Abstract

A new fringe subdivision method that employs a large synthetic wavelength to subdivide fringes formed by a small single wavelength is proposed. Based on this subdivision method, we demonstrate a novel dual-wavelength interferometric technique with subnanometric resolution, whose potential fringe subdivision factor derived from an evaluation of the interferometer can reach up to 1/440,000. Theoretical analysis and experimental results with a resolution of 0.05 nm are presented to show the feasibility of the interferometric technique.

© 2002 Optical Society of America

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References

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  1. T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
    [CrossRef]
  2. O. Cip, F. Petru, “Compensation method for the scale linearization of the high-precision laser interferometer,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovsky, A. Strba, W. Urbanczyk, eds., Proc. SPIE3820, 144–153 (1998).
    [CrossRef]
  3. H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
    [CrossRef]
  4. R. Onodera, Y. Ishi, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. P. Long, W. Pei, D. Hsu, “Direct subdivision of moire fringe with CCD,” in International Conference on Optoelectronic Science and Engineering ’90, D. Wang, ed., Proc. SPIE1230, 165–166 (1990).
  8. B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).
  9. R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
    [CrossRef]
  10. V. Mahal, A. Arie, “Distance measurements using two frequency-stabilized Nd:YAG lasers,” Appl. Opt. 35, 3010–3015 (1996).
    [CrossRef] [PubMed]
  11. E. Gelmini, U. Minoni, F. Docchio, “Tunable, double-wavelength heterodyne detection interferometer for absolute-distance measurements,” Opt. Lett. 19, 213–215 (1994).
    [CrossRef] [PubMed]
  12. R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), Chap. 4.3.4, pp. 167–170.
  13. R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J. 34, 3–13 (1983).
  14. N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
    [CrossRef]
  15. R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett-Packard J. 34, 10 (1983).

2001 (2)

B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

1998 (1)

R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
[CrossRef]

1996 (2)

1994 (2)

1993 (1)

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

1990 (1)

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195–198 (1990).
[CrossRef]

1983 (2)

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett-Packard J. 34, 10 (1983).

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J. 34, 3–13 (1983).

Araki, T.

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

Arie, A.

Birch, K. P.

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195–198 (1990).
[CrossRef]

Brault, J. W.

Cao, J.

H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
[CrossRef]

Chen, B.

B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).

Cip, O.

O. Cip, F. Petru, “Compensation method for the scale linearization of the high-precision laser interferometer,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovsky, A. Strba, W. Urbanczyk, eds., Proc. SPIE3820, 144–153 (1998).
[CrossRef]

Dandliker, R.

R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
[CrossRef]

Docchio, F.

Gelmini, E.

Hetrick, P. S.

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

Hsu, D.

P. Long, W. Pei, D. Hsu, “Direct subdivision of moire fringe with CCD,” in International Conference on Optoelectronic Science and Engineering ’90, D. Wang, ed., Proc. SPIE1230, 165–166 (1990).

Ishi, Y.

Kothiyal, M. P.

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), Chap. 4.3.4, pp. 167–170.

Kramar, J. A.

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

Li, D.

B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).

Long, P.

P. Long, W. Pei, D. Hsu, “Direct subdivision of moire fringe with CCD,” in International Conference on Optoelectronic Science and Engineering ’90, D. Wang, ed., Proc. SPIE1230, 165–166 (1990).

Lu, H.

H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
[CrossRef]

Mahal, V.

Minoni, U.

Oldham, N. M.

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

Onodera, R.

Pei, W.

P. Long, W. Pei, D. Hsu, “Direct subdivision of moire fringe with CCD,” in International Conference on Optoelectronic Science and Engineering ’90, D. Wang, ed., Proc. SPIE1230, 165–166 (1990).

Petru, F.

O. Cip, F. Petru, “Compensation method for the scale linearization of the high-precision laser interferometer,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovsky, A. Strba, W. Urbanczyk, eds., Proc. SPIE3820, 144–153 (1998).
[CrossRef]

Quenelle, R. C.

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J. 34, 3–13 (1983).

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett-Packard J. 34, 10 (1983).

Salvade, Y.

R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), Chap. 4.3.4, pp. 167–170.

Su, S.

H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
[CrossRef]

Suzuki, N.

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

Tang, G.

H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
[CrossRef]

Teague, T. C.

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

Wuerz, L. J.

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J. 34, 3–13 (1983).

Yokoyama, S.

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

Yokoyama, T.

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

Zhu, R.

B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).

Zimmermann, E.

R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
[CrossRef]

Appl. Opt. (3)

Hewlett-Packard J. (2)

R. C. Quenelle, “Nonlinearity in interferometer measurements,” Hewlett-Packard J. 34, 10 (1983).

R. C. Quenelle, L. J. Wuerz, “A new microcomputer-controlled laser dimensional measurement and analysis system,” Hewlett-Packard J. 34, 3–13 (1983).

J. Opt. (1)

R. Dandliker, Y. Salvade, E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105–114 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

T. Yokoyama, T. Araki, S. Yokoyama, N. Suzuki, “A subnanometre heterodyne interferometric system with improved phase sensitivity using a three-longitudinal-mode He-Ne laser,” Meas. Sci. Technol. 12, 157–162 (2001).
[CrossRef]

Opt. Lett. (1)

Opt. Technique (1)

B. Chen, D. Li, R. Zhu, “Algorithm for automatic tracing of interference fringes and its application to nanometer measurement,” Opt. Technique 27, 223–225, 228 (2001).

Precis. Eng. (2)

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195–198 (1990).
[CrossRef]

N. M. Oldham, J. A. Kramar, P. S. Hetrick, T. C. Teague, “Electronic limitations in phase meters for heterodyne interferometry,” Precis. Eng. 15, 173–179 (1993).
[CrossRef]

Other (4)

R. S. Sirohi, M. P. Kothiyal, Optical Components, Systems, and Measurement Techniques (Marcel Dekker, New York, 1991), Chap. 4.3.4, pp. 167–170.

P. Long, W. Pei, D. Hsu, “Direct subdivision of moire fringe with CCD,” in International Conference on Optoelectronic Science and Engineering ’90, D. Wang, ed., Proc. SPIE1230, 165–166 (1990).

O. Cip, F. Petru, “Compensation method for the scale linearization of the high-precision laser interferometer,” in 11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, M. Hrabovsky, A. Strba, W. Urbanczyk, eds., Proc. SPIE3820, 144–153 (1998).
[CrossRef]

H. Lu, J. Cao, S. Su, G. Tang, “Displacement sensor with nonsymmetrical double gratings,” in International Conference on Sensors and Control Techniques, D. Jiang, A. Wang, eds., Proc. SPIE4077, 40–43 (2000).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the dual-wavelength interferometer based on the fringe subdivision method: P, polarizers; other abbreviations are defined in the text.

Fig. 2
Fig. 2

Schematic of the tested phase differences Δϕ and Δϕ′. V1) is the interference signal formed by wavelength λ1; V2) is the interference signal formed by wavelength λ2; V′(λ2) is the interference signal formed by wavelength λ2 and produced when we used the MCC for nanometer displacement; other abbreviations are defined in the text.

Fig. 3
Fig. 3

First displacement experiment with a step-voltage value of approximately 2 V in the PZT: (a) deviations of the measurement results and (b) measurement results and their linear fit.

Fig. 4
Fig. 4

Second displacement experiment with a step-voltage value of approximately 0.1 V in the PZT: (a) deviations of the measurement results and (b) measurement results and their linear fit.

Fig. 5
Fig. 5

Schematic of the experimental setup that shows the comparison of the MCC with the ML10.

Fig. 6
Fig. 6

Comparison of the experimental results: (a) deviations of the measurement results and (b) measurement results obtained with the two interferometers to determine the same displacement and linear fit.

Equations (6)

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ϕ1=2πL/λ1,
ϕ2=2πLλ2+L2λ2,
Δϕ=2πLλs-L2λ2,
Δϕ=2πLλs-L2+Δl2λ2.
Δl2=λ2λs ΔL.
Kdiv=λ2/λs.

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