Abstract

Digitally enhanced homodyne interferometry enables robust interferometric sensitivity to be achieved in an optically simple configuration by shifting optical complexity into the digital signal processing regime. We use digitally enhanced homodyne interferometry in a simple, all-fiber Michelson interferometer to achieve a frequency reference stability of better than 20 Hz/√Hz from 10 mHz to 1 Hz, satisfying, for the first time in an all fiber system, the stability requirements for the Gravity Recovery and Climate Experiment Follow On mission. In addition, we have demonstrated stability that satisfies the future mission objectives at frequencies down to 1 mHz. This frequency domain stability translates into a fractional Allan deviation of 3.3 × 10−17 for an integration time of 55 seconds.

© 2014 Optical Society of America

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  1. M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).
  2. J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
    [CrossRef]
  3. T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.
  4. G. A. Cranch, “Frequency noise reduction in erbium-doped fiber distributed-feedback lasers by electronic feedback,” Opt. Lett. 27, 1114–1116 (2002).
    [CrossRef]
  5. K. Takahashi, M. Ando, and K. Tsubono, “Stabilization of laser intensity and frequency using optical fiber,” Opt. Lett. 32, 3355–3357 (2007).
  6. F. Kéfélian, H. Jiang, P. Lemonde, and G. Santarelli, “Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line,” Opt. Lett. 34, 914–916 (2009).
    [CrossRef] [PubMed]
  7. T. T-Y Lam, M. B. Gray, D. A. Shaddock, D. M. McClelland, and J. H. Chow, “Subfrequency noise signal extraction in fiber-optic strain sensors using postprocessing,” Opt. Lett. 37, 2169–2171 (2012).
    [CrossRef] [PubMed]
  8. T. G. McRae, S. Ngo, D. A. Shaddock, M. T. L. Hsu, and M. B. Gray, “Digitally enhanced optical fiber frequency reference,” Opt. Lett. 39, 1752–1755 (2014).
    [CrossRef] [PubMed]
  9. D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett. 32, 3355–3357 (2007).
    [CrossRef] [PubMed]
  10. D. M. Wuchenich, T. T. Y. Lam, J. H. Chow, D. E. McClelland, and D. A. Shaddock, “Laser frequency noise immunity in multiplexed displacement sensing,” Opt. Lett. 36(5), 672–674 (2011).
    [CrossRef] [PubMed]
  11. G. de Vine, D. S. Rabeling, B. J. J. Slagmolen, T. T. Y. Lam, S. Chua, D. M. Wuchenich, D. E. McClelland, and D. A. Shaddock, “Picometer level displacement metrology with digitally enhanced heterodyne interferometry,” Opt. Express 17, 828–837 (2009).
    [CrossRef] [PubMed]
  12. J. Miller, S. Ngo, A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Control and tuning of a suspended Fabry-Perot cavity using digitally enhanced heterodyne interferometry,” Opt. Lett. 37, 4952–4954 (2012).
    [CrossRef] [PubMed]
  13. E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag. 36, 48–54 (1998).
    [CrossRef]
  14. A. J. Sutton, O. Gerberding, G. Heinzel, and D. A. Shaddock, “Digitally enhanced homodyne interferometry,” Opt. Express 20, 22195–22207 (2012).
    [CrossRef] [PubMed]
  15. P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
    [CrossRef]
  16. W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).
  17. http://www.orbitslightwave.com .
  18. B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
    [CrossRef]

2014 (1)

2012 (4)

2011 (1)

2009 (2)

2008 (1)

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

2007 (2)

2002 (1)

1998 (1)

E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag. 36, 48–54 (1998).
[CrossRef]

1982 (1)

P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
[CrossRef]

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Ando, M.

Bender, P.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

Braxmaier, C.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Brown, N.

P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
[CrossRef]

Chow, J. H.

Chua, S.

Craig, R.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

Cranch, G. A.

Danzmann, K.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

de Vine, G.

deVine, G.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Dinan, E. H.

E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag. 36, 48–54 (1998).
[CrossRef]

Döringshoff, K.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Folkner, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Gerberding, O.

Gohlke, M.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Gray, M. B.

Hänsch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Hariharan, P.

P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
[CrossRef]

Heinzel, G.

A. J. Sutton, O. Gerberding, G. Heinzel, and D. A. Shaddock, “Digitally enhanced homodyne interferometry,” Opt. Express 20, 22195–22207 (2012).
[CrossRef] [PubMed]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

Hsu, M. T. L.

Jabbari, B.

E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag. 36, 48–54 (1998).
[CrossRef]

Jiang, H.

Johann, U.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Keetman, A.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Kéfélian, F.

Klipstein, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Kovalchuk, E.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Lam, T. T. Y.

Lam, T. T.-Y.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Lam, T. T-Y

Leitch, J.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Lemonde, P.

Loomis, B.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

McClelland, D. E.

McClelland, D. M.

McKenzie, K.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

McRae, T. G.

Miller, J.

Mullavey, A. J.

Nagel, M.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Neerim, R. S.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

Ngo, S.

Oreb, B. F.

P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
[CrossRef]

Peters, A.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Pierce, R.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Rabeling, D. S.

Reggentin, M.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Santarelli, G.

Schuldt, T.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Shaddock, D. A.

T. G. McRae, S. Ngo, D. A. Shaddock, M. T. L. Hsu, and M. B. Gray, “Digitally enhanced optical fiber frequency reference,” Opt. Lett. 39, 1752–1755 (2014).
[CrossRef] [PubMed]

T. T-Y Lam, M. B. Gray, D. A. Shaddock, D. M. McClelland, and J. H. Chow, “Subfrequency noise signal extraction in fiber-optic strain sensors using postprocessing,” Opt. Lett. 37, 2169–2171 (2012).
[CrossRef] [PubMed]

A. J. Sutton, O. Gerberding, G. Heinzel, and D. A. Shaddock, “Digitally enhanced homodyne interferometry,” Opt. Express 20, 22195–22207 (2012).
[CrossRef] [PubMed]

J. Miller, S. Ngo, A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Control and tuning of a suspended Fabry-Perot cavity using digitally enhanced heterodyne interferometry,” Opt. Lett. 37, 4952–4954 (2012).
[CrossRef] [PubMed]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

D. M. Wuchenich, T. T. Y. Lam, J. H. Chow, D. E. McClelland, and D. A. Shaddock, “Laser frequency noise immunity in multiplexed displacement sensing,” Opt. Lett. 36(5), 672–674 (2011).
[CrossRef] [PubMed]

G. de Vine, D. S. Rabeling, B. J. J. Slagmolen, T. T. Y. Lam, S. Chua, D. M. Wuchenich, D. E. McClelland, and D. A. Shaddock, “Picometer level displacement metrology with digitally enhanced heterodyne interferometry,” Opt. Express 17, 828–837 (2009).
[CrossRef] [PubMed]

D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett. 32, 3355–3357 (2007).
[CrossRef] [PubMed]

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Sheard, B. S.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

Slagmolen, B. J. J.

Spero, R.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Stephens, M.

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Sutton, A. J.

Takahashi, K.

Thompson, R.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

Tsubono, K.

Udem, Th.

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Weise, D.

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

Wuchenich, D. M.

Yu, N.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

IEEE Commun. Mag. (1)

E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and wideband CDMA cellular networks,” IEEE Commun. Mag. 36, 48–54 (1998).
[CrossRef]

J. Geod. (1)

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the grace follow-on mission,” J. Geod. 86, 1083–1095 (2012).
[CrossRef]

Opt. Commun. (1)

P. Hariharan, B. F. Oreb, and N. Brown, “A digital phase-measurement system for real-time holographic interferometry,” Opt. Commun. 41(6), 393–396 (1982).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

J. Miller, S. Ngo, A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Control and tuning of a suspended Fabry-Perot cavity using digitally enhanced heterodyne interferometry,” Opt. Lett. 37, 4952–4954 (2012).
[CrossRef] [PubMed]

G. A. Cranch, “Frequency noise reduction in erbium-doped fiber distributed-feedback lasers by electronic feedback,” Opt. Lett. 27, 1114–1116 (2002).
[CrossRef]

K. Takahashi, M. Ando, and K. Tsubono, “Stabilization of laser intensity and frequency using optical fiber,” Opt. Lett. 32, 3355–3357 (2007).

F. Kéfélian, H. Jiang, P. Lemonde, and G. Santarelli, “Ultralow-frequency-noise stabilization of a laser by locking to an optical fiber-delay line,” Opt. Lett. 34, 914–916 (2009).
[CrossRef] [PubMed]

T. T-Y Lam, M. B. Gray, D. A. Shaddock, D. M. McClelland, and J. H. Chow, “Subfrequency noise signal extraction in fiber-optic strain sensors using postprocessing,” Opt. Lett. 37, 2169–2171 (2012).
[CrossRef] [PubMed]

T. G. McRae, S. Ngo, D. A. Shaddock, M. T. L. Hsu, and M. B. Gray, “Digitally enhanced optical fiber frequency reference,” Opt. Lett. 39, 1752–1755 (2014).
[CrossRef] [PubMed]

D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett. 32, 3355–3357 (2007).
[CrossRef] [PubMed]

D. M. Wuchenich, T. T. Y. Lam, J. H. Chow, D. E. McClelland, and D. A. Shaddock, “Laser frequency noise immunity in multiplexed displacement sensing,” Opt. Lett. 36(5), 672–674 (2011).
[CrossRef] [PubMed]

Phys. Rev. A (1)

J. Alnis, A. Matveev, N. Kolachevsky, Th. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Other (4)

T. Schuldt, A. Keetman, K. Döringshoff, M. Reggentin, E. Kovalchuk, M. Nagel, M. Gohlke, U. Johann, D. Weise, A. Peters, and C. Braxmaier, “An ultra-stable optical frequency reference for space applications,” in Proceedings of the European Frequency and Time Forum (EFTF), Gothenburg (Sweden) (2012), pp. 554–558.

W. M. Folkner, G. deVine, W. M. Klipstein, K. McKenzie, R. Spero, R. Thompson, N. Yu, M. Stephens, J. Leitch, R. Pierce, T. T.-Y. Lam, and D. A. Shaddock, “Laser frequency stabilization for GRACE-2,” in Proceedings of the 2011 Earth Science Technology Forum(2011).

http://www.orbitslightwave.com .

M. Stephens, R. Craig, J. Leitch, R. Pierce, R. S. Neerim, P. Bender, and B. Loomis, “Interferometric Range Transceiver for Measuring Temporal Gravity Variations,” in Proceedings of the 2006 Earth Science Technology Conference, College Park, MD (2006).

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Figures (5)

Fig. 1
Fig. 1

Phase space (or constellation) diagram showing how the imaginary (Im) and real (Re) components of a light field are encoded with one of four different phases. The logical combinations of pseudo-random noise codes 1 and 2 (C1 and C2 respectively) determines the amount of phase modulation.

Fig. 2
Fig. 2

Experimental setup. The laser is encoded with a 4–level phase shift via the acousto-optic modulator (AOM) and is split into two optical fiber Michelson interferometers (OFMI’s). We demodulate both OFMI outputs and form the subtraction and addition terms for phase extraction.

Fig. 3
Fig. 3

a) The Isig and Qsig components of a single, freely drifting interferometer. b) As with a) but with an induced linear phase ramp of 5 cycles/second. c) The resulting phase for the drifting interferometer (green) and with the linear phase ramp (red). d) A spectral density plot of the unwrapped optical phase for the drifting interferometer (green) and the linear phase ramp (red). The traces differ significantly only at 5 Hz (fundamental) and 10 Hz (second harmonic), corresponding to the cyclic error harmonic components, as shown by the arrows in the red trace.

Fig. 4
Fig. 4

a) These two traces show the near identical free running outputs from both fiber interferometers. b) By subtracting the two and then applying TDI, we obtain the green trace, which meets c) the GRACE Follow-On requirements of 30 Hz/√Hz [9] between 20 mHz and 1 Hz as shown in red. Future mission objectives [18] are shown as the red dashed curve.

Fig. 5
Fig. 5

Fractional Allan deviation plot of the time domain difference measurement of the two fiber interferometers. The deviation is minimized to 3.3 × 10−17 at an integration time (τ) of 55 seconds.

Equations (12)

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ϕ QPSK = [ ( C 1 & C 2 ) × 1 + ( C 1 ¯ & C 2 ) × 3 ( C 1 ¯ & C 2 ¯ ) × 3 ( C 1 & C 2 ¯ ) × 1 ] × π / 4
ϕ RF = sin ( 2 π f NCO + ϕ QPSK )
ϕ AOM = ϕ RF + ϕ L
I out ( τ ) = ( C 1 ( τ ) & C 2 ( τ ) C 1 ( τ ) ¯ & C 2 ( τ ) ¯ ) × V PD
Q out ( τ ) = ( C 1 ( τ ) ¯ & C 2 ( τ ) + C 1 ( τ ) & C 2 ( τ ) ¯ ) × V PD
II = I out ( τ 1 ) × I out ( τ 2 ) × V PD
IQ = I out ( τ 1 ) × Q out ( τ 2 ) × V PD
QI = Q out ( τ 1 ) × I out ( τ 2 ) × V PD
QQ = Q out ( τ 1 ) × Q out ( τ 2 ) × V PD
I sig = II + QQ
Q sig = IQ QI
ϕ sig = arctan ( Q sig I sig )

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