Abstract

We report on a displacement metrology setup that provides subpm resolution in air. The setup is based on a Fabry-Perot cavity. However, unlike current Fabry-Perot cavity based displacement setups we incorporate a novel fs-laser based arbitrary wavelength synthesizer that provides efficient suppression of atmospheric disturbances while providing very wide and precise tuning of the output wavelength. The wavelength synthesizer provides sub-10 attometer wavelength resolution. The setup provides subpm length stability for integration times of up to one minute and sub-10 pm for up to half an hour without airtight enclosure of the Fabry-Perot cavities.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, "Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales," Meas. Sci. Technol. 16, 2080-2090 IOP Publishing (2005).
    [CrossRef]
  2. H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
    [CrossRef]
  3. W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
    [CrossRef]
  4. C.-M. Wu and R. D. Deslattes, "Analytical modeling of the periodic nonlinearity in heterodyne interferometry," Appl. Opt. 37, 6696-6700 (1998).
    [CrossRef]
  5. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, "Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems," Appl. Opt. 43, 2443-2448 (2004).
    [CrossRef] [PubMed]
  6. J. R. Lawall, "Fabry-Perot metrology for displacements up to 50 mm," J. Opt. Soc. Am. A,  22, 2786-2789 (2005).
    [CrossRef]
  7. 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 (2006).
    [CrossRef] [PubMed]
  8. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  9. T. R. Schibli, K. Minoshima, F.-L. Hong, H. Inaba, Y. Bitou, A. Onae, and H. Matsumoto, "Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb," Opt. Lett. 30, 2323 (2005).
    [CrossRef] [PubMed]
  10. Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
    [CrossRef]
  11. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]

2006

2005

2004

2000

H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
[CrossRef]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

1999

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

1998

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Bitou, Y.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Deslattes, R. D.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Gonda, S.

Haitjema, H.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Hansch, T. W.

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

Holzwarth, R.

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

Hong, F.-L.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Huang, Q.

Inaba, H.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Keem, T.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kurosawa, T.

Lawall, J. R.

Liu, D.-K.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Liu, T.-T.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Matsumoto, H.

Mei, H.-H.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Minoshima, K.

Misumi, I.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ni, W.-T.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Onae, A.

Pang, C.-P.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Reichert, J.

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

Schellekens, P. H. J.

H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
[CrossRef]

Schibli, T. R.

Shi Pan, S.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Udem, Th.

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

Wetzels, S. F. C. L

H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Wu, C.-M.

Yeh, H.-C.

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. B

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, "Laser phase and frequency stabilization using an optical resonator," Appl. Phys. B 31, 97 (1983).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol

W.-T. Ni, D.-K. Liu, T.-T. Liu, H.-H. Mei, S. Shi Pan, C.-P. Pang, and H.-C. Yeh, "The application of laser metrology and resonant optical cavity techniques to the measurement of G," Meas. Sci. Technol 10, 495-498 (1999).
[CrossRef]

Metrologia

H. Haitjema, P. H. J. Schellekens, and S. F. C. L Wetzels, "Calibration of displacement sensors up to 300 μm with nanometer accuracy and direct traceability to a primary standard of length," Metrologia,  37, 25-33 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

Th. Udem, J. Reichert, R. Holzwarth, and T. W. Hansch, "Absolute Optical Frequency Measurement of the Cesium D1 line with a mode-locked laser" Phys. Rev. Lett. 82, 3568 (1999).
[CrossRef]

Science

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of Femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Other

I. Misumi, S. Gonda, Q. Huang, T. Keem, T. Kurosawa, A. Fujii, N. Hisata, T. Yamagishi, H. Fujimoto, K. Enjoji, S. Aya, and H. Sumitani, "Sub-hundred nanometer pitch measurements using an AFM with differential laser interferometers for designing usable lateral scales," Meas. Sci. Technol. 16, 2080-2090 IOP Publishing (2005).
[CrossRef]

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.

Experimental setup. Solid and dashed lines represent optical and electrical signals respectively. AOM: acousto-optic modulator; EOM: electro-optic modulator; PBS: Polarizing beamsplitter; PZT: Piezo-electric transducer; FP1/2: Fabry-Perot cavities with a finesse: ~156 on common CLEARCERAM-Z base. MISER: monolithic isolated single-mode end-pumped ring oscillator; PDH: Pound-Drever-Hall error-signal. The ‘Enclosure’ is not airtight but it reduces airflow and rapid temperature changes. Mode-matching optics for coupling to the FP cavities are not shown in this figure.

Fig. 2.
Fig. 2.

Left: Stability of the displacement measurement setup over 50 hours of operation when using a ‘Wavelength stabilized comb’ (blue) and using a ‘Frequency comb’ (red). The inset shows the same data for the wavelength-stabilized case on a 300 times magnified scale. All data was taken with a 1s averaging time. Right: Stability (Allan deviation) obtained from the data shown on the left side. The wavelength-stabilized configuration (blue) provides sub-pm stability for up to 1 minute, and sub-10 pm stability for over 30 minutes. The standard deviation over the full 50 hours is 47 pm. The trace labeled with “Servo drift” shows the approximate systematic drift caused by imperfections of locking the cw-lasers to the FP cavities.

Fig. 3.
Fig. 3.

Nonlinearity measurements of a P-752.1CD nanopositioner from PI for 12 µm displacements when operated in closed-loop mode using an E-750.CP (PI) stage controller. The three traces correspond to three independent measurements. The measurement time per trace was about 20 minutes (12 µm displacements at a rate of 10 nm/s). The averaging time per data point is 1 s.

Tables (2)

Tables Icon

Table 1. Estimated systematic errors for 12 µm displacements excluding Abbe error.

Tables Icon

Table 2. Uncertainties caused by the initial calibration.

Equations (4)

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

f m = m f r e p + f C E O , m = 1 , 2 , 3...
λ Δ m = c n λ Δ m ( m 0 + Δ m ) f rep c ( c λ 0 m 0 f rep + Δ m f rep n f f = m 0 f rep ) ( m 0 + Δ m ) f rep
λ Δ m λ 0 m 0 m 0 + Δ m
Δ L N 2 Δ λ , with N FSR mean f 0

Metrics