Abstract

Multiple scattering is studied in a Cs magneto-optical trap (MOT). We use two Abel inversion algorithms to recover density distributions of the MOT from fluorescence images. Deviations of the density distribution from a Gaussian are attributed to multiple scattering.

© 2005 Optical Society of America

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References

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  1. D. W. Sesko , T. G. Walker , and C. E. Wieman , “ Behavior of neutral atoms in a spontaneous force trap ,” J. Opt. Soc. Am. B   8 , 946 ( 1991 ).
    [Crossref]
  2. C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
    [Crossref] [PubMed]
  3. M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
    [Crossref]
  4. S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
    [Crossref]
  5. C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
    [Crossref]
  6. A. Vorozcovs , M. Weel , S. Beattie , S. Cauchi , and A. Kumarakrishnan , “ Measurements of temperature scaling laws in an optically dense magneto-optical trap ,” J. Opt. Soc. Am. B   22 , 943 ( 2005 ).
    [Crossref]
  7. C. J. Dasch , “ One-dimensional tomography: a comparison of Abel, onion peeling, and filtered backprojection methods ,” Appl. Opt.   31 , 1146 ( 1992 ).
    [Crossref] [PubMed]
  8. R. N. Strickland and D. W. Chandler , “ Reconstruction of an axissymmetric image from its blurred and noisy projection ,” Appl. Opt.   30 , 1811 ( 1991 ).
    [Crossref] [PubMed]
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    [Crossref]
  10. V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
    [Crossref]
  11. K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
    [Crossref]
  12. G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
    [Crossref] [PubMed]
  13. T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
    [Crossref]
  14. C.D. Wallace , T.P. Dinneen , K.Y.N. Tan , A. Kumarakrishnan , P.L. Gould , and J. Javanainen , “ Measurements of temperature and spring constant in a magneto-optical trap ,” J. Opt. Soc. Am. B   11 , 703 ( 1994 ).
    [Crossref]
  15. J.P. Shaffer and Ph.D. Thesis , University of Rochester ( 1999 ).
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    [Crossref]
  17. R. N. Bracewell , The Fourier Transform and Its Applications ( McGraw-Hill , 2000 ).
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  19. C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
    [Crossref]
  20. G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
    [Crossref]
  21. K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
    [Crossref] [PubMed]
  22. K. Iizuka , Engineering Optics ( Springer-Verlag , 1987 ).

2005 (1)

2004 (1)

K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
[Crossref]

2002 (2)

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

2001 (1)

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

1999 (1)

G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
[Crossref]

1997 (1)

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

1996 (1)

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

1995 (1)

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

1994 (4)

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
[Crossref] [PubMed]

C.D. Wallace , T.P. Dinneen , K.Y.N. Tan , A. Kumarakrishnan , P.L. Gould , and J. Javanainen , “ Measurements of temperature and spring constant in a magneto-optical trap ,” J. Opt. Soc. Am. B   11 , 703 ( 1994 ).
[Crossref]

D. Hoffmann , P. Feng , and T. Walker , “ Measurements of Rb trap-loss collision spectra ,” J. Opt. Soc. Am. B   11 , 712 ( 1994 ).
[Crossref]

1992 (2)

C. J. Dasch , “ One-dimensional tomography: a comparison of Abel, onion peeling, and filtered backprojection methods ,” Appl. Opt.   31 , 1146 ( 1992 ).
[Crossref] [PubMed]

K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
[Crossref] [PubMed]

1991 (2)

1988 (1)

L. M. Smith , D. R. Keefer , and S. I. Sudharsanan , “ Abel Inversion Using Transform Techniques ,” J. Quant. Spect. Radiat. Transfer   39 , 367 ( 1988 ).
[Crossref]

1980 (1)

Arimondo, E.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Beattie, S.

Bracewell, R. N.

R. N. Bracewell , The Fourier Transform and Its Applications ( McGraw-Hill , 2000 ).

Brzozowski, T.M.

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

Burnett, K.

G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
[Crossref] [PubMed]

Castin, Y.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Cauchi, S.

Chandler, D. W.

Clairon, A.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Colla, M.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Cooper, C. J.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Dalibard, J.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Dasch, C. J.

Dinneen, T.P.

Drewsen, M.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Dribinski, V.

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

Edwards, N. H.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Evangelista, A.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

Feng, P.

Fioretti, A.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Foot, C. J.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
[Crossref] [PubMed]

Franklin, J.

K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
[Crossref]

Gabbanini, C.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

Gawalik, W.

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

Gebhardt, C. R.

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

Golub, G. H.

G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
[Crossref]

Gould, P.L.

Gozzini, S.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

Grego, S.

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Grison, D.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Hansen, P. C.

G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
[Crossref]

Hillenbrand, G.

G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
[Crossref] [PubMed]

Hoffmann, D.

Ichioka, Y.

Iizuka, K.

K. Iizuka , Engineering Optics ( Springer-Verlag , 1987 ).

Javanainen, J.

Kawata, S.

Keefer, D. R.

L. M. Smith , D. R. Keefer , and S. I. Sudharsanan , “ Abel Inversion Using Transform Techniques ,” J. Quant. Spect. Radiat. Transfer   39 , 367 ( 1988 ).
[Crossref]

Kitsopoulos, T. N.

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

Kumarakrishnan, A.

Ladopoulos, V.

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

Lindquist, K.

K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
[Crossref] [PubMed]

Lucchesini, A.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

Maczynska, M.

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

Mandelshtam, V. A.

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

Muller, J. H.

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Nadir, A.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

O’Leary, D. P.

G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
[Crossref]

Osssadtchi, A.

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

Overstreet, K. R.

K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
[Crossref]

P., Laurent

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Perrin, H.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Rakitzis, T. P.

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

Reisler, H.

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

Salomon, C.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Samartzis, P. C.

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

Santarelli, G.

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Sesko, D. W.

Shaffer, J. P.

K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
[Crossref]

Shaffer, J.P.

J.P. Shaffer and Ph.D. Thesis , University of Rochester ( 1999 ).

Smith, L. M.

L. M. Smith , D. R. Keefer , and S. I. Sudharsanan , “ Abel Inversion Using Transform Techniques ,” J. Quant. Spect. Radiat. Transfer   39 , 367 ( 1988 ).
[Crossref]

Steane, A. M.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Stephens, M.

K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
[Crossref] [PubMed]

Strickland, R. N.

Sudharsanan, S. I.

L. M. Smith , D. R. Keefer , and S. I. Sudharsanan , “ Abel Inversion Using Transform Techniques ,” J. Quant. Spect. Radiat. Transfer   39 , 367 ( 1988 ).
[Crossref]

Szriftgiser, P.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Tan, K.Y.N.

Thesis, Ph.D.

J.P. Shaffer and Ph.D. Thesis , University of Rochester ( 1999 ).

Townsend, C. G.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Verkerk, P.

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Vorozcovs, A.

Walker, T.

Walker, T. G.

Wallace, C.D.

Weel, M.

Wieman, C.

K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
[Crossref] [PubMed]

Wieman, C. E.

Zachorowski, J.

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

Zawada, M.

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

Zetie, K. P.

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

M. Drewsen , Laurent P. , A. Nadir , G. Santarelli , A. Clairon , Y. Castin , D. Grison , and C. Salomon , “ Investigation of sub-Doppler cooling effects in a cesium magneto-optical trap ,” Appl. Phys. B   59 , 283 ( 1994 ).
[Crossref]

Europhys. Lett. (1)

C. Gabbanini , A. Evangelista , S. Gozzini , A. Lucchesini , A. Fioretti , J. H. Muller , M. Colla , and E. Arimondo , “ Scaling laws in magneto-optical traps ,” Europhys. Lett.   37 , 251 ( 1997 ).
[Crossref]

J. Opt. B: Quant. Semiclass. Opt. (1)

T.M. Brzozowski , M. Maczynska , M. Zawada , J. Zachorowski , and W. Gawalik , “ Time-of-flight measurement of the temperature of cold atoms for short trap-probe beam distances ,” J. Opt. B: Quant. Semiclass. Opt. ,   4 , 62 ( 2002 ).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

J. Quant. Spect. Radiat. Transfer (1)

L. M. Smith , D. R. Keefer , and S. I. Sudharsanan , “ Abel Inversion Using Transform Techniques ,” J. Quant. Spect. Radiat. Transfer   39 , 367 ( 1988 ).
[Crossref]

Opt. Commun. (1)

S. Grego , M. Colla , A. Fioretti , J. H. Muller , P. Verkerk , and E. Arimondo , “ A cesium magneto-optical trap for cold collision studies ,” Opt. Commun.   132 , 519 ( 1996 ).
[Crossref]

Phys. Rev. A (3)

C. G. Townsend , N. H. Edwards , C. J. Cooper , K. P. Zetie , C. J. Foot , A. M. Steane , P. Szriftgiser , H. Perrin , and J. Dalibard , “ Phase-space density in the magneto-optical trap ,” Phys. Rev. A   52 , 1423 ( 1995 ).
[Crossref] [PubMed]

G. Hillenbrand , C. J. Foot , and K. Burnett , “ Heating due to long-range photon exchange interactions between cold atoms ,” Phys. Rev. A   50 , 1479 ( 1994 ).
[Crossref] [PubMed]

K. Lindquist , M. Stephens , and C. Wieman , ” Experimental and Theoretical Study of the Vapor-cell Zeeman Optical Trap ,” Phys. Rev. A   46 , 4082 ( 1992 ).
[Crossref] [PubMed]

Rev. Sci. Instrum. (3)

C. R. Gebhardt , T. P. Rakitzis , P. C. Samartzis , V. Ladopoulos , and T. N. Kitsopoulos , “ Slice imaging: A new approach to ion imaging and velocity mapping ,” Rev. Sci. Instrum.   72 , 2001 ( 2001 ).
[Crossref]

V. Dribinski , A. Osssadtchi , V. A. Mandelshtam , and H. Reisler , “ Reconstruction of Abel-transformed images: The Gaussian basis-set expansion Abel transform method ,” Rev. Sci. Instrum.   73 , 2634 ( 2002 ).
[Crossref]

K. R. Overstreet , J. Franklin , and J. P. Shaffer , “ Zeeman effect spectroscopically locked Cs diode laser system for atomic physics ,” Rev. Sci. Instrum.   75 , 4749 ( 2004 ).
[Crossref]

SIAM J. Matrix Anal. Appl. (1)

G. H. Golub , P. C. Hansen , and D. P. O’Leary , “ Tikhonov Regularization and Total Least Squares ,” SIAM J. Matrix Anal. Appl.   21 , 185 ( 1999 ).
[Crossref]

Other (3)

J.P. Shaffer and Ph.D. Thesis , University of Rochester ( 1999 ).

K. Iizuka , Engineering Optics ( Springer-Verlag , 1987 ).

R. N. Bracewell , The Fourier Transform and Its Applications ( McGraw-Hill , 2000 ).

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Figures (4)

Fig. 1.
Fig. 1.

Mapping of a 3-D distribution onto a 2-D plane. Also depicted is the projection of a slice at constant z.

Fig. 2.
Fig. 2.

(a.) MOT density versus Natoms trapped. (b.) MOT volume versus Natoms trapped. (c.) Natoms1/3 versus MOT radius. (d.) Temperature as a function of detuning as measured from time-of-flight velocity distributions for I = 30mW/cm2 and magnetic field gradient dB/dz= 15G/cm. Open triangles (△) represent data analyzed using the BASEX transform, closed circles (●) were analyzed using the Fourier-Hankel transform.

Fig. 3.
Fig. 3.

Comparison of raw image to the Fourier-Hankel and BASEX transform methods. Additional structure is visible in both transformed images. The raw image was taken for Natoms = 2.0×106, a laser intensity of 30mW/cm2, and a magnetic field gradient dB/dz = 15G/cm.

Fig. 4.
Fig. 4.

Correlation of the (a.) raw images, (b.) Fourier-Hankel transform (●) and BASEX (⊕) to a Gaussian fit. The inset in (b.) shows an adjacent averaging of the R2 data.

Equations (16)

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R h ¯ ω L Γ 2 C 1 2 Ω tot 2 2 δ 2 + Γ 2 4 + C 2 2 Ω tot 2 2 ,
f ( x , y , z ; v x , v y , v z , t ) i = x , y , z e ( i v i t ) 2 / 2 σ i 2 e m v i 2 / 2 k B T .
f ( z , t ) e m z 2 / 2 σ z ( t ) 2 .
P ( x , z ) = 2 x I ( r , z ) r r 2 x 2 d r ,
I ( r , z ) = 1 π r d P ( x , z ) / d x x 2 r 2 d x .
F { P ( x ) } = I ( x 2 + y 2 ) e 2 πixk d x d y .
F { P ( x ) } = 2 π 0 r I ( r ) J 0 ( 2 πkr ) d r .
I ( r ) = 2 π 0 k J 0 ( 2 πkr ) P ( x ) e 2 πixk d x d k .
P ( x , z ) = Abel { I ( r , z ) } = k = 0 N 1 C k Abel { f k ( r , z ) } = k = 0 N 1 C k G k ( x , z ) .
P ij = k = 0 K 1 C k G ij ( k ) ,
G ij ( k ) = 2 h ( x x i , z z j ) x r f k ( r , z ) r 2 x 2 d x d z d r ,
X mi = 2 h x ( x x i ) x r ρ m ( r ) r 2 x 2 d x d r
Z nj = h z ( z z j ) ξ n ( z ) d z .
P ij = m = 0 N x 1 n = 0 N z 1 C mn X mi Z nj
ρ m ( r ) = ( e m 2 ) m 2 ( r σ ) 2 m 2 e ( r / σ ) 2 ,
B ( k ) = 1 1 + ( k k 0 ) 2 n ,

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