Abstract

Digitally enhanced heterodyne interferometry is a metrology technique that uses pseudo-random noise codes for modulating the phase of the laser light. Multiple interferometric signals from the same beam path can thereby be isolated based on their propagation delay, allowing one to use advantageous optical layouts in comparison to classic laser interferometers. We present here a high speed version of this technique for measuring multiple targets spatially separated by only a few centimetres. This allows measurements of multiplexed signals using free beams, making the technique attractive for several applications requiring compact optical set-ups like for example space-based interferometers. In an experiment using a modulation and sampling rate of 1.25 GHz we are able to demonstrate multiplexing between targets only separated by 36 cm and we achieve a displacement measurement noise floor of <3pm/Hz at 10 Hz between them. We identify a limiting excess noise at low frequencies which is unique to this technique and is probably caused by the finite bandwidth in our measurement set-up. Utilising an active clock jitter correction scheme we are also able to reduce this noise in a null measurement configuration by one order of magnitude.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. 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]
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    [Crossref]
  5. A. J. Sutton, O. Gerberding, G. Heinzel, and D. A. Shaddock, “Digitally enhanced homodyne interferometry,” Opt. Express 20, 22195–22207 (2012).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  11. O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
    [Crossref]
  12. O. P. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, “Coherent range-gated laser displacement metrology with compact optical head,” Opt. Lett. 32(20), 2933–2935 (2007).
    [Crossref] [PubMed]
  13. J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
    [Crossref]

2013 (2)

T. Kissinger, T. O. H. Charrett, and R. P. Tatam, “Fibre segment interferometry using code-division multiplexed optical signal processing for strain sensing applications,” Meas. Sci. Technol. 24(9), 094011 (2013).
[Crossref]

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

2012 (3)

2011 (1)

2010 (1)

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

2009 (1)

2008 (1)

P. McNamara, S. Vitale, and K. Danzmann, and on behalf of the LISA Pathfinder Science Working Team, “LISA Pathfinder,” Classical Quant. Grav. 25(11), 11403 (2008).
[Crossref]

2007 (2)

2006 (1)

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

1996 (1)

K. Danzmann, and the LISA study team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Classical Quant. Grav. 13(11A), A247 (1996).
[Crossref]

Bykov, I.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Charrett, T. O. H.

T. Kissinger, T. O. H. Charrett, and R. P. Tatam, “Fibre segment interferometry using code-division multiplexed optical signal processing for strain sensing applications,” Meas. Sci. Technol. 24(9), 094011 (2013).
[Crossref]

Chow, J. H.

Chua, S.

Danzmann, K.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

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(12), 1083–1095 (2012).
[Crossref]

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

P. McNamara, S. Vitale, and K. Danzmann, and on behalf of the LISA Pathfinder Science Working Team, “LISA Pathfinder,” Classical Quant. Grav. 25(11), 11403 (2008).
[Crossref]

K. Danzmann, and the LISA study team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Classical Quant. Grav. 13(11A), A247 (1996).
[Crossref]

de Vine, G.

Dubovitsky, S.

Eichholz, J.

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Esteban, J. J.

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Esteban Delgado, J. J.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

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(12), 1083–1095 (2012).
[Crossref]

García, A. F.

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Gerberding, O.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

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

Halverson, P. G.

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

Heinzel, G.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

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(12), 1083–1095 (2012).
[Crossref]

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

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Kissinger, T.

T. Kissinger, T. O. H. Charrett, and R. P. Tatam, “Fibre segment interferometry using code-division multiplexed optical signal processing for strain sensing applications,” Meas. Sci. Technol. 24(9), 094011 (2013).
[Crossref]

Klipstein, B.

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

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(12), 1083–1095 (2012).
[Crossref]

Kullmann, J.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

Lam, T. T.-Y.

Lay, O. P.

McClelland, D. E.

McNamara, P.

P. McNamara, S. Vitale, and K. Danzmann, and on behalf of the LISA Pathfinder Science Working Team, “LISA Pathfinder,” Classical Quant. Grav. 25(11), 11403 (2008).
[Crossref]

Miller, J.

Mullavey, A. J.

Ngo, S.

Peinado, A. M.

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Rabeling, D. S.

Shaddock, D.

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

Shaddock, D. A.

Sheard, B.

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

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(12), 1083–1095 (2012).
[Crossref]

Slagmolen, B. J. J.

Spero, R. E.

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

Sutton, A. J.

Tatam, R. P.

T. Kissinger, T. O. H. Charrett, and R. P. Tatam, “Fibre segment interferometry using code-division multiplexed optical signal processing for strain sensing applications,” Meas. Sci. Technol. 24(9), 094011 (2013).
[Crossref]

Vitale, S.

P. McNamara, S. Vitale, and K. Danzmann, and on behalf of the LISA Pathfinder Science Working Team, “LISA Pathfinder,” Classical Quant. Grav. 25(11), 11403 (2008).
[Crossref]

Ware, B.

O. P. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, “Coherent range-gated laser displacement metrology with compact optical head,” Opt. Lett. 32(20), 2933–2935 (2007).
[Crossref] [PubMed]

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

Wuchenich, D. M.

AIP Conf. Proc. (1)

D. Shaddock, B. Ware, P. G. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 654 (2006).
[Crossref]

Classical Quant. Grav. (3)

O. Gerberding, B. Sheard, I. Bykov, J. Kullmann, J. J. Esteban Delgado, K. Danzmann, and G. Heinzel, “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments,” Classical Quant. Grav. 30(23), 235029 (2013).
[Crossref]

K. Danzmann, and the LISA study team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Classical Quant. Grav. 13(11A), A247 (1996).
[Crossref]

P. McNamara, S. Vitale, and K. Danzmann, and on behalf of the LISA Pathfinder Science Working Team, “LISA Pathfinder,” Classical Quant. Grav. 25(11), 11403 (2008).
[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(12), 1083–1095 (2012).
[Crossref]

J. Phys. Conf. Ser. (1)

J. J. Esteban, A. F. García, J. Eichholz, A. M. Peinado, I. Bykov, G. Heinzel, and K. Danzmann, “Ranging and phase measurement for LISA,” J. Phys. Conf. Ser. 228(1), 012045 (2010).
[Crossref]

Meas. Sci. Technol. (1)

T. Kissinger, T. O. H. Charrett, and R. P. Tatam, “Fibre segment interferometry using code-division multiplexed optical signal processing for strain sensing applications,” Meas. Sci. Technol. 24(9), 094011 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

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Figures (4)

Fig. 1
Fig. 1 Simplified schematic of the experimental set-up for digitally enhanced heterodyne interferometry. The optical part is shown on the left. Here, two laser beams with an offset frequency are used to establish the heterodyne interferometer. The phase measurement system (PMS) is shown on the right. It generates the PRN code that is used for the optical phase modulation via an EOM and for the digital demodulation, and it also extracts the phase and amplitude of the digitised and demodulated heterodyne signals.
Fig. 2
Fig. 2 Measured signal amplitudes of a delay scan using the two-mirror set-up (see inset) with a mirror separation of 36 cm and a PRN rate of 1.25 GHz. The amplitude of the model is determined by the power levels expected from the cavity response for collimated beams. The model also assumes that the bandwidth of the PRN code generation and the signal detection is infinite.
Fig. 3
Fig. 3 Displacement spectral density of the two-mirror set-up using a phase modulation of 1.25 GHz and a mirror separation of 36 cm. Shown is the phase noise of the initial signals x (blue), the relative mirror motions ba (orange) and ca (green) and the null measurement Δ (red).
Fig. 4
Fig. 4 Displacement spectral density of the single-mirror set-up sampled with 1.25 GHz and with and without active clock stabilisation. Shown is the displacement noise of the initial signals x (blue) by using a PRN modulation rate of 1.25 GHz and without DLL, the corresponding null measurement ε̃ is shown in the second plot (green). A reduction of the modulation rate to 625 MHz shows likely the same displacement noise x (blue) and a similar ε̃ (red). The achieved performance for ε̃, by applying the clock stabilisation, is given by the final plot (black).

Equations (6)

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

v = c ( t τ d , x ) v ¯ sin ( ω t + φ + c ( t ) ) v PD ( t )
= c ( t τ d , x ) c ( t ) c corr ( τ d , x ) v ¯ sin ( ω t + φ ) v het .
l ˜ ba = 2 π λ ( φ b φ a ) = : 2 π λ φ ba .
l ˜ ca = 2 π λ ( φ c φ a ) / 2 = : 2 π λ φ ca / 2 .
Δ l ˜ = l ˜ ba l ˜ ca 0 .
ε ˜ = 2 π λ ( φ a + φ a ) 0 .

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