Abstract

We demonstrate the retrieval of column-density images of cold atoms, using a noninterferometric phase-recovery technique based on a single off-resonant and defocused intensity image. The quantitative column density is retrieved via Fourier inversion and remains robust with respect to detuning and defocus. The technique offers excellent prospects for simple, nondestructive imaging of atoms in magnetic and optical traps and condensates.

© 2004 Optical Society of America

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  1. M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
    [CrossRef] [PubMed]
  2. M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
    [CrossRef]
  3. S. Kadlecek, J. Sebby, R. Newell, and T. G. Walker, Opt. Lett. 26, 137 (2000).
    [CrossRef]
  4. F. Zernike, Physica 9, 686 (1942).
    [CrossRef]
  5. F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
    [CrossRef]
  6. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
    [CrossRef]
  7. W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1981).
    [CrossRef]
  8. M. R. Teague, J. Opt. Soc. Am. 73, 1434 (1983).
  9. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
    [CrossRef] [PubMed]
  10. A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
    [CrossRef]

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

2000 (1)

1998 (1)

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

1997 (2)

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

1996 (1)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

1983 (1)

1942 (1)

F. Zernike, Physica 9, 686 (1942).
[CrossRef]

Andrews, M. R.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Chu, S.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Demtröder, W.

W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1981).
[CrossRef]

Durfee, D. S.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

Gomer, V.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Gureyev, T. E.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

Haubrich, D.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Inouye, S.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

Kadlecek, S.

Ketterle, W.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Kurn, D. M.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

Meschede, D.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Mewes, M.-O.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Miesner, H.-J.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

Newell, R.

Paganin, D.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

Pogany, A.

A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Pritchard, D. E.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Schadwinkel, H.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Sebby, J.

Strauch, F.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Teague, M. R.

Townsend, C. G.

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

Ueberholz, B.

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

van Druten, N. J.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Walker, T. G.

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

Zernike, F.

F. Zernike, Physica 9, 686 (1942).
[CrossRef]

J. Microsc. (Oxford) (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, J. Microsc. (Oxford) 206, 33 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

F. Strauch, V. Gomer, H. Schadwinkel, B. Ueberholz, D. Haubrich, and D. Meschede, Opt. Commun. 145, 57 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

M. R. Andrews, D. M. Kurn, H.-J. Miesner, D. S. Durfee, C. G. Townsend, S. Inouye, and W. Ketterle, Phys. Rev. Lett. 79, 553 (1997).
[CrossRef]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987).
[CrossRef] [PubMed]

Physica (1)

F. Zernike, Physica 9, 686 (1942).
[CrossRef]

Rev. Sci. Instrum. (1)

A. Pogany, D. Gao, and S. W. Wilkins, Rev. Sci. Instrum. 68, 2774 (1997).
[CrossRef]

Science (1)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Science 273, 84 (1996).
[CrossRef] [PubMed]

Other (1)

W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1981).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the imaging configuration. A cloud of Rb85 atoms was illuminated with a fiber-coupled and collimated laser beam detuned from resonance. A lens reimaged the light from a plane at defocus distance R onto a CCD. Rays illustrate the antilensing for above-resonance illumination.

Fig. 2
Fig. 2

Defocused image for detuning δ=+3Γ and defocus R=30 mm. Line profiles (three-pixel rows averaged) are shown for the defocus image and (gray curve) for a conventional in-focus absorption image at the same detuning.

Fig. 3
Fig. 3

Column-density gray-scale image retrieved from the defocus image of Fig. 2. Line profiles (single pixel row) are shown for the column density derived from our method compared with that retrieved from conventional in-focus absorption imaging at the same detuning (gray curve).

Equations (10)

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

Ur,z=0=Uin expik0nr,z-1dz,
nr,z=1+3λ0ρr,z2k02i-2δ1+4δ2,
1+ρr,znr+ini.
Ir,z=0=Ur,z=02=Iin exp-2k0niρr,
ϕr,z=0=k0nrρr,
·Ir,zϕr,z=-k0zIr,z,
nr2k0niIin2 exp-2k0niρr=zIr,z=0.
1-Rδk02exp-2k0niρr=Ir,z=RIin.
exp-2k0niρr=F-1FIr,z=R/Iin1+Rδk0k2.
Ir,z=RIin=Iabs-IfluoroIbright-Idark,

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