Abstract

A positioning system based on a new zooming interferometer was developed for calibrating ultrahigh-resolution linear encoders. In the system, the positioning resolution is scaled down from that of the driving stage to that of the controlled stage by a zooming ratio that is determined by the ratio bettween the wavelengths of the optical sources for the zooming interferometer, so that the resolution in the controlled stage becomes very high. A femtosecond optical comb is used to stabilize two external-cavity diode lasers that are used as optical sources for the interferometer. The system realized a resolution of better than 30 pm and a stability of 1 nm.

© 2008 Optical Society of America

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References

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  1. G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, "Combined optical and X-ray interferometry for high-precision dimensional metrology," Proc. R. Soc. London, Ser. A 456, 701-729 (2000).
    [CrossRef]
  2. C. M. Wu and R. D. Deslattes, "Analytical modeling of the periodic nonlinearity in heterodyne interferometry," Appl. Opt. 37,6696-6700 (1998).
    [CrossRef]
  3. N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
    [CrossRef]
  4. L. Chassagne, S. Topcu, Y. Alayli, and P. Juncar, "Highly accurate positioning control method for piezoelectric actuators based on phase-shifting optoelectronics," Meas. Sci. Technol. 16, 1771-1777 (2005).
    [CrossRef]
  5. J. Lawall and E. Kessler, "Michelson interferometry with 10 pm accuracy," Rev. Sci. Instrum. 71, 2669-2676 (2000).
    [CrossRef]
  6. S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, "Improving the accuracy of homodyne Michelson interferometers using polarization state measurement techniques," Opt. Commun. 247, 133-139 (2005).
    [CrossRef]
  7. C. M. Wu and C. S. Su, "Nonlinearity in measurements of length by optical interferometry," Meas. Sci. Technol. 7, 62-68 (1996).
    [CrossRef]
  8. L. Howard, J. Stone, and J. Fu, "Real-time displacement measurements with a Fabry-Perot cavity and a diode laser," Precision Eng. 25, 321-335 (2001).
    [CrossRef]
  9. Y. Bitou, T. R. Schibli, and K. Minoshima, "Accurate wide-range displacement measurement using tunable diode laser and optical frequency comb generator," Opt. Express 14, 644-654 (2006).
    [CrossRef] [PubMed]
  10. H. Matsumoto and K. Minoshima, "High-accuracy ultrastable moving stage using a novel self-zooming optical scale," Opt. Commun. 132, 417-420 (1996).
    [CrossRef]
  11. Y. Zhao, X. H. Cheng, and D. C. Li, "Dual-wavelength parallel interferometer with superhigh resolution," Opt. Lett. 27, 503-505 (2002).
    [CrossRef]

2006 (1)

2005 (2)

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, "Improving the accuracy of homodyne Michelson interferometers using polarization state measurement techniques," Opt. Commun. 247, 133-139 (2005).
[CrossRef]

L. Chassagne, S. Topcu, Y. Alayli, and P. Juncar, "Highly accurate positioning control method for piezoelectric actuators based on phase-shifting optoelectronics," Meas. Sci. Technol. 16, 1771-1777 (2005).
[CrossRef]

2002 (1)

2001 (1)

L. Howard, J. Stone, and J. Fu, "Real-time displacement measurements with a Fabry-Perot cavity and a diode laser," Precision Eng. 25, 321-335 (2001).
[CrossRef]

2000 (2)

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

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, "Combined optical and X-ray interferometry for high-precision dimensional metrology," Proc. R. Soc. London, Ser. A 456, 701-729 (2000).
[CrossRef]

1998 (1)

1996 (2)

C. M. Wu and C. S. Su, "Nonlinearity in measurements of length by optical interferometry," Meas. Sci. Technol. 7, 62-68 (1996).
[CrossRef]

H. Matsumoto and K. Minoshima, "High-accuracy ultrastable moving stage using a novel self-zooming optical scale," Opt. Commun. 132, 417-420 (1996).
[CrossRef]

1993 (1)

N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Appl. Opt. (1)

Meas. Sci. Technol. (3)

N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

L. Chassagne, S. Topcu, Y. Alayli, and P. Juncar, "Highly accurate positioning control method for piezoelectric actuators based on phase-shifting optoelectronics," Meas. Sci. Technol. 16, 1771-1777 (2005).
[CrossRef]

C. M. Wu and C. S. Su, "Nonlinearity in measurements of length by optical interferometry," Meas. Sci. Technol. 7, 62-68 (1996).
[CrossRef]

Opt. Commun. (2)

S. Topcu, L. Chassagne, Y. Alayli, and P. Juncar, "Improving the accuracy of homodyne Michelson interferometers using polarization state measurement techniques," Opt. Commun. 247, 133-139 (2005).
[CrossRef]

H. Matsumoto and K. Minoshima, "High-accuracy ultrastable moving stage using a novel self-zooming optical scale," Opt. Commun. 132, 417-420 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Precision Eng. (1)

L. Howard, J. Stone, and J. Fu, "Real-time displacement measurements with a Fabry-Perot cavity and a diode laser," Precision Eng. 25, 321-335 (2001).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

G. Basile, P. Becker, A. Bergamin, G. Cavagnero, A. Franks, K. Jackson, U. Kuetgens, G. Mana, E. W. Palmer, C. J. Robbie, M. Stedman, J. Stümpel, A. Yacoot, and G. Zosi, "Combined optical and X-ray interferometry for high-precision dimensional metrology," Proc. R. Soc. London, Ser. A 456, 701-729 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

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

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of zooming interferometer. BS: beam splitter, PD: photo detector, CC: corner reflector. Two interferometers with different operating wavelengths were combined into one optical zooming interferometer.

Fig. 2
Fig. 2

Frequency stabilization system of an ECDL to a fs-comb laser. The phase locking image in frequency(a) and the control scheme of one ECDL(b). ECDL: external-cavity diode laser, APD: avalanche photo diode, Grating: holographic grating.

Fig. 3.
Fig. 3.

Beat frequency behavior of the stabilized ECDLs. The beat frequency between the center frequency of ECDL1 and the frequency of a mode in the fs-comb (left-hand axis) and the beat frequency between the center frequency of ECDL2 and the frequency of the other mode in the fs-comb (right-hand axis) were well stabilized. The fluctuations of these beat frequencies were 4.9 kHz and 5.4 kHz, respectively.

Fig. 4.
Fig. 4.

Optical system of the zooming control system. ECDLs: external-cavity diode lasers, AOMs: acousto-optic modulators, CCs: corner reflectors, PDs: photodetectors, DSs: displacement sensors used for sensing the displacement of the corner reflectors. The 100-kHz heterodyned interference signal of the He–Ne laser is detected by PD1. The 100-kHz heterodyned beat signal of the interference signals of ECDL1 and ECDL2 is detected by PD2. The phase difference between the signals detected by PD1 and PD2 is measured by a lock-in amplifier and fed back to Stage 1 to control the position of CC1 through the PID controller.

Fig. 5.
Fig. 5.

Control of corner cube displacement by zooming control. Black line: displacement of CC1 in nm. Gray line: displacement of CC2 in µm.

Fig. 6.
Fig. 6.

Phase fluctuations of each of the interferometers. Gray line: the phase fluctuation of 633-nm wavelength interferometer, White line: the phase fluctuation of 0.4-mm wavelength interferometer, Black line: the phase difference between the two interferometers.

Fig. 7.
Fig. 7.

Position control error in CC1. left axis: Left axis: the fluctuations in phase difference during zooming control, right axis: corresponding position control error

Equations (4)

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δ ϕ 1 = 4 π n 1 x 1 λ 1
δ ϕ 2 = 4 π n 2 x 2 λ 2
Δ ϕ = δ ϕ 1 δ ϕ 2 = 4 π ( n 1 x 1 λ 1 n 2 x 2 λ 2 ) = 0
x 1 = n 2 n 1 λ 1 λ 2 · x 2 = 1 K · x 2

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