Abstract

We present a method for the linearization and minimization of interferometer cyclic error. We utilize a polynomial curve fitting and resampling algorithm to correct for nonlinear mirror displacement. In the frequency domain, this algorithm compresses cyclic error into a single-frequency component and enables the precise measurement of cyclic error in a noise-dominated environment. We have applied the technique to determine the cyclic error for a range of interferometer components. In addition, we have used these measurements to optimize interferometer configuration and performance such that we routinely achieve a cyclic error of 50pm for our custom Glan–Laser interferometer and 100pm for a commercial interferometer.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
    [CrossRef]
  2. J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
    [CrossRef]
  3. B. Schirinzadeh, Ind. Rob. 25, 35 (1998).
    [CrossRef]
  4. L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
    [CrossRef]
  5. ZMI Optics Guide, OMP-0326W (Zygo Corporation, 2010).
  6. O. P. Lay and S. Dubovitsky, Opt. Lett. 27, 797 (2002).
    [CrossRef]
  7. D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).
  8. M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, Opt. Lett. 35, 4202 (2010).
    [CrossRef]
  9. I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
    [CrossRef]
  10. G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
    [CrossRef]
  11. D. Shaddock, Class. Quantum Grav. 25, 114012 (2008).
    [CrossRef]

2011 (2)

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

2010 (2)

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, Opt. Lett. 35, 4202 (2010).
[CrossRef]

2008 (1)

D. Shaddock, Class. Quantum Grav. 25, 114012 (2008).
[CrossRef]

2006 (1)

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

2003 (1)

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

2002 (1)

1998 (1)

B. Schirinzadeh, Ind. Rob. 25, 35 (1998).
[CrossRef]

Abramovici, A.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

An, X.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

Azizi, A.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

Carneiro, K.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

Chapsky, J.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

De Chiffre, L.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

de Vine, G.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Dekens, F.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

Dubovitsky, S.

Gonda, S.

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

Gray, M. B.

Haitjema, H.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

Halverson, P.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

Hansen, H. N.

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

Herrmann, J.

Hsu, M. T. L.

Ji, Q.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Klipstein, W.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Korpelainen, V.

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

Kurosawa, T.

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

Lassila, A.

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

Lay, O. P.

Littler, I. C. M.

Liu, X.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

McKenzie, K.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Merimaa, M.

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

Misumi, I.

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

Picotto, G. B.

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

Ryan, D.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

Schirinzadeh, B.

B. Schirinzadeh, Ind. Rob. 25, 35 (1998).
[CrossRef]

Seppä, J.

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

Shaddock, D.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

D. Shaddock, Class. Quantum Grav. 25, 114012 (2008).
[CrossRef]

Shaddock, D. A.

Spero, R.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Takamasu, K.

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

Wang, L.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Ware, B.

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Warrington, R. B.

Xu, X.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Yan, J.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Zhang, T.

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Zhao, F.

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

CIRP Ann. (1)

H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, CIRP Ann. 55, 721 (2006).
[CrossRef]

Class. Quantum Grav. (1)

D. Shaddock, Class. Quantum Grav. 25, 114012 (2008).
[CrossRef]

Ind. Rob. (1)

B. Schirinzadeh, Ind. Rob. 25, 35 (1998).
[CrossRef]

Meas. Sci. Technol. (2)

J. Seppä, V. Korpelainen, M. Merimaa, G. B. Picotto, and A. Lassila, Meas. Sci. Technol. 22, 094027 (2011).
[CrossRef]

I. Misumi, S. Gonda, T. Kurosawa, and K. Takamasu, Meas. Sci. Technol. 14, 463 (2003).
[CrossRef]

Opt. Eng. (1)

L. Wang, X. Xu, X. Liu, T. Zhang, J. Yan, and Q. Ji, Opt. Eng. 50, 074402 (2011).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

G. de Vine, B. Ware, K. McKenzie, R. Spero, W. Klipstein, and D. Shaddock, Phys. Rev. Lett. 104, 211103 (2010).
[CrossRef]

Other (2)

ZMI Optics Guide, OMP-0326W (Zygo Corporation, 2010).

D. Ryan, A. Abramovici, F. Zhao, F. Dekens, X. An, A. Azizi, J. Chapsky, and P. Halverson, “Measuring cyclic error in laser heterodyne interferometers,” NASA Tech Briefs NPO-45157 (2010).

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 (3)

Fig. 1.
Fig. 1.

(a) Schematic of signal field contamination by spurious field, e.g., due to polarization cross coupling. (b) Schematic of the distortion of the ideal optical phase change due to cyclic error. (c) Schematic of the heterodyne interferometer used to measure cyclic error. PBS, polarizing beam splitter with extinction ratio 105; AOM, acousto-optic modulator; ωH/V, drive frequency for horizontal/vertical polarized beam; λ/2, half-wave plate for polarization compensation; P, polarizer; ADC, analog-to-digital converter; PLL, phase-locked loop; ϕPM, phasemeter difference signal; GL, Glan–Laser polarizer with extinction ratio 105.

Fig. 2.
Fig. 2.

(a) Schematic of the curvature of the phase ramp (solid line) and the cubic fit (dotted line, displaced for clarity). The curvature of the original data has been exaggerated by approximately a factor of 3 to make the nonlinearity obvious. (b) Data are measured at constant time intervals (nN) and then resampled at regular spacings of θfit. This causes the cyclic error to be linear with respect to θfit. (c) (i) Spectrum of original data. (ii) Spectrum of resampled data.

Fig. 3.
Fig. 3.

Spectrum of cyclic error measured in terms of phase (left axis) and displacement (right axis) scaled for peak amplitude with an effective bandwidth of 0.05 Hz. (a) Glan–Laser interferometer: (i) cyclic error fundamental (amplitude 0.05°), (ii) second harmonic. (b) Double-pass interferometer: (i) cyclic error subharmonic, (ii) fundamental (amplitude 0.2°), (iii) second harmonic. FFT, fast Fourier transform.

Tables (1)

Tables Icon

Table 1. Cyclic Error Measured for Various Optical Components

Metrics