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 381, 48 (1983).

Rev. Sci. Instrum. (1)

T. J. Edwards, “Observations on the Stability of Thermistors,” Rev. Sci. Instrum. 54, 613 (1983).
[CrossRef]

Sci. Am. (1)

R. Revelle, “Carbon Dioxide and World Climate,” Sci. Am. 247, No. 2, 35 (Aug.1982).
[CrossRef]

UCRL-53960-5 (1)

R. R. Donaldson, “Technology of Machine Tools,” Vol. 5, UCRL-53960-5 (1980), Sec. 9.14.

Other (1)

The identification of commercial instruments is given only for the sake of clarity. In no instance does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the particular equipment described is necessarily the best available for the described purpose.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the interferometer system.

Fig. 2
Fig. 2

Schematic diagram of the optical geometry used to test compensation of the interferometer system for changes in the refractive index of air.

Fig. 3
Fig. 3

Variation of atmospheric pressure during test of refractive-index compensation.

Fig. 4
Fig. 4

Variation of air temperature during test of refractive-index compensation.

Fig. 5
Fig. 5

Variation of relative humidity during test of refractive-index compensation.

Fig. 6
Fig. 6

Displacement measured by the interferometer system during test of refractive-index compensation. The solid curve is the fictitious displacement measured along the open air path caused by changes in the refractive index of the ambient air. The dashed curve, which is nearly coincident with the time axis, is the result after subtraction of the displacement computed using Eq. (12) in the text.

Fig. 7
Fig. 7

Magnified view of the data after correction from the test of refractive-index compensation. The random behavior is due to air turbulence along the measurement path. The rms value of this random error is ∼2.5 microinches or one part of 108.

Fig. 8
Fig. 8

Linear displacement error of the LODTM X axis. The data are completely within the approximately one part in 107 calculated error of the NBS interferometer system.

Fig. 9
Fig. 9

Linear displacement error of the LODTM Z axis. As with the X axis, the data are within the calculated error of the NBS interferometer system.

Tables (1)

Tables Icon

Table I Environmental Parameters Which Affect the Refractive Index of Air; Sensitivities are Computed from Eqs. (4)(6)

Equations (12)

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λ air = λ vac / n air ,
λ vac = c / f 0 ,
c = 299 , 792 , 458 m / s , exactly .
n ( P , T , H , y ) = 1 + A B ,
A = 78.603 [ 1 + 0.540 ( y 0.0003 ) ] P / T Z × 10 8 ,
B = ( 0.00042066 f e s H ) × 10 8 .
( Δ n air / n air ) P = ± 2 × 10 8 .
R ( T ) = R 0 exp ( b / T ) ,
( Δ n air / n air ) T = ± 1 × 10 8 .
( Δ n air / n air ) H = ± 0.5 × 10 8 .
( Δ n air / n air ) total = ± 8.5 × 10 8 .
Δ x = 2.4 × 10 8 Δ n ( P , T , H ) microinches , Δ x = 6 × 10 6 Δ n micrometers .

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