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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 19076–19086

Deep phase modulation interferometry

Gerhard Heinzel, Felipe Guzmán Cervantes, Antonio F. García Marín, Joachim Kullmann, Wang Feng, and Karsten Danzmann  »View Author Affiliations

Optics Express, Vol. 18, Issue 18, pp. 19076-19086 (2010)

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We have developed a method to equip homodyne interferometers with the capability to operate with constant high sensitivity over many fringes for continuous real-time tracking. The method can be considered as an extension of the “J1J4” methods, and its enhancement to deliver very sensitive angular measurements through Differential Wavefront Sensing is straightforward. Beam generation requires a sinusoidal phase modulation of several radians in one interferometer arm. On a stable optical bench, we have demonstrated a long-term sensitivity over thousands of seconds of 0 . 1 mrad Hz that correspond to 20 pm Hz in length, and 10 nrad Hz in angle at millihertz frequencies.

© 2010 Optical Society of America

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5060) Instrumentation, measurement, and metrology : Phase modulation

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: July 7, 2010
Revised Manuscript: August 13, 2010
Manuscript Accepted: August 19, 2010
Published: August 23, 2010

Gerhard Heinzel, Felipe Guzmán Cervantes, Antonio F. García Marin, Joachim Kullmann, Wang Feng, and Karsten Danzmann, "Deep phase modulation interferometry," Opt. Express 18, 19076-19086 (2010)

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  1. S. Anza, M. Armano, E. Balaguer, M. Benedetti, C. Boatella, P. Bosetti, D. Bortoluzzi, N. Brandt, C. Braxmaier, M. Caldwell, L. Carbone, D. Bortoluzzi, N. Brandt, C. Braxmaier, M. Caldwell, L. Carbone, D. Bortoluzzi, N. Brandt, C. Braxmaier, M. Caldwell, L. Carbone, E. García-Berro, A. F. García Marín, R. Gerndt, A. Gianolio, D. Giardini, R. Gruenagel, A. Hammesfahr, G. Heinzel, J. Hough, D. Hoyland, 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," Class. Quantum Gravity 22, S125-S138 (2005). [CrossRef]
  2. T. Schuldt, H. J. Kraus, D. Weise, A. Peters, U. Johann, and C. Braxmaier, "A High Sensitivity Heterodyne Interferometer as Optical Readout for the LISA Inertial Sensor," AIP Conf. Proc. 873, 374-378 (2006). [CrossRef]
  3. S. M. Aston, and C. C. Speake, "An Interferometric Based Optical Read-Out Scheme for the LISA Proof-Mass," AIP Conf. Proc. 873, 326-333 (2006). [CrossRef]
  4. F. Acernese, R. De Rosa, L. Di Fiore, F. Garufi, A. La Rana, and L. Milano, "Some Progress In The Development Of An Optical Readout System For The LISA Gravitational Reference Sensor," AIP Conf. Proc. 873, 339-343 (2006). [CrossRef]
  5. G. Heinzel, C. Braxmaier, M. Caldwell, K. Danzmann, F. Draaisma, A. García, J. Hough, O. Jennrich, U. Johann, C. Killow, K. Middleton, M. te Plate, D. Robertson, A. Rüdiger, R. Schilling, F. Steier, V. Wand, and H. Ward, "Successful testing of the LISA Technology Package (LTP) interferometer engineering model," Class. Quantum Gravity 22, S149-S154 (2005). [CrossRef]
  6. F. Guzmán Cervantes, F. Steier, G. Wanner, G. Heinzel, and K. Danzmann, "Subtraction of test mass angular noise in the LISA technology package interferometer," Appl. Phys. B 90, 395-400 (2008). [CrossRef]
  7. S. Hild and the LIGO Scientific Collaboration, "The status of GEO 600," Class. Quantum Gravity 23, S643-S651 (2006). [CrossRef]
  8. O. Sasaki, and H. Okazaki, "Analysis of measurement accuracy in sinusoidal phase modulating interferometry," Appl. Opt. 25, 3152 (1986). [CrossRef] [PubMed]
  9. O. Sasaki, H. Okazaki, and M. Sakai, "Sinusoidal phase modulating interferometer using the integrating-bucket method," Appl. Opt. 26, 1089 (1987). [CrossRef] [PubMed]
  10. P. de Groot, and L. Deck, "New algorithms and error analysis for sinusoidal phase shifting interferometry," Proc. SPIE 7063, 70630K (2008). [CrossRef]
  11. P. de Groot, "Design of error-compensating algorithms for sinusoidal phase shifting interferometry," Appl. Opt. 48, 6788-6796 (2009). [CrossRef] [PubMed]
  12. K. Falaggis, D. P. Towers, and C. E. Towers, "Phase measurement through sinusoidal excitation with application to multi-wavelength Interferometry," J. Opt. A, Pure Appl. Opt. 11, 054008 (2009). [CrossRef]
  13. A. Patil, and P. Rastogi, "Nonlinear regression techniques applied to generalized phase-shifting interferometry," J. Mod. Opt. 52, 573-582 (2005). [CrossRef]
  14. V. S. Sudarshanam, and K. Srinivasan, "Linear readout of dynamic phase-change in a fiber-optic homodyne interferometer," Opt. Lett. 14, 140-142 (1989). [CrossRef] [PubMed]
  15. W. Jin, L. M. Zhang, D. Uttamchandani, and B. Culshaw, "Modified J1... J4 method for linear readout of dynamic phase-changes in a fiber-optic homodyne interferometer," Appl. Opt. 30, 4496-4499 (1991). [CrossRef] [PubMed]
  16. V. S. Sudarshanam, and R. O. Claus, "Generic J1...J4 method of optical-phase detection: Accuracy and range enhancement," J. Mod. Opt. 40, 483-492 (1993). [CrossRef]
  17. D. Marquardt, "An Algorithm for Least-Squares Estimation of Nonlinear Parameters," SIAM J. Appl. Math. 11, 431-441 (1963). [CrossRef]
  18. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing (Cambridge University Press, 1992).
  19. J. A. Nelder, and R. Mead, "A simplex method for function minimization," Comput. J. 7, 308-313 (1965).
  20. E. J. Elliffe, J. Bogenstahl, A. Deshpande, J. Hough, C. Killow, S. Reid, D. Robertson, S. Rowan, H. Ward, and G. Cagnoli, "Hydroxide-catalysis bonding for stable optical systems for space," Class. Quantum Gravity 22, S257-S267 (2005). [CrossRef]
  21. A.F. García Marín et al, Albert-Einstein-Institut Hannover, Callinstr. 38, 30167 Hannover, Germany, are preparing a manuscript on "Ground testing of LISA Pathfinder optical metrology system."
  22. FFTW subroutine package, available from http://www.fftw.org/.
  23. 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 Gravity 21, S581-S587 (2004). [CrossRef]
  24. F. Guzmán Cervantes, "Gravitational Wave Observation from Space: optical measurement techniques for LISA and LISA Pathfinder," Ph.D. Thesis, Leibniz Universität Hannover, Germany (2009), http://edok01.tib.uni-hannover.de/edoks/e01dh09/606793232.pdf.
  25. F. Guzmán Cervantes, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA, is preparing a manuscript on "Estimation and subtraction of noise contributions in the LISA Pathfinder optical metrology system."
  26. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, "Experimental demonstration of an automatic alignment system for optical interferometers," Appl. Opt. 33, 5037-5040 (1994). [CrossRef] [PubMed]
  27. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, "Automatic alignment of optical interferometers," Appl. Opt. 33, 5041-5049 (1994). [CrossRef] [PubMed]
  28. V. Wand, J. Bogenstahl, C. Braxmaier, K. Danzmann, A. García, F. Guzmán, G. Heinzel, J. Hough, O. Jennrich, C. Killow, D. Robertson, Z. Sodnik, F. Steier, and H. Ward, "Noise sources in the LTP heterodyne interferometer," Class. Quantum Gravity 23, S159-S167 (2006). [CrossRef]
  29. G. Heinzel, V. Wand, A. García, F. Guzmán, F. Steier, C. Killow, D. Robertson, and H. Ward, "Investigation of noise sources in the LTP interferometer," Technical note (2008), http://edoc.mpg.de/display.epl?mode=doc&id=395069&col=6&grp=1154.

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