Abstract

Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
    [CrossRef]
  2. C. M. Wu and C. S. Su, “Nonlinearity in measurement of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
    [CrossRef]
  3. R. C. Quenelle, “Nonlinearity in interferometric measurement,” Hewlett Packard J. 34, 3–13 (1983).
  4. N. Bobroff, “Residual errors in laser interferometry from air turbulence and nonlinearity,” Appl. Opt. 26(13), 2676–2682 (1987).
    [CrossRef] [PubMed]
  5. W. Hou and X. Zhao, “The drift of the nonlinearity of heterodyne interferometers,” Precis. Eng. 16(1), 25–35 (1994).
    [CrossRef]
  6. J. M. De Freitas and M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Technol. 4(10), 1173–1176 (1993).
    [CrossRef]
  7. A. Rosenbluth and N. Bobroff, “Optical source of nonlinearity of heterodyne interferometers,” Precis. Eng. 12(1), 7–11 (1990).
    [CrossRef]
  8. A. Yacoot and M. J. Downs, “The use of X-ray interferometry to investigate the linearity of NPL differential plane mirror optical interferometer,” Meas. Sci. Technol. 11(8), 1126–1130 (2000).
    [CrossRef]
  9. V. Badami, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
    [CrossRef]
  10. W. Hou, “Optical parts and the nonlinearity in heterodyne interferometers,” Precis. Eng. 30(3), 337–346 (2006).
    [CrossRef]
  11. W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
    [CrossRef]
  12. C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38(19), 4089–4094 (1999).
    [CrossRef]
  13. O. P. Lay and S. Dubovitsky, “Polarization compensation: a passive approach to a reducing heterodyne interferometer nonlinearity,” Opt. Lett. 27(10), 797–799 (2002).
    [CrossRef]
  14. S. Dubovitsky, O. P. Lay, and D. J. Seidel, “Elimination of heterodyne interferometer nonlinearity by carrier phase modulation,” Opt. Lett. 27(8), 619–621 (2002).
    [CrossRef]
  15. C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interometry,” Opt. Commun. 215(1-3), 17–23 (2003).
    [CrossRef]
  16. J. Lawall and E. Kessler, “Michelson interferometry with 10pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
    [CrossRef]
  17. B. Efron, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods,” Biometrika 68(3), 589–599 (1981).
    [CrossRef]
  18. S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).
  19. G. E. Sommargren, “A new laser measurement system for precision metrology,” Precis. Eng. 9(4), 179–184 (1987).
    [CrossRef]
  20. S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2(2), 88–95 (1991).
    [CrossRef]
  21. N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
    [CrossRef]
  22. S. H. Lu, C. I. Chiueh, and C. C. Lee, “Differential wavelength-scanning heterodyne interferometer for measuring large step height,” Appl. Opt. 41(28), 5866–5871 (2002).
    [CrossRef] [PubMed]
  23. T. L. Schmitz and H. S. Kim, “Monte Carlo evaluation of periodic error uncertainty,” Precis. Eng. 31(3), 251–259 (2007).
    [CrossRef]
  24. D. Chu, and A. Ray, “Nonlinearity measurement and correction of metrology data from an interferometer system,” Proc. of 4th Euspen Int. Conf., 300–301 (2004).
  25. T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
    [CrossRef]
  26. T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
    [CrossRef]
  27. T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
    [CrossRef]
  28. K. N. Joo, J. D. Ellis, E. S. Buice, J. W. Spronck, and R. H. M. Schmidt, “High resolution heterodyne interferometer without detectable periodic nonlinearity,” Opt. Express 18(2), 1159–1165 (2010).
    [CrossRef] [PubMed]
  29. J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
    [CrossRef]

2010 (1)

2009 (2)

T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
[CrossRef]

W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
[CrossRef]

2008 (1)

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

2007 (1)

T. L. Schmitz and H. S. Kim, “Monte Carlo evaluation of periodic error uncertainty,” Precis. Eng. 31(3), 251–259 (2007).
[CrossRef]

2006 (3)

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

W. Hou, “Optical parts and the nonlinearity in heterodyne interferometers,” Precis. Eng. 30(3), 337–346 (2006).
[CrossRef]

2003 (1)

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interometry,” Opt. Commun. 215(1-3), 17–23 (2003).
[CrossRef]

2002 (3)

2000 (3)

J. Lawall and E. Kessler, “Michelson interferometry with 10pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

A. Yacoot and M. J. Downs, “The use of X-ray interferometry to investigate the linearity of NPL differential plane mirror optical interferometer,” Meas. Sci. Technol. 11(8), 1126–1130 (2000).
[CrossRef]

V. Badami, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

1999 (1)

1996 (1)

C. M. Wu and C. S. Su, “Nonlinearity in measurement of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[CrossRef]

1994 (1)

W. Hou and X. Zhao, “The drift of the nonlinearity of heterodyne interferometers,” Precis. Eng. 16(1), 25–35 (1994).
[CrossRef]

1993 (1)

J. M. De Freitas and M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Technol. 4(10), 1173–1176 (1993).
[CrossRef]

1992 (1)

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

1991 (1)

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2(2), 88–95 (1991).
[CrossRef]

1990 (1)

A. Rosenbluth and N. Bobroff, “Optical source of nonlinearity of heterodyne interferometers,” Precis. Eng. 12(1), 7–11 (1990).
[CrossRef]

1989 (1)

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

1988 (1)

S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).

1987 (2)

G. E. Sommargren, “A new laser measurement system for precision metrology,” Precis. Eng. 9(4), 179–184 (1987).
[CrossRef]

N. Bobroff, “Residual errors in laser interferometry from air turbulence and nonlinearity,” Appl. Opt. 26(13), 2676–2682 (1987).
[CrossRef] [PubMed]

1983 (1)

R. C. Quenelle, “Nonlinearity in interferometric measurement,” Hewlett Packard J. 34, 3–13 (1983).

1981 (1)

B. Efron, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods,” Biometrika 68(3), 589–599 (1981).
[CrossRef]

Akatsu, T.

S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).

Badami, V.

V. Badami, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

Bobroff, N.

A. Rosenbluth and N. Bobroff, “Optical source of nonlinearity of heterodyne interferometers,” Precis. Eng. 12(1), 7–11 (1990).
[CrossRef]

N. Bobroff, “Residual errors in laser interferometry from air turbulence and nonlinearity,” Appl. Opt. 26(13), 2676–2682 (1987).
[CrossRef] [PubMed]

Bosse, H.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Buice, E. S.

Chiueh, C. I.

Chu, D.

T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
[CrossRef]

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

De Freitas, J. M.

J. M. De Freitas and M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Technol. 4(10), 1173–1176 (1993).
[CrossRef]

Deslattes, R. D.

Downs, M. J.

A. Yacoot and M. J. Downs, “The use of X-ray interferometry to investigate the linearity of NPL differential plane mirror optical interferometer,” Meas. Sci. Technol. 11(8), 1126–1130 (2000).
[CrossRef]

Dubovitsky, S.

Efron, B.

B. Efron, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods,” Biometrika 68(3), 589–599 (1981).
[CrossRef]

Ellis, J. D.

Elster, C.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Flügge, J.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Geckeler, R. D.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Hagiwara, N.

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

Hosoe, S.

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2(2), 88–95 (1991).
[CrossRef]

Hou, W.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
[CrossRef]

W. Hou, “Optical parts and the nonlinearity in heterodyne interferometers,” Precis. Eng. 30(3), 337–346 (2006).
[CrossRef]

W. Hou and X. Zhao, “The drift of the nonlinearity of heterodyne interferometers,” Precis. Eng. 16(1), 25–35 (1994).
[CrossRef]

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

Houck, L.

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

Hu, H.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
[CrossRef]

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Joo, K. N.

Kalem, L.

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

Kessler, E.

J. Lawall and E. Kessler, “Michelson interferometry with 10pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

Kim, H. S.

T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
[CrossRef]

T. L. Schmitz and H. S. Kim, “Monte Carlo evaluation of periodic error uncertainty,” Precis. Eng. 31(3), 251–259 (2007).
[CrossRef]

Köning, R.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Lawall, J.

J. Lawall and E. Kessler, “Michelson interferometry with 10pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38(19), 4089–4094 (1999).
[CrossRef]

Lay, O. P.

Lee, C. C.

Lu, S. H.

Miyazaki, C.

S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).

Mori, S.

S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).

Nishitani, Y.

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

Player, M. A.

J. M. De Freitas and M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Technol. 4(10), 1173–1176 (1993).
[CrossRef]

Quenelle, R. C.

R. C. Quenelle, “Nonlinearity in interferometric measurement,” Hewlett Packard J. 34, 3–13 (1983).

Rosenbluth, A.

A. Rosenbluth and N. Bobroff, “Optical source of nonlinearity of heterodyne interferometers,” Precis. Eng. 12(1), 7–11 (1990).
[CrossRef]

Saegusa, T.

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

Schmidt, R. H. M.

Schmitz, T. L.

T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
[CrossRef]

T. L. Schmitz and H. S. Kim, “Monte Carlo evaluation of periodic error uncertainty,” Precis. Eng. 31(3), 251–259 (2007).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

Schulz, M.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Seidel, D. J.

Sommargren, G. E.

G. E. Sommargren, “A new laser measurement system for precision metrology,” Precis. Eng. 9(4), 179–184 (1987).
[CrossRef]

Spronck, J. W.

Su, C. S.

C. M. Wu and C. S. Su, “Nonlinearity in measurement of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[CrossRef]

Weichert, Ch.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Wiegmann, A.

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Wilkening, G.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

Wu, C. M.

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interometry,” Opt. Commun. 215(1-3), 17–23 (2003).
[CrossRef]

C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38(19), 4089–4094 (1999).
[CrossRef]

C. M. Wu and C. S. Su, “Nonlinearity in measurement of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[CrossRef]

Yacoot, A.

A. Yacoot and M. J. Downs, “The use of X-ray interferometry to investigate the linearity of NPL differential plane mirror optical interferometer,” Meas. Sci. Technol. 11(8), 1126–1130 (2000).
[CrossRef]

Yanase, M.

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

Zhang, Y.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
[CrossRef]

Zhao, X.

W. Hou and X. Zhao, “The drift of the nonlinearity of heterodyne interferometers,” Precis. Eng. 16(1), 25–35 (1994).
[CrossRef]

Appl. Opt. (3)

Biometrika (1)

B. Efron, “Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods,” Biometrika 68(3), 589–599 (1981).
[CrossRef]

Hewlett Packard J. (1)

R. C. Quenelle, “Nonlinearity in interferometric measurement,” Hewlett Packard J. 34, 3–13 (1983).

IEEE Trans. Instrum. Meas. (1)

N. Hagiwara, Y. Nishitani, M. Yanase, and T. Saegusa, “A phase encoding method for improving the resolution and reliability of laser interferometers,” IEEE Trans. Instrum. Meas. 38(2), 548–551 (1989).
[CrossRef]

Meas. Sci. Technol. (5)

T. L. Schmitz, D. Chu, and L. Houck, “First-order periodic error correction: validation for constant and nonconstant velocities with variable error magnitudes,” Meas. Sci. Technol. 17(12), 3195–3203 (2006).
[CrossRef]

W. Hou, Y. Zhang, and H. Hu, “A simple technique for eliminating the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).
[CrossRef]

C. M. Wu and C. S. Su, “Nonlinearity in measurement of length by optical interferometry,” Meas. Sci. Technol. 7(1), 62–68 (1996).
[CrossRef]

J. M. De Freitas and M. A. Player, “Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry,” Meas. Sci. Technol. 4(10), 1173–1176 (1993).
[CrossRef]

A. Yacoot and M. J. Downs, “The use of X-ray interferometry to investigate the linearity of NPL differential plane mirror optical interferometer,” Meas. Sci. Technol. 11(8), 1126–1130 (2000).
[CrossRef]

Nanotechnology (1)

S. Hosoe, “Laser interferometric system for displacement measurement with high precision,” Nanotechnology 2(2), 88–95 (1991).
[CrossRef]

Opt. Commun. (1)

C. M. Wu, “Periodic nonlinearity resulting from ghost reflections in heterodyne interometry,” Opt. Commun. 215(1-3), 17–23 (2003).
[CrossRef]

Opt. Eng. (1)

S. Mori, T. Akatsu, and C. Miyazaki, “Laser measurement system for precise and fast positioning,” Opt. Eng. 27, 823–829 (1988).

Opt. Express (1)

Opt. Lett. (2)

Precis. Eng. (9)

G. E. Sommargren, “A new laser measurement system for precision metrology,” Precis. Eng. 9(4), 179–184 (1987).
[CrossRef]

V. Badami, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).
[CrossRef]

W. Hou, “Optical parts and the nonlinearity in heterodyne interferometers,” Precis. Eng. 30(3), 337–346 (2006).
[CrossRef]

A. Rosenbluth and N. Bobroff, “Optical source of nonlinearity of heterodyne interferometers,” Precis. Eng. 12(1), 7–11 (1990).
[CrossRef]

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng. 14(2), 91–98 (1992).
[CrossRef]

W. Hou and X. Zhao, “The drift of the nonlinearity of heterodyne interferometers,” Precis. Eng. 16(1), 25–35 (1994).
[CrossRef]

T. L. Schmitz, D. Chu, and H. S. Kim, “First and second order periodic error measurement for non-constant velocity motions,” Precis. Eng. 33(4), 353–361 (2009).
[CrossRef]

T. L. Schmitz, L. Houck, D. Chu, and L. Kalem, “Bench-top setup for validation of real time, digital periodic error correction,” Precis. Eng. 30(3), 306–313 (2006).
[CrossRef]

T. L. Schmitz and H. S. Kim, “Monte Carlo evaluation of periodic error uncertainty,” Precis. Eng. 31(3), 251–259 (2007).
[CrossRef]

Proc. SPIE (1)

J. Flügge, Ch. Weichert, H. Hu, R. Köning, H. Bosse, A. Wiegmann, M. Schulz, C. Elster, and R. D. Geckeler, “Interferometry at the PTB Nanometer Comparator: design, status and development,” Proc. SPIE 7133, 713346 (2008).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Lawall and E. Kessler, “Michelson interferometry with 10pm accuracy,” Rev. Sci. Instrum. 71(7), 2669–2676 (2000).
[CrossRef]

Other (1)

D. Chu, and A. Ray, “Nonlinearity measurement and correction of metrology data from an interferometer system,” Proc. of 4th Euspen Int. Conf., 300–301 (2004).

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 (5)

Fig. 1
Fig. 1

a typical scheme of heterodyne interferometer: BS, beam splitter; PBS, polarizing beam splitter; P, polarization analyzer; D, photodiode detector; LPF, low-pass filter; A/D, analogue-digital converter; FPGA, field programmable gate array; PC, personal computer.

Fig. 2
Fig. 2

The nonlinearity of heterodyne interferometer

Fig. 3
Fig. 3

Results of group 1 in simulation 1

Fig. 4
Fig. 4

Result of group 1 in simulation 2

Fig. 5
Fig. 5

Result of group 1 in simulation 3

Tables (4)

Tables Icon

Table 1 Parameters of the simulations

Tables Icon

Table 2 Results in simulation 1

Tables Icon

Table 3 Results in simulation 2

Tables Icon

Table 4 Results in simulation 3

Equations (26)

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

L = λ 2 0 T Δ f d t ,
L = λ 4 π Δ ϕ ,
I m 1 = I m 0 cos [ 2 π ( f 2 f 1 ) t + Δ ϕ + ϕ m 0 ] ,
I m 2 = I m 0 sin [ 2 π ( f 2 f 1 ) t + Δ ϕ + ϕ m 0 ] ,
I r = I r 0 cos [ 2 π ( f 2 f 1 ) t + ϕ r 0 ] ,
I m r 1 = I m 1 I r                   = 1 2 I m 0 I r 0 { cos [ 2 π ( 2 f 2 2 f 1 ) t + Δ ϕ + ϕ m 0 + ϕ r 0 ] + cos ( Δ ϕ + ϕ m 0 ϕ r 0 ) } ,
I m r 2 = I m 2 I r                     = 1 2 I m 0 I r 0 { sin [ 2 π ( 2 f 2 2 f 1 ) t + Δ ϕ + ϕ m 0 + ϕ r 0 ] + sin ( Δ ϕ + ϕ m 0 ϕ r 0 ) } .
I 1 = 1 2 I m 0 I r 0 cos ( Δ ϕ + ϕ m r 0 ) ,
I 2 = 1 2 I m 0 I r 0 sin ( Δ ϕ + ϕ m r 0 ) ,
Δ ϕ = arctan I 2 I 1 ϕ m r 0 .
ϕ m r 0 = arctan I 2 s I 1 s ,
γ = arctan b a sin ( Δ ϕ + θ a ) 1 + b a cos ( Δ ϕ + θ a ) + arctan d c sin ( Δ ϕ + θ c ) 1 + d c cos ( Δ ϕ + θ c ) ,
Δ ϕ m = Δ ϕ + γ .
Δ f = v c f ,
Δ ϕ = 2 π Δ f t .
Δ ϕ = 2 π v f c t .
Δ ϕ = arctan I 2 I 1 ϕ m r 0                   = k t ,
k = 2 π v f c .
Δ ϕ m = k t + γ .
Δ ϕ m i = k n i + γ i , i = 1 , 2 , 3 , , N ,
k * = i = 1 N ( n i n ¯ ) ( Δ ϕ m i Δ ϕ ¯ m ) i = 1 N ( n i n ¯ ) 2 .
k ^ = N k * N 1 N j = 1 N k ( j ) .
σ k 2 = N 1 N j = 1 N ( k ( j ) 1 N j = 1 N k ( j ) ) 2 .
γ ^ i = Δ ϕ m i k ^ n i .
Δ ϕ m e i = k n i + γ i + η i , i = 1 , 2 , 3 , , N ,
Δ ϕ m e s i = ( k + ε i ) n i + γ i + η i , i = 1 , 2 , 3 , , N ,

Metrics