Abstract

Homodyne interferometry with a frequency comb as multi-wavelength source is a powerful method to measure long distances with high accuracy. The measurement principle requires that individual comb modes are spectrally resolved, making hundreds or thousands of accurately known wavelengths available for interferometry. For this reason the method cannot be applied directly to frequency combs with a low repetition rate (e.g. 100 MHz), since the modes are too close to be resolved. In this paper we use cavity mode filtering to increasing the pulse repetition rate of a comb and we apply the filtered comb for mode-resolved absolute distance measurement. Mode-filtering takes place with a single Fabry-Pérot cavity in a Vernier configuration, allowing to set mode spacings ranging from 10s of GHz to more than 100 GHz. Large mode-spacings significantly reduce the requirements on the resolution of the spectrometer. We demonstrate absolute long distance measurement with a mode-filtered frequency comb using a simple array spectrometer for mode-resolved detection. Here a 1 GHz comb is used, that is converted into a 56 GHz comb by mode-filtering. A trade-off between non-ambiguity range and spectral resolution needs to be made when choosing a filter ratio. The pulse-to-pulse distance after filtering is 5.3 mm in this case, so to overcome ambiguity a rough measurement with an accuracy of about 2.5 mm is required. We show that in comparison to a conventional counting interferometer an agreement within 0.5 μm for distances up to 50 m is found. The presented method may enable the field application of low-repetition rate frequency comb lasers, like fiber lasers, for multi-wavelength homodyne interferometry. It relaxes the requirements on the spectral resolution, allowing for simple grating spectrometers as detector.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2016 (1)

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

2015 (1)

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

2013 (2)

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

2012 (2)

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

2011 (1)

2010 (1)

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

2009 (7)

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[Crossref] [PubMed]

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[Crossref] [PubMed]

S.-W Kim, “Metrology: combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

S. Diddams, M. Kirchner, T. Fortier, D. Braje, A. Weiner, and L. Holberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17(5), 3331–3340 (2009).
[Crossref] [PubMed]

2008 (5)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Y. Salvadé, N. Schuhler, S. Léveque, and S. Le Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008).
[Crossref] [PubMed]

M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Appl. Phys. B 91, 397–414 (2008).
[Crossref]

2007 (2)

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

2006 (1)

2004 (1)

2000 (2)

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

1993 (1)

K.P. Birch and M. J. Downs, “An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Araujo-Hauck, C.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Araujo-Hauck, P. L. C.

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Bae, E.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Balling, P.

Benedick, A. J.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Bhattacharya, N.

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[Crossref] [PubMed]

Birch, K.P.

K.P. Birch and M. J. Downs, “An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Braat, J. J.

Braje, D.

Braje, D. A.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Coddington, I.

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Cui, M.

D’Odorico, S.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Dekker, H.

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Diddams, S.

Diddams, S. A.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Downs, M. J.

K.P. Birch and M. J. Downs, “An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Fendel, P.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Fischer, M.

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Fortier, T.

S. Diddams, M. Kirchner, T. Fortier, D. Braje, A. Weiner, and L. Holberg, “Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb,” Opt. Express 17(5), 3331–3340 (2009).
[Crossref] [PubMed]

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Glenday, A. G.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Gohle, Ch.

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Han, H. N.

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Han, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Hänsch, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

Hänsch, T. W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Holberg, L.

Holzwarth, R.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Hou, L.

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Hyun, S.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Jin, J.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Joo, K. N.

Kaeufl, H. U.

P. O. Schmidt, S. Kimeswenger, and H. U. Kaeufl, “A new Generation of Spectrometer Calibration Techniques based on Optical Frequency Combs,” arXiv:0705.0763, (2007).

Kärtner, F. X.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Kentischer, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Kim, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

Kim, S. W.

Kim, S.-W

S.-W Kim, “Metrology: combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

Kim, S.-W.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Kim, Y.

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Kim, Y.-J.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Kimeswenger, S.

P. O. Schmidt, S. Kimeswenger, and H. U. Kaeufl, “A new Generation of Spectrometer Calibration Techniques based on Optical Frequency Combs,” arXiv:0705.0763, (2007).

Kirchner, M.

Kirchner, M. S.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Knight, J. C.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Kok, G. J.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Kren, P.

Le Floch, S.

Lee, J.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, K.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, S.

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lešundák, A.

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

Léveque, S.

Li, C.-H.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Li, D. H.

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Manescau, A.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Mašika, P.

Matsumoto, H.

Minoshima, K.

Murphy, M. T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Murphy, T. M.

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Nenadovic, L.

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Newbury, N.

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Osterman, S.

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Pasquini, L.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Persijn, S. T.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Phillips, D. F.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Russell, P. S. J.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Salvadé, Y.

Sasselov, D.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Schliesser, A.

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Schmidt, P. O.

P. O. Schmidt, S. Kimeswenger, and H. U. Kaeufl, “A new Generation of Spectrometer Calibration Techniques based on Optical Frequency Combs,” arXiv:0705.0763, (2007).

Schmidt, W.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Schuhler, N.

Sizmann, A.

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Stein, B.

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Steinmetz, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Swann, W.

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Szentgyorgyi, A.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Takahashi, S.

Takamasu, K.

Thorpe, M. J.

M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Appl. Phys. B 91, 397–414 (2008).
[Crossref]

Udem, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Urbach, H. P.

van den Berg, S. A.

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[Crossref] [PubMed]

P. Balling, P. Křen, P. Mašika, and S. A. van den Berg, “Femtosecond frequency comb based distance measurement in air,” Opt. Express 17(11), 9300–9313 (2009).
[Crossref] [PubMed]

van Eldik, S.

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

Voigt, D.

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

Wadsworth, W. J.

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

Walsworth, R. L.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Wei, D.

Wei, Z. Y.

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Weiner, A.

Wilken, T.

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

Ye, J.

M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Appl. Phys. B 91, 397–414 (2008).
[Crossref]

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004).
[Crossref] [PubMed]

Zeitouny, M. G.

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34(13), 1982–1984 (2009).
[Crossref] [PubMed]

Zhang, J. W.

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (2)

M. J. Thorpe and J. Ye, “Cavity-enhanced direct frequency comb spectroscopy,” Appl. Phys. B 91, 397–414 (2008).
[Crossref]

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. Hänsch, and T. Udem, “Fabry–Pérot filter cavities for wide-spaced frequency combs with large spectral bandwidth,” Appl. Phys. B,  96, 251–256 (2009).
[Crossref]

Chinese Phys. Lett. (1)

L. Hou, H. N. Han, J. W. Zhang, D. H. Li, and Z. Y. Wei, “A Wide Spaced Femtosecond Ti:Sapphire Frequency Comb at 15 GHz by a Fabry–Pérot Filter Cavity,” Chinese Phys. Lett.,  30(10), 104203 (2013).
[Crossref]

Meas. Sci. Technol. (3)

J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013).
[Crossref]

J. Lee, K. Lee, S. Lee, S.-W. Kim, and Y.-J. Kim, “High precision laser ranging by time-of-flight measurement of femtosecond pulses,” Meas. Sci. Technol. 23(6), 065203 (2012).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Metrologia (1)

K.P. Birch and M. J. Downs, “An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Mon.Not.Roy.Astron.Soc (1)

T. M. Murphy, T. Udem, R. Holzwarth, A. Sizmann, P. L. C. Araujo-Hauck, H. Dekker, S. D’Odorico, M. Fischer, and T. W. Hänsch, “High-precision wavelength calibration of astronomical spectrographs with laser frequency combs,” Mon.Not.Roy.Astron.Soc,  380, 839–847 (2007).

Nat. Photonics (3)

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

I. Coddington, W. Swann, L. Nenadovic, and N. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

S.-W Kim, “Metrology: combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

Nature (1)

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1,” Nature 452, 610–612 (2008).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (3)

R. Holzwarth, T. Udem, T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Optical frequency synthesizer for precision spectroscopy,” Phys. Rev. Lett. 85(11), 2264–2267 (2000).
[Crossref] [PubMed]

S. A. van den Berg, S. T. Persijn, G. J. Kok, M. G. Zeitouny, and N. Bhattacharya, “Many-wavelength interferometry with thousands of lasers for absolute distance measurement,” Phys. Rev. Lett. 108(18), 183901 (2012).
[Crossref] [PubMed]

Ch. Gohle, B. Stein, A. Schliesser, T. Udem, and T. W. Hänsch, “Frequency comb vernier spectroscopy for broadband, high-resolution, high-sensitivity absorption and dispersion spectra,” Phys. Rev. Lett. 99, 263902 (2007).
[Crossref]

Proc. SPIE (1)

D. Voigt, S. A. van den Berg, A. Lešundák, S. van Eldik, and N. Bhattacharya, “High-accuracy absolute distance measurement with a mode-resolved optical frequency comb,” Proc. SPIE 9899, Optical Sensing and Detection IV, 989906 (2016).
[Crossref]

Sci. Rep. (1)

S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5, 14661 (2015).
[Crossref] [PubMed]

Science (1)

T. Steinmetz, T. Wilken, C. Araujo-Hauck, R. Holzwarth, T. W. Hänsch, L. Pasquini, A. Manescau, S. D’Odorico, M. T. Murphy, T. Kentischer, W. Schmidt, and T. Udem, “Laser Frequency Combs for Astronomical Observations,” Science 321, 1335 (2008).
[Crossref] [PubMed]

The European Physical Journal D (1)

D. A. Braje, M. S. Kirchner, S. Osterman, T. Fortier, and S. A. Diddams, “Astronomical spectrograph calibration with broad-spectrum frequency combs,” The European Physical Journal D,  48(1), 57–66 (2008).
[Crossref]

Other (2)

P. O. Schmidt, S. Kimeswenger, and H. U. Kaeufl, “A new Generation of Spectrometer Calibration Techniques based on Optical Frequency Combs,” arXiv:0705.0763, (2007).

“Resolution 1 of the 17th CGPM,” BIPM, (1983).

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Figures (5)

Fig. 1
Fig. 1 a) Example of transmission of low finesse F = 7 Fabry-Pérot resonator (gray) in frequency domain, frequency components of optical comb (red). The FSR of the resonator is 1.1 times the comb mode spacing and thus every 11th comb mode is resonant with the resonator. b) Total transmission versus cavity length change of Fabry-Pérot resonator for two values of f0 = 0 GHz (solid) and f0 = 0.18 GHz (dotted). Other parameters are: central frequency f = 365 THz, FSR = 1.1 GHz, frep = 1 GHz and finesse F = 313.
Fig. 2
Fig. 2 Simulation of frequency comb mode suppression by filter cavity with FSR = 18 2 3 GHz. The comb repetition rate is frep = 1 GHz, the offset frequency f0 = 180 MHz and the bandwidth of 14 nm is centered at 820 nm. With a cavity finesse F = 313 (mirror reflection 99%), the suppression of unwanted modes remains below 20 dB. The transmission of wanted modes is suppressed at the edges of the spectrum due to the offset frequency only by 0.1 dB. On the left side a small zoomed part of the spectrum is shown, to visualize individual modes. On the right side the mode suppression is shown for the full spectrum.
Fig. 3
Fig. 3 Experimental setup split into 3 sections. a) Filtering part showing the frequency comb laser, cavity mode-matching optics, cavity with piezo actuator, collimation lens and beam sampler. The green parts are the detector and electronics for locking the cavity length. The filtered frequency comb is led through an optical circulator towards the 50 m bench part. b) This part shows two Michelson interferometers with a common measurement arm for the filtered frequency comb and the HeNe laser. c) Spectral analysis of the interferometer output with a diffraction grating and linear CCD camera.
Fig. 4
Fig. 4 Top: typical reference measurement-blue, used for finding I(f) positions at CCD and I0 intensities - red circles. Middle: interference measurement - blue, with values of I(f) · I0 intensities - red circles. Bottom: normalized intensities I(f) - blue circles and cosine fit - red.
Fig. 5
Fig. 5 Measured differences between distance measurement with a filtered frequency comb and a HeNe laser interferometer for distances up to 50 m. The error bars show the standard deviation of the measurements.

Equations (11)

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T ( f , R , L c ) = ( 1 R ) 2 ( 1 R ) 2 + 4 R sin 2 ( 2 π f L c / c )
i FSR = m f rep ,
L c = i m c 2 f rep .
Δ L c c 2 f f rep i FSR = λ 2 m .
Δ L f 0 λ 2 f 0 FSR .
Φ = 4 π L n f c ,
I ( f ) = I 0 cos ( 4 π L n f c ) .
L = C m f rep c 4 π n g .
L pp 2 = c m f rep n g .
L t = 1 2 k L pp ,
L t = 1 2 k L pp + L ,

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