We present two variations of a novel interferometry technique capable of simultaneously measuring multiple targets with high sensitivity. The technique performs a homodyne phase measurement by application of a four point phase shifting algorithm, with pseudo-random switching between points to allow multiplexed measurement based upon propagation delay alone. By multiplexing measurements and shifting complexity into signal processing, both variants realise significant complexity reductions over comparable methods. The first variant performs a typical coherent detection with a dedicated reference field and achieves a displacement noise floor 0.8pm/√Hz above 50Hz. The second allows for removal of the dedicated reference, resulting in further simplifications and improved low frequency performance with a 1pm/√Hz noise floor measured down to 20Hz. These results represent the most sensitive measurement performed using this style of interferometry whilst simultaneously reducing the electro-optic footprint.

© 2012 OSA

1. The LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Rep. Prog. Phys.72, 076901 (2009).
2. T. T.-Y. Lam, M. B. Gray, D. A. Shaddock, D. E. McClelland, and J. H. Chow, “Subfrequency noise signal extraction in fiber-optic strain sensors using postprocessing,” Opt. Lett.37, 2169–2171 (2012). [CrossRef]
3. B. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. Klipstein, and W. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J Geodesy 10.1007/s00190-012-0566-3 (2012). [CrossRef]
4. M. Evans, N. Mavalvala, P. Fritschel, R. Bork, B. Bhawal, R. Gustafson, W. Kells, M. Landry, D. Sigg, R. Weiss, S. Whitcomb, and H. Yamamoto, “Lock acquisition of a gravitational-wave interferometer,” Opt. Lett.27, 598– 600 (2002). [CrossRef]
5. A. Bouchez, B. McLeod, D. Acton, and S. Kanneganti, “The Giant Magellan Telescope phasing system,” Proc. SPIE7 (2012).
6. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4, 907–926 (1993). [CrossRef]
7. G. de Vine, B. Ware, K. McKenzie, R. E. Spero, W. M. Klipstein, and D. A. Shaddock, “Experimental demonstration of time-delay interferometry for the Laser Interferometer Space Antenna,” Phys. Rev. Lett.104, 1–4 (2010). [CrossRef]
8. S. Anza, M. Armano, E. Balaguer, M. Benedetti, C. Boatella, P. Bosetti, D. Bortoluzzi, N. Brandt, C. Braxmaier, M. Caldwell, L. Carbone, A. Cavalleri, A. Ciccolella, I. Cristofolini, M. Cruise, M. Da Lio, K. Danzmann, D. Desiderio, R. Dolesi, N. Dunbar, W. Fichter, C. Garcia, E. Garcia-Berro, A. F. Garcia Marin, R. Gerndt, A. Gianolio, D. Giardini, R. Gruenagel, A. Hammesfahr, G. Heinzel, J. Hough, D. Hoyl, M. Hueller, O. Jennrich, U. Johann, S. Kemble, C. Killow, D. Kolbe, M. Landgraf, A. Lobo, V. Lorizzo, D. Mance, K. Middleton, F. Nappo, M. Nofrarias, G. Racca, J. Ramos, D. Robertson, M. Sallusti, M. Sandford, J. Sanjuan, P. Sarra, A. Selig, D. Shaul, D. Smart, M. Smit, L. Stagnaro, T. Sumner, C. Tirabassi, S. Tobin, S. Vitale, V. Wand, H. Ward, W. J. Weber, and P. Zweifel, “The LTP experiment on the LISA Pathfinder mission,” Classical Quant. Grav.22, S125 (2005). [CrossRef]
9. D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett.32, 3355–3357 (2007). [CrossRef]
10. S. Golomb, “On the classification of balanced binary sequences of period 2n-1(Corresp.),” IEEE Trans. Inform. Theory26, 730–732 (1980). [CrossRef]
11. S. Raghavan, M. Shane, and R. Yowell, “Spread spectrum codes for GPS L5,” in 2006 Aerosp. Conf. Proc., 1–7 (2006). [CrossRef]
12. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation CW lidar,” Appl. Opt.22, 1382–1386 (1983). [CrossRef]
13. 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. Express17, 828–837 (2009). [CrossRef]
14. D. M. R. 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, 672–674 (2011). [CrossRef]
15. O. P. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, “Coherent range-gated laser displacement metrology with compact optical head,” Opt. Lett.32, 2933–2935 (2007). [CrossRef]
16. K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav.29095024 (2012). [CrossRef]
17. O. Jennrich, “LISA technology and instrumentation,” Class. Quantum Grav.26153001 (2009). [CrossRef]
18. D. Shaddock, B. Ware, P. Halverson, R. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” “6th International LISA Symposium”, AIP Conf. Proc.873, 654–660 (2006). [CrossRef]
19. I. Bykov, J. J. E. Delgado, A. F. G. Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: advanced prototyping,” J. Phys. Conf. Ser.154, 012017 (2009). [CrossRef]
20. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt.35, 51–60 (1996). [CrossRef]
21. Y. Surrel, “Fringe analysis,” Top. Appl. Phys.77/2000, 55–102 (2000). [CrossRef]
22. E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum.82, 061101 (2011). [CrossRef]
23. G. Heinzel, F. Guzmán Cervantes, A. F. García Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express18, 19076–19086 (2010). [CrossRef]
24. P. Hariharan and B. Oreb, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt.5–7 (1987).
25. J. Proakis and M. Salehi, Communication Systems Engineering (Prentice Hall, 1994).
26. P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-loop bias control of optical quadrature modulator,” IEEE Photon. Technol. Lett.18, 2209–2211 (2006). [CrossRef]
27. M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Light-wave Technol.27, 901–914 (2009). [CrossRef]
28. P. L. M. Heydemann, “Determination and correction of quadrature fringe measurement errors in interferometers,” Appl. Opt.20, 3382–3384 (1981). [CrossRef]
29. A. E. Rosenbluth and N. Bobroff, “Optical sources of non-linearity in heterodyne interferometers,” Precis. Eng.12, 7–11 (1990). [CrossRef]
30. W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14, 91–98 (1992). [CrossRef]
31. T. G. McRae, M. T. L. Hsu, C. H. Freund, D. A. Shaddock, J. Herrmann, and M. B. Gray, “Linearization and minimization of cyclic error with heterodyne laser interferometry,” Opt. Lett.37, 2448–2450 (2012). [CrossRef]

2006 Aerosp. Conf. Proc.

• S. Raghavan, M. Shane, and R. Yowell, “Spread spectrum codes for GPS L5,” in 2006 Aerosp. Conf. Proc., 1–7 (2006). [CrossRef]

AIP Conf. Proc.

• D. Shaddock, B. Ware, P. Halverson, R. Spero, and B. Klipstein, “Overview of the LISA phasemeter,” “6th International LISA Symposium”, AIP Conf. Proc.873, 654–660 (2006). [CrossRef]

Appl. Opt.

• Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt.35, 51–60 (1996). [CrossRef]
• P. Hariharan and B. Oreb, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt.5–7 (1987).
• P. L. M. Heydemann, “Determination and correction of quadrature fringe measurement errors in interferometers,” Appl. Opt.20, 3382–3384 (1981). [CrossRef]
• N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation CW lidar,” Appl. Opt.22, 1382–1386 (1983). [CrossRef]

Class. Quantum Grav.

• K. Dahl, G. Heinzel, B. Willke, K. A. Strain, S. Goler, and K. Danzmann, “Suspension platform interferometer for the AEI 10 m prototype: concept, design and optical layout,” Class. Quantum Grav.29095024 (2012). [CrossRef]
• O. Jennrich, “LISA technology and instrumentation,” Class. Quantum Grav.26153001 (2009). [CrossRef]

Classical Quant. Grav.

• S. Anza, M. Armano, E. Balaguer, M. Benedetti, C. Boatella, P. Bosetti, D. Bortoluzzi, N. Brandt, C. Braxmaier, M. Caldwell, L. Carbone, A. Cavalleri, A. Ciccolella, I. Cristofolini, M. Cruise, M. Da Lio, K. Danzmann, D. Desiderio, R. Dolesi, N. Dunbar, W. Fichter, C. Garcia, E. Garcia-Berro, A. F. Garcia Marin, R. Gerndt, A. Gianolio, D. Giardini, R. Gruenagel, A. Hammesfahr, G. Heinzel, J. Hough, D. Hoyl, M. Hueller, O. Jennrich, U. Johann, S. Kemble, C. Killow, D. Kolbe, M. Landgraf, A. Lobo, V. Lorizzo, D. Mance, K. Middleton, F. Nappo, M. Nofrarias, G. Racca, J. Ramos, D. Robertson, M. Sallusti, M. Sandford, J. Sanjuan, P. Sarra, A. Selig, D. Shaul, D. Smart, M. Smit, L. Stagnaro, T. Sumner, C. Tirabassi, S. Tobin, S. Vitale, V. Wand, H. Ward, W. J. Weber, and P. Zweifel, “The LTP experiment on the LISA Pathfinder mission,” Classical Quant. Grav.22, S125 (2005). [CrossRef]

IEEE Photon. Technol. Lett.

• P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-loop bias control of optical quadrature modulator,” IEEE Photon. Technol. Lett.18, 2209–2211 (2006). [CrossRef]

IEEE Trans. Inform. Theory

• S. Golomb, “On the classification of balanced binary sequences of period 2n-1(Corresp.),” IEEE Trans. Inform. Theory26, 730–732 (1980). [CrossRef]

J. Light-wave Technol.

• M. G. Taylor, “Phase estimation methods for optical coherent detection using digital signal processing,” J. Light-wave Technol.27, 901–914 (2009). [CrossRef]

J. Phys. Conf. Ser.

• I. Bykov, J. J. E. Delgado, A. F. G. Marín, G. Heinzel, and K. Danzmann, “LISA phasemeter development: advanced prototyping,” J. Phys. Conf. Ser.154, 012017 (2009). [CrossRef]

Meas. Sci. Technol.

• N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4, 907–926 (1993). [CrossRef]

Opt. Express

• 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. Express17, 828–837 (2009). [CrossRef]
• G. Heinzel, F. Guzmán Cervantes, A. F. García Marin, J. Kullmann, W. Feng, and K. Danzmann, “Deep phase modulation interferometry,” Opt. Express18, 19076–19086 (2010). [CrossRef]

Opt. Lett.

• T. G. McRae, M. T. L. Hsu, C. H. Freund, D. A. Shaddock, J. Herrmann, and M. B. Gray, “Linearization and minimization of cyclic error with heterodyne laser interferometry,” Opt. Lett.37, 2448–2450 (2012). [CrossRef]
• D. M. R. 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, 672–674 (2011). [CrossRef]
• O. P. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, “Coherent range-gated laser displacement metrology with compact optical head,” Opt. Lett.32, 2933–2935 (2007). [CrossRef]
• D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett.32, 3355–3357 (2007). [CrossRef]
• T. T.-Y. Lam, M. B. Gray, D. A. Shaddock, D. E. McClelland, and J. H. Chow, “Subfrequency noise signal extraction in fiber-optic strain sensors using postprocessing,” Opt. Lett.37, 2169–2171 (2012). [CrossRef]
• M. Evans, N. Mavalvala, P. Fritschel, R. Bork, B. Bhawal, R. Gustafson, W. Kells, M. Landry, D. Sigg, R. Weiss, S. Whitcomb, and H. Yamamoto, “Lock acquisition of a gravitational-wave interferometer,” Opt. Lett.27, 598– 600 (2002). [CrossRef]

Phys. Rev. Lett.

• G. de Vine, B. Ware, K. McKenzie, R. E. Spero, W. M. Klipstein, and D. A. Shaddock, “Experimental demonstration of time-delay interferometry for the Laser Interferometer Space Antenna,” Phys. Rev. Lett.104, 1–4 (2010). [CrossRef]

Precis. Eng.

• A. E. Rosenbluth and N. Bobroff, “Optical sources of non-linearity in heterodyne interferometers,” Precis. Eng.12, 7–11 (1990). [CrossRef]
• W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14, 91–98 (1992). [CrossRef]

Proc. SPIE

• A. Bouchez, B. McLeod, D. Acton, and S. Kanneganti, “The Giant Magellan Telescope phasing system,” Proc. SPIE7 (2012).

Rep. Prog. Phys.

• The LIGO Scientific Collaboration, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Rep. Prog. Phys.72, 076901 (2009).

Rev. Sci. Instrum.

• E. Hack and J. Burke, “Invited review article: measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum.82, 061101 (2011). [CrossRef]

Top. Appl. Phys.

• Y. Surrel, “Fringe analysis,” Top. Appl. Phys.77/2000, 55–102 (2000). [CrossRef]

Other

• J. Proakis and M. Salehi, Communication Systems Engineering (Prentice Hall, 1994).
• B. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. Klipstein, and W. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J Geodesy 10.1007/s00190-012-0566-3 (2012). [CrossRef]

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