Abstract

We present a method of analysis involving ellipse-specific fitting of sinusoidally coupled data from two gravimeters in a gradiometer configuration. This method permits rapid extraction of induced gradient phase shifts in the presence of common-mode vibrational phase noise. Gravity gradients can be accurately measured in the presence of large vibrational accelerations.

© 2002 Optical Society of America

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References

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  1. M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
    [CrossRef]
  2. J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
    [CrossRef]
  3. A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
    [CrossRef]
  4. M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
    [CrossRef] [PubMed]
  5. P. Berman, ed., Atom Interferometry (Academic, New York, 1997).
  6. J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, Opt. Lett. 26, 364 (2001).
    [CrossRef]
  7. W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
    [CrossRef]
  8. J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
    [CrossRef] [PubMed]
  9. D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
    [CrossRef]

2002 (1)

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

2001 (1)

1999 (1)

A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

1998 (1)

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

1995 (2)

J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
[CrossRef] [PubMed]

D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
[CrossRef]

1994 (1)

W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
[CrossRef]

1991 (1)

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Bouyer, P.

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

Chu, S.

D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
[CrossRef]

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Fisher, R.

A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Fitzgibbon, A.

A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Fixler, J. B.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, Opt. Lett. 26, 364 (2001).
[CrossRef]

Foster, G. T.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, Opt. Lett. 26, 364 (2001).
[CrossRef]

Gander, W.

W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
[CrossRef]

Golub, G.

W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
[CrossRef]

Haritos, K. G.

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

Kasapi, S.

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Kasevich, M.

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Kasevich, M. A.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, Opt. Lett. 26, 364 (2001).
[CrossRef]

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

Maleki, L.

J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
[CrossRef] [PubMed]

McGuirk, J. M.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, Opt. Lett. 26, 364 (2001).
[CrossRef]

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

Moller, K.

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Pilu, M.

A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Prestage, J. D.

J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
[CrossRef] [PubMed]

Riis, E.

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Snadden, M. J.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

Strebel, R.

W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
[CrossRef]

Tjoelker, R. L.

J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
[CrossRef] [PubMed]

Weiss, D. S.

D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
[CrossRef]

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

Young, B. C.

D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
[CrossRef]

BIT (1)

W. Gander, G. Golub, and R. Strebel, BIT 34, 558 (1994).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

A. Fitzgibbon, M. Pilu, and R. Fisher, IEEE Trans. Pattern Anal. Mach. Intell. 21, 476 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, Phys. Rev. A 65, 033608 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

M. J. Snadden, J. M. McGuirk, P. Bouyer, K. G. Haritos, and M. A. Kasevich, Phys. Rev. Lett. 81, 971 (1998).
[CrossRef]

M. Kasevich, D. S. Weiss, E. Riis, K. Moller, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[CrossRef] [PubMed]

J. D. Prestage, R. L. Tjoelker, and L. Maleki, Phys. Rev. Lett. 74, 3511 (1995).
[CrossRef] [PubMed]

D. S. Weiss, B. C. Young, and S. Chu, Phys. Rev. Lett. 70, 2706 (1995).
[CrossRef]

Other (1)

P. Berman, ed., Atom Interferometry (Academic, New York, 1997).

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Figures (2)

Fig. 1
Fig. 1

(a) Signals from the two gravimeters exhibiting a high level of vibrationally induced phase noise. The phase of each interferometer is scanned over 2π every 16 data points. The top data plot is offset by one amplitude unit for clarity. (b) Upper trace y versus the lower trace x, demonstrating the elliptic constraint of the data. The solid curve is an ellipse fit to the data. (c) Simulated scanned data without vibrational phase noise. We have included amplitude noise at the same level as the data.

Fig. 2
Fig. 2

Phase extracted by ellipse fitting of Doppler-sensitive data (high phase noise) with a series of increasing applied magnetic bias pulse phase shifts. The inset shows the deviation from linearity of the ellipse-fit phase shift around the applied magnetic shift of π/2 rad. The bold curve in the inset shows this behavior exhibited in simulations with amplitude noise of a percent. The line is the fit from the entire data set in the main plot.

Equations (5)

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

x=A sinϕ+B,    y=C sinϕ+Δϕ+D.
a·x=Ax2+Bxy+Cy2+Dx+Ey+F=0,
Δϕ=cos-1-B/2AC.
minDa2,
P|4=121-cosϕ0+Δϕg.

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