Abstract

In an absolute gravity meter, a laser interferometer measures the position of a test mass that is falling in a vacuum. The calculated value of gravity is the average acceleration of the mass during a set of drops. Since systematic accelerations of the optical system will bias the measured value of gravity, various interferometer geometries have been implemented in the past to isolate the optical system from ground motion. We have developed and tested a low-finesse fiber-optic extrinsic Fabry–Perot interferometer that is fixed to the mass of a critically damped seismometer in which the effects of systematic ground motion and acoustic vibrations are reduced.

© 1996 Optical Society of America

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  1. W. Torge, Gravimetry (de Gruyter, Berlin, 1989), Chap. 5, pp. 128–168.
  2. M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
    [CrossRef]
  3. I. Marson, J. E. Faller, “Review article: the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
    [CrossRef]
  4. Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).
  5. R. L. Rinker, J. E. Faller, “Super spring—long period mechanical vibration isolator,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, eds., Natl. Bur. Stand. U.S. Spec. Publ.617, 411–417 (1984).
  6. J. L. Santos, A. P. Leite, D. A. Jackson, “Optical fiber sensing with a low-finesse Fabry–Perot cavity,” Appl. Opt. 31, 7361–7366 (1992).
    [CrossRef] [PubMed]
  7. V. S. Sudarshanam, R. O. Claus, “Split-cavity crosscoupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
    [CrossRef] [PubMed]
  8. A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
    [CrossRef]
  9. J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).
  10. P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).
  11. M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

1995

P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

1994

M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

1993

1992

1991

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

1986

I. Marson, J. E. Faller, “Review article: the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

1982

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
[CrossRef]

Arnautov, G.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Becker, M.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Bernard, B.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Boulanger, Y.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Cannizzo, L.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Canuteson, E. L.

M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

Cerutti, G.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Claus, R. O.

V. S. Sudarshanam, R. O. Claus, “Split-cavity crosscoupled extrinsic fiber-optic interferometric sensor,” Opt. Lett. 18, 543–545 (1993).
[CrossRef] [PubMed]

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

Courtie, N.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Da-Lun, Huang

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

De-Xi, Li

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Faller, J.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Faller, J. E.

I. Marson, J. E. Faller, “Review article: the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
[CrossRef]

R. L. Rinker, J. E. Faller, “Super spring—long period mechanical vibration isolator,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, eds., Natl. Bur. Stand. U.S. Spec. Publ.617, 411–417 (1984).

Fried, J.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Groten, E.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Guang-Yuan, Zhang

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Hanada, H.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Hildebrand, J. A.

M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

Jackson, D. A.

Javan, A.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Kalish, E.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Kelly, M. J.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Klopping, F.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Kurnit, N. A.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Lee, P. H.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Leite, A. P.

Leord, J.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Makinen, J.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Marson, I.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

I. Marson, J. E. Faller, “Review article: the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

Miller, M. S.

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

Monchalin, J.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Murphy, K. A.

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

Ooe, M.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Parker, P. R.

P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Parker, R. L.

P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Peter, G.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Rinker, R. L.

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
[CrossRef]

R. L. Rinker, J. E. Faller, “Super spring—long period mechanical vibration isolator,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, eds., Natl. Bur. Stand. U.S. Spec. Publ.617, 411–417 (1984).

Roder, R.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Ruess, D.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Sakuma, A.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Santos, J. L.

Scheglov, S.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Schnull, N.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Stus, F.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Sudarshanam, V. S.

Sun, D.

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

Szoke, A.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Tarasuk, W.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Thomas, J. E.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Timmen, L.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Torge, W.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

W. Torge, Gravimetry (de Gruyter, Berlin, 1989), Chap. 5, pp. 128–168.

Tsubokawa, T.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Vanska, A.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Wang, A.

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

You-Guang, Guo

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Youg-Yuan, Feng

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

Zernike, F.

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

Zumberge, M. A.

P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
[CrossRef]

Appl. Opt.

Bull. Inf. Bur. Gravimetrique Int.

Y. Boulanger, J. Faller, E. Groten, G. Arnautov, M. Becker, B. Bernard, L. Cannizzo, G. Cerutti, N. Courtie, Feng Youg-Yuan, J. Fried, Guo You-Guang, H. Hanada, H. Hanada, Huang Da-Lun, E. Kalish, F. Klopping, Li De-Xi, J. Leord, J. Makinen, I. Marson, M. Ooe, G. Peter, R. Roder, D. Ruess, A. Sakuma, A. Sakuma, N. Schnull, F. Stus, S. Scheglov, W. Tarasuk, L. Timmen, W. Torge, T. Tsubokawa, T. Tsubokawa, A. Vanska, Zhang Guang-Yuan, “Results of 3rd international comparison of absolute gravimeters in Sèvres, 1989,” Bull. Inf. Bur. Gravimetrique Int. 68, 24–44 (1991).

J. Phys. E

I. Marson, J. E. Faller, “Review article: the acceleration of gravity: its measurement and its importance,” J. Phys. E 19, 22–32 (1986).
[CrossRef]

Manuscripta Geodaetica

P. R. Parker, M. A. Zumberge, R. L. Parker, “A new method for fringe-signal processing in absolute gravity meters,” Manuscripta Geodaetica 20, 173–181 (1995).

Metrologia

M. A. Zumberge, R. L. Rinker, J. E. Faller, “A portable apparatus for absolute measurements of the earth's gravity,” Metrologia 18, 145–152 (1982).
[CrossRef]

Opt. Lett.

Ridge Events

M. A. Zumberge, E. L. Canuteson, J. A. Hildebrand, “The Ocean Bottom Absolute Gravity Meter,” Ridge Events 4, 9–12 (1994).

Other

A. Wang, M. S. Miller, D. Sun, K. A. Murphy, R. O. Claus, “Advances in the extrinsic Fabry–Perot interferometric optical fiber sensors,” in Fiber Optic Smart Structures and Skins V, R. O. Claus, R. S. Rogowski, eds., Proc. SPIE1798, 32–41 (1993).
[CrossRef]

J. Monchalin, M. J. Kelly, J. E. Thomas, N. A. Kurnit, A. Szoke, A. Javan, F. Zernike, P. H. Lee, “Wavelength comparison between lasers,” R. Balian, S. Heroche, S. Liberman, eds., Les Houches, Session XXVII, 1975—Frontiers in laser spectroscopy (1977).

W. Torge, Gravimetry (de Gruyter, Berlin, 1989), Chap. 5, pp. 128–168.

R. L. Rinker, J. E. Faller, “Super spring—long period mechanical vibration isolator,” in Precision Measurement and Fundamental Constants II, B. N. Taylor, W. D. Phillips, eds., Natl. Bur. Stand. U.S. Spec. Publ.617, 411–417 (1984).

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Figures (5)

Fig. 1
Fig. 1

Acceleration of a retroreflector falling in a vacuum chamber determined interferometrically.

Fig. 2
Fig. 2

New optical system that is essentially a low-finesse Fabry–Perot fiber-optic interferometer.

Fig. 3
Fig. 3

Interferometer rests on a critically damped short period seismometer to achieve vibration isolation.

Fig. 4
Fig. 4

Comparative residuals between (a) bulk optics and (b) fiber-optic systems at a site with good coupling between the dropping chamber and the optics platform.

Fig. 5
Fig. 5

Stacked residuals at a site with the optics resting on an isolated pier.

Equations (5)

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

F ( t ) = C 0 + C 1 sin [ ϕ 0 + 2 k ( υ 0 t + g t 2 ) ] + C 2 sin [ ϕ 0 + 4 k ( υ 0 t + g t 2 ) ] ,
crack error = ( 9 2 π 1 / 2 a 0 w 0 ) × diffraction error ,
F ( t ) = F 0 + A sin [ ϕ 0 + 2 k ( υ 0 t + g t 2 ) ] .
F ( t ) = F + A 1 sin [ 2 k ( υ 0 t + g t 2 ) ] + A 2 cos [ 2 k ( υ 0 t + g t 2 ) ] ,
F ( t ) = F 0 + A 1 sin [ 2 k ( υ 0 t + g t 2 ) ] + A 2 cos [ 2 k ( υ 0 t + g t 2 ) ] + A 3 sin [ 4 k ( υ 0 t + g t 2 ) ] + A 4 cos [ 4 k ( υ 0 t + g t 2 ) ] ,

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