Abstract

A heterodyne metrology interferometer was stabilized down to a noise level of 20 picometers (pm) as a root-mean-square (RMS) value integrated between 0.3mHz and 1Hz. This noise level was achieved by employing active and passive interferometer stabilization techniques. The heterodyne interferometer was built on a 50mm square ultralow expansion glass plate in order to reduce an optical path length change caused by temperature variation. An optical configuration of the interferometer is a Mach– Zehnder interferometer with a design as symmetric as possible so that a detection signal can be insensitive to homogeneous thermal expansion of the glass plate. The heterodyne frequency is actively controlled in order to suppress residual noises caused by optical path length changes outside of the glass plate as well as phase fluctuations of the heterodyne frequency source. Our stabilization scheme is considered useful in achieving the 20pm noise level without a stable heterodyne frequency source, as well as temperature stabilization around a whole apparatus. This interferometer can be used in precise metrology applications, such as characterization of deformation for satellite optical components against thermal exposure.

© 2009 Optical Society of America

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  1. 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]
  2. T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
    [CrossRef]
  3. J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
    [CrossRef]
  4. X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
    [CrossRef]
  5. F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
    [CrossRef]
  6. K. Numata and J. Camp, “Interferometric testbed for nanometer level stabilization of environmental motion over long time scales,” Appl. Opt. 47, 6832-6841 (2008).
    [CrossRef] [PubMed]
  7. N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.
  8. W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25-35 (1994).
    [CrossRef]
  9. C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38, 4089-4094 (1999).
    [CrossRef]
  10. P. G. Halverson and F. M. Loya, “Signal processing for order 10 pm accuracy displacement metrology in real-world scientific applications,” in Proceedings of the 5th International Conference on Space Optics (ICSO 2004), B. Warmbein, ed. (ESA, 2004), pp. 571-577.
  11. 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 Grav. 22, S149-S154 (2005).
    [CrossRef]
  12. 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 Grav. 22, S257-S267 (2005).
    [CrossRef]

2009

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]

2008

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

K. Numata and J. Camp, “Interferometric testbed for nanometer level stabilization of environmental motion over long time scales,” Appl. Opt. 47, 6832-6841 (2008).
[CrossRef] [PubMed]

2005

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 Grav. 22, S149-S154 (2005).
[CrossRef]

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 Grav. 22, S257-S267 (2005).
[CrossRef]

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

1999

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

C. M. Wu, J. Lawall, and R. D. Deslattes, “Heterodyne interferometer with subatomic periodic nonlinearity,” Appl. Opt. 38, 4089-4094 (1999).
[CrossRef]

1994

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25-35 (1994).
[CrossRef]

An, X.

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

Bogenstahl, J.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

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]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Cagnoli, G.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Caldwell, M.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Camp, J.

Danzmann, K.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Deshpande, A.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Deslattes, R. D.

Draaisma, F.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Elliffe, E. J.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

García, A.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

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]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Gouda, N.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

Goullioud, R.

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

Halverson, P. G.

P. G. Halverson and F. M. Loya, “Signal processing for order 10 pm accuracy displacement metrology in real-world scientific applications,” in Proceedings of the 5th International Conference on Space Optics (ICSO 2004), B. Warmbein, ed. (ESA, 2004), pp. 571-577.

Heinrich, T.

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Heinzel, G.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Hou, W.

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25-35 (1994).
[CrossRef]

Hough, J.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Jennrich, O.

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 Grav. 22, S149-S154 (2005).
[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]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Killow, C.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Kobayashi, Y.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

Lawall, J.

Logan, J. E.

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

Loya, F. M.

P. G. Halverson and F. M. Loya, “Signal processing for order 10 pm accuracy displacement metrology in real-world scientific applications,” in Proceedings of the 5th International Conference on Space Optics (ICSO 2004), B. Warmbein, ed. (ESA, 2004), pp. 571-577.

Lucarelli, S.

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Machado, J. C.

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Marx, D. S.

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

Middleton, K.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Numata, K.

Perryman, M. A. C.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

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]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Platais, I.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

Reid, S.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Robertson, D.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Rowan, S.

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Rüdiger, A.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Schilling, R.

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 Grav. 22, S149-S154 (2005).
[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]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

Shaklan, S.

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

Shao, M.

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

Steier, F.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

te Plate, M.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Wand, V.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

Ward, H.

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 Grav. 22, S149-S154 (2005).
[CrossRef]

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 Grav. 22, S257-S267 (2005).
[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]

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

Wu, C. M.

Yamada, Y.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

Yano, T.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

Zhao, F.

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

Zhao, X.

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25-35 (1994).
[CrossRef]

Appl. Opt.

Class. Quantum Grav.

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, 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 Grav. 22, S149-S154 (2005).
[CrossRef]

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 Grav. 22, S257-S267 (2005).
[CrossRef]

Precis. Eng.

W. Hou and X. Zhao, “Drift of nonlinearity in the heterodyne interferometer,” Precis. Eng. 16, 25-35 (1994).
[CrossRef]

Proc. SPIE

T. Schuldt, M. Gohlke, D. Weise, A. Peters, U. Johann, and C. Braxmaier, “A compact high-sensitivity heterodyne interferometer for industrial metrology,” Proc. SPIE 7003, 70030Y (2008).
[CrossRef]

J. C. Machado, T. Heinrich, T. Schuldt, M. Gohlke, S. Lucarelli, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer resolution interferometric characterization of the dimensional stability of zero CTE CFRP,” Proc. SPIE 7018, 70183D (2008).
[CrossRef]

X. An, D. S. Marx, R. Goullioud, and F. Zhao, “Laser metrology in the micro-arcsecond metrology testbed,” Proc. SPIE 5634, 293-303 (2005).
[CrossRef]

F. Zhao, J. E. Logan, S. Shaklan, and M. Shao, “A common-path, multi-channel heterodyne laser interferometer for sub-nanometer surface metrology,” Proc. SPIE 3740, 642-645(1999).
[CrossRef]

Other

P. G. Halverson and F. M. Loya, “Signal processing for order 10 pm accuracy displacement metrology in real-world scientific applications,” in Proceedings of the 5th International Conference on Space Optics (ICSO 2004), B. Warmbein, ed. (ESA, 2004), pp. 571-577.

N. Gouda, Y. Kobayashi, Y. Yamada, T. Yano, and JASMINE Working Group, “Infrared space astrometry project JASMINE,” in Proceedings of IAU Symposium No. 248, A Giant Step: from Milli- to Micro-arcsecond Astrometry, W. J. Jin, I. Platais, and M. A. C. Perryman, eds. (Cambridge Univ. Press, 2008), pp. 248-251.

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Figures (6)

Fig. 1
Fig. 1

Schematic drawing of a heterodyne metrology interferometer: NPBS1–NPBS5, nonpolarized beam splitters; M, mirror; PD1 and PD2, photodetectors; f 1 , and f 2 , modulation frequency of AOM1 and AOM2, respectively; f het , heterodyne frequency; L 1 , optical path length between NPBS1 and NPBS2; L 2 , between NPBS1 and NPBS4; L 3 L 6 , distances between NPBSs, being arranged to have the same distance; l, distance between NPBS3 (NPBS5) and PD1 (PD2). Thick lines show optical paths of interference lights generated from recombining two beams frequency modulated by AOM1 and AOM2. An area framed by solid and dashed line indicates the inside of an optical base plate and a vacuum chamber, respectively.

Fig. 2
Fig. 2

Block diagram of the phase detection of the two beat signals and the phase-locking system of the reference signal: LO1 and LO2, local oscillators; DBM, double balanced mixer; DAQ, data acquisition device; PC, personal computer; VCO, voltage controlled oscillator. Other notations are the same as those in Fig. 1.

Fig. 3
Fig. 3

Schematic drawing of an optical axis control: PZT, piezoelectric actuator; QPD, quadrant photodetector. The QPDs are the monitors for the positional fluctuations of the two beams incident on the vacuum chamber. The positional error signals are fed back to the PZTs. The mirrors, which are attached to the PZTs, are actuated in the tip and tilt direction in order to stabilize the optical axis fluctuations.

Fig. 4
Fig. 4

Stabilization result. The left and the right axis shows the displacement linear spectral density (LSD) and the RMS displacement, respectively. The measurement signal noise levels: (a) the displacement LSD, (b) the RMS displacement.

Fig. 5
Fig. 5

Effect of the optical axis control. The displacement LSD was compared with and without the control loop: (a) the noise level of the measurement signal with all the control loops, (b) the noise level of the measurement signal without the optical axis control loop, (c) an estimated noise contribution of the optical axis fluctuations, (d) an estimated noise contribution of the suppressed optical axis fluctuations.

Fig. 6
Fig. 6

Investigation of the achievable noise level: (a) the displacement noise level of the measurement signal, (b) the displacement noise level of the reference signal, (c) the phase noise level of the digital lock-in amplifier.

Equations (1)

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σ ( f ) = ( f f c [ S ( f ) ] 2 d f ) 1 / 2 ,

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