Abstract

Laser displacement interferometry is used extensively in precision equipment for semiconductor manufacture. In these applications it is often necessary to introduce a high velocity airflow to the measurement environment to minimize the density of airborne particulate contaminants. The performance of the heterodyne interferometer is degraded by the resulting fluctuations in the index of refraction along the beam path. The magnitude, correlation length, and probability distribution of the optical path length (OPL) fluctuations are measured for several airflow conditions. The data are interpreted in terms of the path length errors for some common interferometric configurations. The OPL fluctuations are generally less significant than the systematic sources of measurement error. A more fundamental limit on the accuracy of the heterodyne Michelson interferometer is the periodic nonlinearity caused by leakage of the frequency components in the beamsplitter. The effect is discussed in detail. A direct observation of the nonlinearity is reported. The magnitude of the effect is about λ/64 for the beam splitters used in this experiment. A simple technique which indicates the presence and magnitude of the nonlinearity is described.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. Hewlett-Packard model 5517 Laser Head, Hewlett-Packard J. 34, No. 4 (1983).
  3. Excel model 1001A Laser Head; J. Tsai, “Stabilizing Laser Frequencies for Metrology Applications,” Proc. Soc. Photo-Opt. Instrum. Eng.741, (1987), in press.
  4. B. Popella, “The Influence of the Atmosphere on the Wavelength of the He–Ne Laser and the Solution of Correction of the Laser Interferometer,” Opt. Acta 19, No. 7, 604 (1972).
    [Crossref]
  5. W. Tyler Estler, “High-Accuracy Displacement Interferometry in Air,” Appl. Opt. 24, 808 (1985).
    [Crossref]
  6. B. Edlen, “The Refractive Index of Air,” Metrologia 2, 71 (1966).
    [Crossref]
  7. F. Jones, “The Refractivity of Air,” J. Res. Natl. Bur. Stand. 86, 27 (1981).
    [Crossref]
  8. S. F. Clifford, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), p. 9.
    [Crossref]
  9. V. I. Tatarsk, Wave Propagation in a Turbulent Medium, Translated by R. A. Silverman (McGraw-Hill, New York, 1961).
  10. S. F. Clifford, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
    [Crossref]
  11. M. Bertolotti et al., “Atmospheric Turbulance Effects on the Phase of Laser Beams,” Appl. Opt. 13, 1582 (1974).
    [Crossref] [PubMed]
  12. V. P. Lukin, V. V. Pokasov, “Optical Wave Phase Fluctuations,” Appl. Opt. 20, 121 (1981).
    [Crossref] [PubMed]
  13. V. M. Canuto, G. J. Hartke, “Propagation of Electromagnetic Waves in a Turbulent Medium,” J. Opt. Soc. Am. 3, 808 (1986).
    [Crossref]
  14. R. Quenelle, “Nonlinearity in Interferometric Measurements,” Hewlett-Packard J. 34, No. 4, 10 (1983).
  15. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  16. J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980).

1986 (1)

V. M. Canuto, G. J. Hartke, “Propagation of Electromagnetic Waves in a Turbulent Medium,” J. Opt. Soc. Am. 3, 808 (1986).
[Crossref]

1985 (1)

1983 (3)

R. Quenelle, “Nonlinearity in Interferometric Measurements,” Hewlett-Packard J. 34, No. 4, 10 (1983).

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]

Hewlett-Packard model 5517 Laser Head, Hewlett-Packard J. 34, No. 4 (1983).

1981 (2)

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

V. P. Lukin, V. V. Pokasov, “Optical Wave Phase Fluctuations,” Appl. Opt. 20, 121 (1981).
[Crossref] [PubMed]

1974 (1)

1972 (1)

B. Popella, “The Influence of the Atmosphere on the Wavelength of the He–Ne Laser and the Solution of Correction of the Laser Interferometer,” Opt. Acta 19, No. 7, 604 (1972).
[Crossref]

1971 (1)

1966 (1)

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

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980).

Bertolotti, M.

Canuto, V. M.

V. M. Canuto, G. J. Hartke, “Propagation of Electromagnetic Waves in a Turbulent Medium,” J. Opt. Soc. Am. 3, 808 (1986).
[Crossref]

Clifford, S. F.

S. F. Clifford, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
[Crossref]

S. F. Clifford, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), p. 9.
[Crossref]

Edlen, B.

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

Hartke, G. J.

V. M. Canuto, G. J. Hartke, “Propagation of Electromagnetic Waves in a Turbulent Medium,” J. Opt. Soc. Am. 3, 808 (1986).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Jennings, D. A.

Jones, F.

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

Lukin, V. P.

Piersol, A. G.

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980).

Pokasov, V. V.

Popella, B.

B. Popella, “The Influence of the Atmosphere on the Wavelength of the He–Ne Laser and the Solution of Correction of the Laser Interferometer,” Opt. Acta 19, No. 7, 604 (1972).
[Crossref]

Quenelle, R.

R. Quenelle, “Nonlinearity in Interferometric Measurements,” Hewlett-Packard J. 34, No. 4, 10 (1983).

Tatarsk, V. I.

V. I. Tatarsk, Wave Propagation in a Turbulent Medium, Translated by R. A. Silverman (McGraw-Hill, New York, 1961).

Tsai, J.

Excel model 1001A Laser Head; J. Tsai, “Stabilizing Laser Frequencies for Metrology Applications,” Proc. Soc. Photo-Opt. Instrum. Eng.741, (1987), in press.

Tyler Estler, W.

Appl. Opt. (3)

Hewlett-Packard J. (2)

R. Quenelle, “Nonlinearity in Interferometric Measurements,” Hewlett-Packard J. 34, No. 4, 10 (1983).

Hewlett-Packard model 5517 Laser Head, Hewlett-Packard J. 34, No. 4 (1983).

J. Opt. Soc. Am. (2)

V. M. Canuto, G. J. Hartke, “Propagation of Electromagnetic Waves in a Turbulent Medium,” J. Opt. Soc. Am. 3, 808 (1986).
[Crossref]

S. F. Clifford, “Phase Variations in Atmospheric Optical Propagation,” J. Opt. Soc. Am. 61, 1279 (1971).
[Crossref]

J. Res. Natl. Bur. Stand. (1)

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

Metrologia (1)

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

Opt. Acta (1)

B. Popella, “The Influence of the Atmosphere on the Wavelength of the He–Ne Laser and the Solution of Correction of the Laser Interferometer,” Opt. Acta 19, No. 7, 604 (1972).
[Crossref]

Opt. Lett. (1)

Other (5)

Excel model 1001A Laser Head; J. Tsai, “Stabilizing Laser Frequencies for Metrology Applications,” Proc. Soc. Photo-Opt. Instrum. Eng.741, (1987), in press.

S. F. Clifford, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehn, Ed. (Springer-Verlag, New York, 1978), p. 9.
[Crossref]

V. I. Tatarsk, Wave Propagation in a Turbulent Medium, Translated by R. A. Silverman (McGraw-Hill, New York, 1961).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

J. S. Bendat, A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis (Wiley, New York, 1980).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Primary components of the heterodyne interferometer.

Fig. 2
Fig. 2

Two independent interferometers are oriented with parallel measurement arms. The airflow passes through the two arms.

Fig. 3
Fig. 3

Schematic of the signal processing electronics.

Fig. 4
Fig. 4

Correlation coefficient of OPL fluctuations as a function of path separation.

Fig. 5
Fig. 5

Interferometer measuring the relative displacement between a stage and an instrument viewing the stage.

Fig. 6
Fig. 6

Interferometric measurement of the linear and angular displacements of a precision stage.

Fig. 7
Fig. 7

Nonlinearity of the two-frequency interferometer. The horizontal scale is 50°/div. The vertical scale is 5°/div. The deviation from linearity is 12°.

Tables (1)

Tables Icon

Table I Observed rms Fluctuations in OPL

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

ω = γ ( ω + k · v ) ,
ω = ω + 4 π n v λ 0 = ω + Δ ( t ) .
a exp ( i ω 1 t ) + α exp ( i ω 2 t ) + B ( exp ) { i [ w 2 + Δ ( t ) ] t } + β exp { i [ ω 1 + Δ ( t ) ] t } .
I ( t ) cos [ Δ ω + Δ ( t ) ] t + ( α B + β A ) cos ( Δ ω ) t + ( α A + β B ) cos [ Δ ( t ) ] t .
ϕ ( t ) 2 π = 1 2 π Δ ( t ) d t = S ( t ) λ 0 / 2 n ,
I ( t ) sin ( Ψ ) + ( α B + β A ) cos ( Ψ ) .
Ψ = tan - 1 ( α B + β A ) .
Δ 2 = ( S 1 - S 2 ) 2 = ( S 1 a - S 2 a ) 2 + ( S 1 e - S 2 e ) 2 .
ρ 12 = S 1 S 2 S 2
Δ 2 = 2 S a 2 ( 1 - ρ 12 a ) + 2 S e 2 ( 1 - ρ 12 e ) .
( S m c - S r c ) 2 = 2 S 2 [ 1 - ρ 12 ( D ) ] ,
( δ θ ) 2 = S 2 [ 1 - ρ 12 ( D ) ] D 2 .

Metrics