Abstract

Laser interferometry with pm/Hz precision and multi-fringe dynamic range at low frequencies is a core technology to measure the motion of various objects (test masses) in space and ground based experiments for gravitational wave detection and geodesy. Even though available interferometer schemes are well understood, their construction remains complex, often involving, for example, the need to build quasi-monolithic optical benches with dozens of components. In recent years techniques have been investigated that aim to reduce this complexity by combining phase modulation techniques with sophisticated digital readout algorithms. This article presents a new scheme that uses strong laser frequency modulations in combination with the deep phase modulation readout algorithm to construct simpler and easily scalable interferometers.

© 2015 Optical Society of America

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References

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  1. G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
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    [Crossref]
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2015 (1)

2014 (2)

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, 094011 (2013).
[Crossref]

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

2012 (2)

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

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

2011 (2)

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

J. J. Esteban, A. F. Garcia Marin, S. Barke, A. M. Peinado, F. Guzman Cervantes, I. Bykov, G. Heinzel, and K. Danzmann, “Experimental demonstration of weak-light laser ranging and data communication for LISA,” Opt. Express 19, 15937 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (2)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

G. de Vine, D. S. Rabeling, B. J. Slagmolen, T. T. 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]

2008 (1)

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

2007 (1)

2006 (1)

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

2004 (2)

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

J. Zheng, “Analysis of optical frequency-modulated continuous-wave interference,” Appl. Opt. 43, 4189–4198 (2004).
[Crossref] [PubMed]

2003 (1)

K. Danzmann and A. Rüdiger, “LISA technology - concept, status, prospects,” Class. Quantum Grav. 20, S1 (2003).
[Crossref]

1987 (1)

I. Sakai, R. Youngquist, and G. Parry, “Multiplexing of optical fiber sensors using a frequency-modulated source and gated output,” J. Lightwave Technol. 5, 932–940 (1987).
[Crossref]

1982 (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microw. Theory Techn. 30, 1635–1641 (1982).
[Crossref]

Abramowitz, M.

M. Abramowitz, I. A. Stegun, and et al., Handbook of mathematical functions, vol. 1 (Dover New York, 1972).

Bachman, B.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Bai, Y.-Z.

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

Barke, S.

Braxmaier, C.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Bykov, I.

Cervantes, F. G.

Charrett, T. O.

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, 094011 (2013).
[Crossref]

Chua, S.

Dahl, K.

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

Dandridge, A.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microw. Theory Techn. 30, 1635–1641 (1982).
[Crossref]

Danzmann, K.

T. S. Schwarze, O. Gerberding, F. G. Cervantes, G. Heinzel, and K. Danzmann, “Advanced phasemeter for deep phase modulation interferometry,” Opt. Express 22, 18214–18223 (2014).
[Crossref] [PubMed]

K.-S. Isleif, O. Gerberding, S. Köhlenbeck, A. Sutton, B. Sheard, S. Goßler, D. Shaddock, G. Heinzel, and K. Danzmann, “Highspeed multiplexed heterodyne interferometry,” Opt. Express 22, 24689–24696 (2014).
[Crossref] [PubMed]

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

J. J. Esteban, A. F. Garcia Marin, S. Barke, A. M. Peinado, F. Guzman Cervantes, I. Bykov, G. Heinzel, and K. Danzmann, “Experimental demonstration of weak-light laser ranging and data communication for LISA,” Opt. Express 19, 15937 (2011).
[Crossref] [PubMed]

G. Heinzel, F. Guzmán Cervantes, A. F. García Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express 18, 19076–19086 (2010).
[Crossref] [PubMed]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

K. Danzmann and A. Rüdiger, “LISA technology - concept, status, prospects,” Class. Quantum Grav. 20, S1 (2003).
[Crossref]

de Vine, G.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

G. de Vine, D. S. Rabeling, B. J. Slagmolen, T. T. 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]

Dickson, J.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Esteban, J. J.

Feng, W.

Gao, F.

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

García, A.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Garcia Marin, A. F.

García Marin, A. F.

Gerberding, O.

Gesa, L.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Giallorenzi, T. G.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microw. Theory Techn. 30, 1635–1641 (1982).
[Crossref]

Gibert, F.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

Goßler, S.

K.-S. Isleif, O. Gerberding, S. Köhlenbeck, A. Sutton, B. Sheard, S. Goßler, D. Shaddock, G. Heinzel, and K. Danzmann, “Highspeed multiplexed heterodyne interferometry,” Opt. Express 22, 24689–24696 (2014).
[Crossref] [PubMed]

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

Guzmán, F.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Guzman Cervantes, F.

Guzmán Cervantes, F.

Halverson, P.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Heinzel, G.

K.-S. Isleif, O. Gerberding, S. Köhlenbeck, A. Sutton, B. Sheard, S. Goßler, D. Shaddock, G. Heinzel, and K. Danzmann, “Highspeed multiplexed heterodyne interferometry,” Opt. Express 22, 24689–24696 (2014).
[Crossref] [PubMed]

T. S. Schwarze, O. Gerberding, F. G. Cervantes, G. Heinzel, and K. Danzmann, “Advanced phasemeter for deep phase modulation interferometry,” Opt. Express 22, 18214–18223 (2014).
[Crossref] [PubMed]

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

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

J. J. Esteban, A. F. Garcia Marin, S. Barke, A. M. Peinado, F. Guzman Cervantes, I. Bykov, G. Heinzel, and K. Danzmann, “Experimental demonstration of weak-light laser ranging and data communication for LISA,” Opt. Express 19, 15937 (2011).
[Crossref] [PubMed]

G. Heinzel, F. Guzmán Cervantes, A. F. García Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express 18, 19076–19086 (2010).
[Crossref] [PubMed]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Hoyland, D.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Isleif, K.-S.

Jennrich, O.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Johann, U.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Karnesis, N.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Kissinger, T.

T. Kissinger, T. O. Charrett, and R. P. Tatam, “Range-resolved interferometric signal processing using sinusoidal optical frequency modulation,” Opt. Express 23, 9415–9431 (2015).
[Crossref]

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, 094011 (2013).
[Crossref]

Klipstein, B.

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Klipstein, W.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

Klipstein, W. M.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Köhlenbeck, S.

Kullmann, J.

Lam, T. T.

Luo, J.

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

Martín, V.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Mateos, I.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

McClelland, D. E.

McKenzie, K.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Middleton, K.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Nofrarias, M.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Nowakowski, B. K.

B. K. Nowakowski, D. T. Smith, and S. T. Smith, “Development of a miniature, multichannel, extended fabryperot fiber-optic laser interferometer system for low frequency si-traceable displacement measurement,” in “Proceedings of the 29th ASPE Annual Meeting,” (2014).

Ozawa, T.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Parry, G.

I. Sakai, R. Youngquist, and G. Parry, “Multiplexing of optical fiber sensors using a frequency-modulated source and gated output,” J. Lightwave Technol. 5, 932–940 (1987).
[Crossref]

Peinado, A. M.

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

Rabeling, D. S.

Ramos-Castro, J.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Robertson, D.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Robison, D.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Rüdiger, A.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

K. Danzmann and A. Rüdiger, “LISA technology - concept, status, prospects,” Class. Quantum Grav. 20, S1 (2003).
[Crossref]

Sakai, I.

I. Sakai, R. Youngquist, and G. Parry, “Multiplexing of optical fiber sensors using a frequency-modulated source and gated output,” J. Lightwave Technol. 5, 932–940 (1987).
[Crossref]

Schilling, R.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Schuldt, T.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

Schwarze, T.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Schwarze, T. S.

Shaddock, D.

Shaddock, D. A.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

G. de Vine, D. S. Rabeling, B. J. Slagmolen, T. T. 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]

Shao, C.-G.

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

Sheard, B.

Slagmolen, B. J.

Smith, D. T.

B. K. Nowakowski, D. T. Smith, and S. T. Smith, “Development of a miniature, multichannel, extended fabryperot fiber-optic laser interferometer system for low frequency si-traceable displacement measurement,” in “Proceedings of the 29th ASPE Annual Meeting,” (2014).

Smith, S. T.

B. K. Nowakowski, D. T. Smith, and S. T. Smith, “Development of a miniature, multichannel, extended fabryperot fiber-optic laser interferometer system for low frequency si-traceable displacement measurement,” in “Proceedings of the 29th ASPE Annual Meeting,” (2014).

Spero, R.

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

Spero, R. E.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Stegun, I. A.

M. Abramowitz, I. A. Stegun, and et al., Handbook of mathematical functions, vol. 1 (Dover New York, 1972).

Strain, K. A.

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

Sutton, A.

Sutton, A. J.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

Tatam, R. P.

T. Kissinger, T. O. Charrett, and R. P. Tatam, “Range-resolved interferometric signal processing using sinusoidal optical frequency modulation,” Opt. Express 23, 9415–9431 (2015).
[Crossref]

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, 094011 (2013).
[Crossref]

Terán, M.

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

Tveten, A. B.

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microw. Theory Techn. 30, 1635–1641 (1982).
[Crossref]

Wand, V.

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Ware, B.

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Weise, D.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

Willke, B.

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

Wuchenich, D. M.

Youngquist, R.

I. Sakai, R. Youngquist, and G. Parry, “Multiplexing of optical fiber sensors using a frequency-modulated source and gated output,” J. Lightwave Technol. 5, 932–940 (1987).
[Crossref]

Zheng, J.

J. Zheng, “Analysis of optical frequency-modulated continuous-wave interference,” Appl. Opt. 43, 4189–4198 (2004).
[Crossref] [PubMed]

J. Zheng, Optical frequency-modulated continuous-wave (FMCW) interferometry, vol. 107 (Springer Science & Business Media, 2005).

Zhou, Z.-B.

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

AIP Conf. Proc. (1)

D. Shaddock, B. Ware, P. Halverson, R. E. Spero, and B. Klipstein, “Overview of the LISA Phasemeter,” AIP Conf. Proc. 873, 689–696 (2006).
[Crossref]

Appl. Opt. (1)

Class. Quantum Grav. (6)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Grav. 26, 085008 (2009).
[Crossref]

G. Heinzel, V. Wand, A. García, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, “The LTP interferometer and phasemeter,” Class. Quantum Grav. 21, S581 (2004).
[Crossref]

R. Spero, B. Bachman, G. de Vine, J. Dickson, W. M. Klipstein, T. Ozawa, K. McKenzie, D. A. Shaddock, D. Robison, A. Sutton, and B. Ware, “Progress in Interferometry for LISA at JPL,” Class. Quantum Grav. 28, 094007 (2011).
[Crossref]

K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goßler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav. 29, 095024 (2012).
[Crossref]

A. J. Sutton, K. McKenzie, B. Ware, G. de Vine, R. E. Spero, W. Klipstein, and D. A. Shaddock, “Improved optical ranging for space based gravitational wave detection,” Class. Quantum Grav. 30, 075008 (2013).
[Crossref]

K. Danzmann and A. Rüdiger, “LISA technology - concept, status, prospects,” Class. Quantum Grav. 20, S1 (2003).
[Crossref]

IEEE Trans. Microw. Theory Techn. (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, “Homodyne demodulation scheme for fiber optic sensors using phase generated carrier,” IEEE Trans. Microw. Theory Techn. 30, 1635–1641 (1982).
[Crossref]

J. Lightwave Technol. (1)

I. Sakai, R. Youngquist, and G. Parry, “Multiplexing of optical fiber sensors using a frequency-modulated source and gated output,” J. Lightwave Technol. 5, 932–940 (1987).
[Crossref]

Laser (1)

J. Luo, F. Gao, Y.-Z. Bai, C.-G. Shao, and Z.-B. Zhou, “Test of the equivalence principle with optical readout in space,” Laser 2, f1 (2008).

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, 094011 (2013).
[Crossref]

Opt. Express (7)

T. Kissinger, T. O. Charrett, and R. P. Tatam, “Range-resolved interferometric signal processing using sinusoidal optical frequency modulation,” Opt. Express 23, 9415–9431 (2015).
[Crossref]

G. Heinzel, F. Guzmán Cervantes, A. F. García Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express 18, 19076–19086 (2010).
[Crossref] [PubMed]

T. S. Schwarze, O. Gerberding, F. G. Cervantes, G. Heinzel, and K. Danzmann, “Advanced phasemeter for deep phase modulation interferometry,” Opt. Express 22, 18214–18223 (2014).
[Crossref] [PubMed]

G. de Vine, D. S. Rabeling, B. J. Slagmolen, T. T. 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]

K.-S. Isleif, O. Gerberding, S. Köhlenbeck, A. Sutton, B. Sheard, S. Goßler, D. Shaddock, G. Heinzel, and K. Danzmann, “Highspeed multiplexed heterodyne interferometry,” Opt. Express 22, 24689–24696 (2014).
[Crossref] [PubMed]

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

J. J. Esteban, A. F. Garcia Marin, S. Barke, A. M. Peinado, F. Guzman Cervantes, I. Bykov, G. Heinzel, and K. Danzmann, “Experimental demonstration of weak-light laser ranging and data communication for LISA,” Opt. Express 19, 15937 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Other (4)

B. K. Nowakowski, D. T. Smith, and S. T. Smith, “Development of a miniature, multichannel, extended fabryperot fiber-optic laser interferometer system for low frequency si-traceable displacement measurement,” in “Proceedings of the 29th ASPE Annual Meeting,” (2014).

M. Terán, V. Martín, L. Gesa, I. Mateos, F. Gibert, N. Karnesis, J. Ramos-Castro, T. Schwarze, O. Gerberding, G. Heinzel, F. Guzmán, and M. Nofrarias, “Towards a fpga-controlled deep phase modulation interferometer,” arXiv preprint arXiv:1411.6910 (2014).

M. Abramowitz, I. A. Stegun, and et al., Handbook of mathematical functions, vol. 1 (Dover New York, 1972).

J. Zheng, Optical frequency-modulated continuous-wave (FMCW) interferometry, vol. 107 (Springer Science & Business Media, 2005).

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Figures (6)

Fig. 1
Fig. 1

left: Unequal arm length Mach-Zehnder interferometer with a frequency modulated laser source and two 50/50 beam splitter. The long arm also contains a phase signal φ. right: DFM interferometer photo diode signal (measured in air) for ΔL ≈ 5 cm, with random modulation and signal phase.

Fig. 2
Fig. 2

Sketch of a readout system using DFM. The modulated light is split via a fiber splitter (FS) into a reference interferometer (RI) and into multiple optical heads (OH), where each one reads out the displacement, tip and tilt of one side of a test mass (TM). An optical isolator (ISO) protects the laser from back reflected light. The digital phasemeter (PM) implements a DPM-style readout channel (CH) for each input signal. The depicted OHs were chosen for simplicity, schemes that include polarising optics could, for example, also be used to minimise the amount of light being reflected back to the fiber.

Fig. 3
Fig. 3

Sketch a multiplexed DFM set-up. PRN codes are modulate onto the light with an electro-optic modulator (EOM). The reference interferometer was omitted for simplicity.

Fig. 4
Fig. 4

Sketch of the C-based simulation used to evaluate the performance of DFM. Signal generation and demodulation are performed at a rate equivalent to 250 kHz. After filtering and decimation the complex amplitudes of the signal harmonics are fed into the fit algorithm, which generates the estimated output parameters at a rate of 100 Hz. The time series of the phase and length fed into the measurement interferometer signal generation are also decimated to 100 Hz, to make them available for direct comparisons. The signals vr and vs are modelled versions of the output of the reference interferometer (RI) and the optical head (OH) in Fig. 2.

Fig. 5
Fig. 5

Spectral densities of the phase determined from the simulated measurement interferometer for a purely sinusoidal frequency modulation. The blue curve shows the results without correction, which are completely dominated by laser frequency noise. After the correction using the reference interferometer data the signal itself is fully revealed (green). The residuals, which reveal the underlying noise influence and linearity of the system, are calculated by comparing the corrected phase and the actual phase signal (red). The light blue curve shows a model of the estimated white noise.

Fig. 6
Fig. 6

Spectral densities of the phase determined from the simulated measurement interferometer with an additional frequency modulation component. The blue curve shows the initial results without correction, which are basically equal for all measurements. The residuals calculated between the corrected measurement phase and the actual phase are plotted for four ratios of modulation depths.

Equations (12)

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

f DFM ( t ) = Δ f cos [ 2 π f m t + ψ m ] .
E s = 1 2 E in sin ( ω 0 t + Δ f f m sin [ ω m t + ψ m ] + C ) .
E l = 1 2 E in sin ( ω 0 ( t τ ) + Δ f f m sin [ ω m ( t τ ) + ψ m ] + C φ )
P out ( E s + E l ) 2 P out = P in 2 + P in 2 cos ( ω 0 τ + φ + Δ f f m ( sin [ ω m t + ψ m ] sin [ ω m ( t τ ) + ψ m ] ) ) .
P out = P in 2 + P in 2 cos ( ω 0 τ + φ + Δ f f m ( sin [ ω m t + ψ m ] ) sin [ ω m t + ψ m ] cos [ ω m τ ] + cos [ ω m t + ψ m ] sin [ ω m τ ] ) .
P out = P in 2 + P in 2 cos ( φ + 2 π Δ f τ cos [ ω m t + ψ m ] ) .
Q n = v out ( t ) cos ( n ω m t ) k J n ( m ) cos ( φ + n π 2 ) cos ( n ψ ) I n = v out ( t ) sin ( n ω m t ) k J n ( m ) cos ( φ + n π 2 ) sin ( n ψ ) .
P out = P in 2 + P in 2 [ c ( t ) c ( t τ ) ] · cos ( φ + 2 π Δ f τ sin [ ω m t + ψ m ] ) .
v r = v 0 + v 0 cos ( φ r + 2 π Δ f τ r sin [ ω m t + ψ m , r ] + 2 π f ˜ ( t ) τ r ) + n ˜ r ( t ) .
v s = v 0 + v 0 cos ( φ s + 2 π Δ f τ s ( t ) sin [ ω m t + ψ m , s ] + 2 π f ˜ ( t ) τ s ( t ) ) + n ˜ s ( t ) .
φ s , c = φ s , e ( t ) φ r , e ( t ) m s , e ( t ) m r , e ( t ) = φ s ( t ) + 2 π f ˜ ( t ) τ s ( t ) 2 π f ˜ ( t ) τ r ( t ) τ s , e ( t ) τ r , e ( t ) .
f DFM , mod ( t ) = Δ f cos [ 2 π f m t + ψ m ] + Δ f cos [ 4 π f m t ] .

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