Abstract

Cardiomagnetometry is a growing field of noninvasive medical diagnostics that has triggered a need for affordable high-sensitivity magnetometers. Optical pumping magnetometers (OPMs) are promising candidates for satisfying that need since it has been demonstrated that they can be used to map the magnetic field of the beating human heart. We discuss the principle of a phase-detecting OPM and describe the procedures used to optimize its performance. The optimized OPM has an intrinsic magnetometric sensitivity of 63 fT/Hz1/2 and a measurement bandwidth of 140 Hz with a spatial resolution of 28 mm, measured in a weakly shielded environment. We further discuss the fundamental limitations of frequency- and phase-detecting magnetometers on the basis of information theory.

© 2005 Optical Society of America

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References

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  1. W. Andrä and H. Nowak, eds., Magnetism in Medicine (Wiley-VCH, Berlin, 1998).
  2. J. P. Wikswo, "Biomagnetic sources and their models," in Proceedings of the Seventh International Conference on Biomagnetism , S. J. Williamson, M. Hoke, G. Stroink, and M. Kotani, eds. (Plenum, New York, 1998), pp. 1-18.
  3. D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
    [CrossRef]
  4. A. L. Bloom, "Principles of operation of the rubidium vapor magnetometer," Appl. Opt. 1, 61-68 (1962).
    [CrossRef]
  5. J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
    [CrossRef]
  6. E. B. Alexandrov and V. A. Bonch-Bruevich, "Optically pumped atomic magnetometers after three decades," Opt. Eng. (Bellingham) 31, 711-717 (1992).
    [CrossRef]
  7. A. Kastler, "The Hanle Effect and its use for the measurement of very small magnetic fields," Nucl. Instrum. Methods 110, 259-265 (1973).
    [CrossRef]
  8. D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
    [CrossRef]
  9. M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
    [PubMed]
  10. S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
    [CrossRef]
  11. G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
    [CrossRef]
  12. G. Bison, R. Wynands, and A. Weis, "Dynamical mapping of the human cardiomagnetic field with a room-temperature, laser-optical sensor," Opt. Express 11, 904-909 (2003).
    [CrossRef] [PubMed]
  13. K. L. Corwin, Z.-T. Lu, C. F. Hand, R. J. Epstain, and C. E. Wieman, "Frequency-stabilized diode laser with the Zeeman shift in an atomic vapor," Appl. Opt. 37, 3295-3298 (1998).
    [CrossRef]
  14. D. C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
    [CrossRef]
  15. I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
    [PubMed]
  16. P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
    [CrossRef]

2003 (2)

G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
[CrossRef]

G. Bison, R. Wynands, and A. Weis, "Dynamical mapping of the human cardiomagnetic field with a room-temperature, laser-optical sensor," Opt. Express 11, 904-909 (2003).
[CrossRef] [PubMed]

2002 (1)

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

2000 (1)

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

1998 (1)

1996 (1)

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

1992 (1)

E. B. Alexandrov and V. A. Bonch-Bruevich, "Optically pumped atomic magnetometers after three decades," Opt. Eng. (Bellingham) 31, 711-717 (1992).
[CrossRef]

1981 (1)

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

1974 (1)

D. C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

1973 (1)

A. Kastler, "The Hanle Effect and its use for the measurement of very small magnetic fields," Nucl. Instrum. Methods 110, 259-265 (1973).
[CrossRef]

1970 (1)

D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
[CrossRef]

1969 (2)

J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
[CrossRef]

P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
[CrossRef]

1962 (1)

Alexandrov , E. B.

E. B. Alexandrov and V. A. Bonch-Bruevich, "Optically pumped atomic magnetometers after three decades," Opt. Eng. (Bellingham) 31, 711-717 (1992).
[CrossRef]

Bison, G.

G. Bison, R. Wynands, and A. Weis, "Dynamical mapping of the human cardiomagnetic field with a room-temperature, laser-optical sensor," Opt. Express 11, 904-909 (2003).
[CrossRef] [PubMed]

G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
[CrossRef]

Bloom, A. L.

Bonch-Bruevich, V. A.

E. B. Alexandrov and V. A. Bonch-Bruevich, "Optically pumped atomic magnetometers after three decades," Opt. Eng. (Bellingham) 31, 711-717 (1992).
[CrossRef]

Boorstyn, R. R.

D. C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

Brisinda, D.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Caterina, R. D.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Cohen, D.

D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
[CrossRef]

Cohen-Tannoudji, C.

J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
[CrossRef]

Comani, S.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Corwin, K. L.

Dupont-Roc, J.

J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
[CrossRef]

Dyal, P.

P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
[CrossRef]

Edelsack, E. A.

D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
[CrossRef]

Epstain, R. J.

Fenici, R.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Gallina, S.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Giles, J. C.

P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
[CrossRef]

Gorbach, A. M.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Gratta, C. D.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Hand, C. F.

Hänsch, T.

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Haroche, S.

J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
[CrossRef]

Johnson, R. T.

P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
[CrossRef]

Kanorsky, S.

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Kastler, A.

A. Kastler, "The Hanle Effect and its use for the measurement of very small magnetic fields," Nucl. Instrum. Methods 110, 259-265 (1973).
[CrossRef]

Kholodov, J. A.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Korinewsky, A. V.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Kozlov, A. N.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Lang, S.

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Livanov, M. N.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Lu, Z.-T.

Lücke, S.

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Luzio, S. D.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Markin, V. P.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Rife , D. C.

D. C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Romani, G. L.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Ross, S.

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Sinelnikova, S. E.

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Tavarozzi, I.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Weis, A.

G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
[CrossRef]

G. Bison, R. Wynands, and A. Weis, "Dynamical mapping of the human cardiomagnetic field with a room-temperature, laser-optical sensor," Opt. Express 11, 904-909 (2003).
[CrossRef] [PubMed]

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Wieman, C. E.

Wynands, R.

G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
[CrossRef]

G. Bison, R. Wynands, and A. Weis, "Dynamical mapping of the human cardiomagnetic field with a room-temperature, laser-optical sensor," Opt. Express 11, 904-909 (2003).
[CrossRef] [PubMed]

Yashchuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Zimarino, M.

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Zimmerman, J. E.

D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
[CrossRef]

Zolotorev, M.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

Adv. Cardiol. (1)

M. N. Livanov, A. N. Kozlov, S. E. Sinelnikova, J. A. Kholodov, V. P. Markin, A. M. Gorbach, and A. V. Korinewsky, "Record of the human magnetocardiogram by the quantum gradiometer with optical pumping," Adv. Cardiol. 28, 78-80 (1981).
[PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

G. Bison, R. Wynands, and A. Weis, "A laser-pumped magnetometer for the mapping of human cardiomagnetic fields," Appl. Phys. B 76, 325-328 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

D. Cohen, E. A. Edelsack, and J. E. Zimmerman, "Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer," Appl. Phys. Lett. 16, 278-280 (1970).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. C. Rife and R. R. Boorstyn, "Single-tone parameter estimation from discrete-time observations," IEEE Trans. Inf. Theory 20, 591-598 (1974).
[CrossRef]

Ital. Heart J. (1)

I. Tavarozzi, S. Comani, C. D. Gratta, G. L. Romani, S. D. Luzio, D. Brisinda, S. Gallina, M. Zimarino, R. Fenici, and R. D. Caterina, "Magnetocardiography: current status and perspectives. Part I: physical principles and instrumentation," Ital. Heart J. 3, 75-85 (2002).
[PubMed]

Nucl. Instrum. Methods (1)

A. Kastler, "The Hanle Effect and its use for the measurement of very small magnetic fields," Nucl. Instrum. Methods 110, 259-265 (1973).
[CrossRef]

Opt. Eng. (Bellingham) (1)

E. B. Alexandrov and V. A. Bonch-Bruevich, "Optically pumped atomic magnetometers after three decades," Opt. Eng. (Bellingham) 31, 711-717 (1992).
[CrossRef]

Opt. Express (1)

Phys. Lett. (1)

J. Dupont-Roc, S. Haroche, and C. Cohen-Tannoudji, "Detection of very weak magnetic fields (10−9 gauss) by 87Rb-zero-field level crossing resonances," Phys. Lett. 28A, 638-639 (1969).
[CrossRef]

Phys. Rev. A (2)

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, "Sensitive magnetometry based on nonlinear magneto-optical rotation," Phys. Rev. A 62, 043403 (2000).
[CrossRef]

S. Kanorsky, S. Lang, S. Lücke, S. Ross, T. Hänsch, and A. Weis, "Millihertz magnetic resonance spectroscopy of Cs atoms in body-centered-cubic 4He," Phys. Rev. A 54, R1010-R1013 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

P. Dyal, R. T. Johnson, Jr., and J. C. Giles, "Response of self-oscillating rubidium vapor magnetometers to rapid field changes," Rev. Sci. Instrum. 40, 601-602 (1969).
[CrossRef]

Other (2)

W. Andrä and H. Nowak, eds., Magnetism in Medicine (Wiley-VCH, Berlin, 1998).

J. P. Wikswo, "Biomagnetic sources and their models," in Proceedings of the Seventh International Conference on Biomagnetism , S. J. Williamson, M. Hoke, G. Stroink, and M. Kotani, eds. (Plenum, New York, 1998), pp. 1-18.

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Figures (13)

Fig. 1
Fig. 1

Basic geometry of the Mx-magnetometer setup. The laser (la) emits a beam that traverses the sample (sa) at angle θ with respect to the magnetic field B0. The transmitted power is detected by a photodetector (pd). The static magnetic field B0 is aligned along the z direction. The oscillating magnetic field B1 is aligned along the x direction.

Fig. 2
Fig. 2

(a) Measured magnetic-resonance line shapes of the in-phase (a1) and quadrature signals (a2), measured in a single sweep of 20 s with the cardiomagnetometer placed in a poorly shielded room. Magnetic 50-Hz line interference was suppressed with a fourth-order low-pass filter (time constant 10 ms). The half-width, derived from a fit, was ΔωHW/2π=173 Hz. (b) Magnetic-resonance line shape of the oscillation phase, measured with respect to the driving field Brf. The data were obtained in real time with a digital lock-in amplifier. The fitted half-width is ΔωHWφ/2π=109 Hz.

Fig. 3
Fig. 3

Nyquist plots for three values of S. The solid curve is for S=1, and the dashed curves are for S=0.25 (nearly round) and S=4 (elliptical). If ωrf is scanned toward increasing values, the system evolves clockwise through the Nyquist plot.

Fig. 4
Fig. 4

Nyquist plot of a resonance with S=1 when an interfering sine wave of amplitude ri and phase ϕi is added. A phase offset of Δφ in the demodulation due to a poorly adjusted lock-in phase leads to a rotated ellipse.

Fig. 5
Fig. 5

Nyquist plots for different magnetic field distributions, each scaled to fit in a square of length 1. (a) The deviation from circular for constant magnetic field distributions. The innermost trace is for an unperturbed resonance. The two outer traces are calculated for field distribution widths of xg=40Γ2 and 400Γ2. (b) The deviation from circular for linear field distributions. The (outer) circular trace is for an unperturbed resonance. The other two are calculated for distribution widths of xg=5Γ2 and 10Γ2.

Fig. 6
Fig. 6

Schematic of the experimental setup. Light from the diode laser is delivered via an optical fiber (of) to the experiment in the magnetically shielded room (msr). The light is collimated by a lens (le) and polarized by a polarizing beam splitter cube (po). The beam splitter (bs) reflects 50% of the beam to photodiode 1 (pd1), used for monitoring the initial light power. The remaining beam passes a quarter-wave plate (λ/4) providing circular polarized light to the glass cell (gs) that contains the atomic medium. Photodiode 2 (pd2) measures the transmitted light intensity. Its signal is amplified by a current amplifier and fed to the lock-in amplifier (lia). The reference output of the lia drives the radio frequency coils (rfc). The reference frequency of the lia is controlled by a sweep generator (sg). Automatic control and data aquisition is done by a personal computer (pc) via the general-purpose interface bus (GPIB).

Fig. 7
Fig. 7

Frequency response of the magnetometer, measured by one’s recording the response to an oscillating magnetic field generated by a test coil. The dots show measured points recorded in free-running mode under conditions optimized for maximal magnetometric resolution. (a) Calculated first-order low-pass filter corresponding to a spin-polarization lifetime of 1.67 ms. (b) Fitted frequency response that takes into account (a) and the fourth-order low-pass filter of the lock-in amplifier (time constant=30 µs). (c) Measured frequency response in the phase-stabilized mode.

Fig. 8
Fig. 8

Dots represent a Nyquist plot of the magnetic resonance measured under optimized conditions. The solid curve is a fit of Eq. (15) with added offset and phase rotation to the measured data. The fit model assumes a constant magnetic field distribution. The offset is indicated by the dot close to the origin. The short diameter of the ellipse is drawn to illustrate the phase rotation of 2.4°.

Fig. 9
Fig. 9

Root power spectrum of the photocurrent when the driving field is in resonance with the Larmor frequency. The data sample was recorded at 54 °C under conditions optimized for maximum magnetometric sensitivity with a resolution bandwidth of 1 Hz (sampling time 1 s). The amplitude measured by the lock-in amplifier corresponds to the upper horizontal line. The amplitude of the central peak is depressed in that it is slightly broadened by the Hanning window used by the FFT spectrum analyzer (see text). The level ρI is the shot-noise level calculated from the dc photocurrent. The dashed line marks the rms noise measured at 23 kHz. The RSN with respect to the calculated shot-noise level is 5×105. The rms noise is a factor of 1.55 higher than ρI, resulting in a RSN of 3.2×105.

Fig. 10
Fig. 10

Dependence of the magnetic-resonance linewidth on the rf coil voltage Urf. The points are extracted from measured magnetic-resonance spectra by least-squares fitting of model Eq. (15). The phase signal (a) has a constant linewidth, whereas the common widths of the in-phase and quadrature signals (b) increase rapidly with rf amplitude. The solid curve represents a model fitted to the data that assumed an additional broadening caused by inhomogeneous magnetic fields.

Fig. 11
Fig. 11

Amplitude of the in-phase (a1) and quadrature (a2) signals as a function of rf amplitude Urf. Points represent values extracted from measured magnetic-resonance spectra. Solid curves show a model fit to the data points (see text). The quadrature amplitude a2 is equal to the amplitude of the incoming sine wave on resonance (δ=0).

Fig. 12
Fig. 12

Contour plot of the magnetometric resolution (NEM) as a function of temperature and light power. The map is calculated by numeric interpolation from seven optimization runs (indicated by vertical lines). The labels at the contours mark the NEM in fT/Hz1/2. The points of minimal NEM for each optimization run are indicated by dots. The connecting curve is a cut along which the data of Fig. 13 are obtained. Including the variation of the rf amplitude, 970 parameter sets were recorded and analyzed to produce the map.

Fig. 13
Fig. 13

Magnetic-resonance parameters as a function of incident light power. (a) The width of the phase signal that determines the cutoff frequency of the magnetometer bandwidth; (b) the dc transmission through the Cs cell relative to the incident light power; (c) the S/N ratio of the lock-in input signal with respect to calculated shot noise; (d) the NEM at the points indicated in Fig. 12.

Equations (31)

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ωL=gFμB|Btot|γF|Btot|.
M˙xM˙yM˙z=MxMyMzγFBrf2 cos ωrft0γFB0-γ2Mxγ2Myγ1Mz+ΓP-MxM0 sin θ-My-M0 cos θ-Mz.
Pip(δ)=-P0 sin(2θ) ΩrfδΩrf2Γ2/Γ1+Γ22+δ2,
Pqu(δ)=-P0 sin(2θ) ΩrfΓ2Ωrf2Γ2/Γ1+Γ22+δ2.
ΔωHW=Ωrf2Γ2/Γ1+Γ22=Γ2S+1.
tan φ=PquPip=Γ2δ.
tan φ=-δΓ2.
ΔωHWφ=Γ2<ΔωHW.
t=t0 S(i+x)1+S+x2.
dr=t0S1+S1/2,
di=t0 S1+S.
S=Ωrf2Γ1Γ2=dr2di2-1.
2xg=γFΓ2lzdBz/dz.
t(x)=-xgxgt(x-x)g(x)dx,
t=S4xg{ln[1+S+(xg-x)2]-ln[1+S+(xg+x)2]}-i2xg S1+S1/2arctanxg-x1+S+arctanxg+x1+S.
σB=ρB(fbw)1/2.
RSN=Aσ=Aρ(fbw)1/2.
ρB=σB(fbw)1/2=4(3)1/2(fbw)1/2γFRSN.
ρB=Γ2γFRSN(fbw)1/2.
f0=Γ24(3)1/2,
fC=12πτS=Γ22π=Δν2
fbw=14τS=Γ24=π2Δν2,
ρI=(2eIdc)1/2.
Vω=12σ2A2TM2N,
Vω=12ρi2FbwA2TM2N=6RSN2TM3.
ρB=VBfbw1/2=4(3)1/2(fbw)1/2γFRSN.
Vφ=σ2A2N.
Vφ=ρ2A22TM.
σφ2=Vφ=ρ2fbwA2=fbwRSN2.
σB=σδγF=σφΓγF=Γ(fbw)1/2γFRSN(fbw)1/2.
ρB=ΓγFRSN(fbw)1/2.

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