Abstract

We simulate a three-dimensional optical diffraction tomography experiment in which superresolution is achieved by illuminating the object with evanescent waves generated by a prism. We show that accounting for multiple scattering between the object and the prism interface is mandatory to obtain superresolved images. Because the Born approximation leads to poor results, we propose a nonlinear inversion method for retrieving the map of permittivity of the object from the scattered far field. We analyze the sensitivity to noise of our algorithm and point out the importance of using incident propagative waves together with evanescent waves to improve the robustness of the reconstruction without losing the superresolution.

© 2004 Optical Society of America

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  1. J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).
  2. M. Dyba and S. Hell, Phys. Rev. Lett. 88, 163901 (2002).
    [CrossRef]
  3. S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
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  4. O. Haeberlé, A. Dieterlen, and S. Jacquey, Opt. Lett. 26, 1684 (2001).
    [CrossRef]
  5. J. Enderlein, Opt. Lett. 25, 634 (2000).
    [CrossRef]
  6. M. Gustafsson, J. Microsc. 198, 82 (2000).
    [CrossRef] [PubMed]
  7. N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
    [CrossRef]
  8. V. Lauer, J. Microsc. 205, 165 (2002).
    [CrossRef] [PubMed]
  9. E. Wolf, Opt. Commun. 1, 153 (1969).
    [CrossRef]
  10. P. S. Carney and J. C. Schotland, Opt. Lett. 26, 1072 (2001).
    [CrossRef]
  11. K. Belkebir and A. Sentenac, J. Opt. Soc. Am. A 20, 1223 (2003).
    [CrossRef]
  12. P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
    [CrossRef]
  13. K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1617 (2001).
  14. T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).
  15. A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
    [CrossRef]

2003

2002

M. Dyba and S. Hell, Phys. Rev. Lett. 88, 163901 (2002).
[CrossRef]

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

2001

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1617 (2001).

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[CrossRef]

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

P. S. Carney and J. C. Schotland, Opt. Lett. 26, 1072 (2001).
[CrossRef]

O. Haeberlé, A. Dieterlen, and S. Jacquey, Opt. Lett. 26, 1684 (2001).
[CrossRef]

2000

1998

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

1997

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

1993

T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).

1969

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Belkebir, K.

K. Belkebir and A. Sentenac, J. Opt. Soc. Am. A 20, 1223 (2003).
[CrossRef]

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1617 (2001).

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

Carminati, R.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Carney, P. S.

Chaumet, P. C.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

de Fornel, F.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

de Hon, B.

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

Destouches, N.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

Dieterlen, A.

Dufour, J.-P.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

Dyba, M.

M. Dyba and S. Hell, Phys. Rev. Lett. 88, 163901 (2002).
[CrossRef]

Enderlein, J.

Giovannini, H.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

Groom, R. W.

T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).

Guérin, C. A.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

Gustafsson, M.

M. Gustafsson, J. Microsc. 198, 82 (2000).
[CrossRef] [PubMed]

Habashy, T. M.

T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).

Haeberlé, O.

Hell, S.

M. Dyba and S. Hell, Phys. Rev. Lett. 88, 163901 (2002).
[CrossRef]

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[CrossRef]

Jacquey, S.

Lauer, V.

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

Lequime, M.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

Litman, A.

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

Schotland, J. C.

Sentenac, A.

Spies, B. R.

T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).

Tijhuis, A. G.

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1617 (2001).

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

Ünlü, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[CrossRef]

Wolf, E.

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Appl. Phys. Lett.

S. B. Ippolito, B. B. Goldberg, and M. S. Ünlü, Appl. Phys. Lett. 78, 4071 (2001).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

A. G. Tijhuis, K. Belkebir, A. Litman, and B. de Hon, IEEE Trans. Geosci. Remote Sens. 39, 1316 (2001).
[CrossRef]

Inverse Probl.

K. Belkebir and A. G. Tijhuis, Inverse Probl. 17, 1617 (2001).

J. Appl. Phys.

T. M. Habashy, R. W. Groom, and B. R. Spies, J. Appl. Phys. 98, 1759 (1993).

J. Microsc.

V. Lauer, J. Microsc. 205, 165 (2002).
[CrossRef] [PubMed]

M. Gustafsson, J. Microsc. 198, 82 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Commun.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, Opt. Commun. 198, 233 (2001).
[CrossRef]

E. Wolf, Opt. Commun. 1, 153 (1969).
[CrossRef]

Opt. Lett.

Phys. Rev. B

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, Phys. Rev. B 58, 2310 (1998).
[CrossRef]

Phys. Rev. Lett.

M. Dyba and S. Hell, Phys. Rev. Lett. 88, 163901 (2002).
[CrossRef]

Prog. Surf. Sci.

J.-J. Greffet and R. Carminati, Prog. Surf. Sci. 56, 133 (1997).

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Figures (3)

Fig. 1
Fig. 1

Sketch of the ODT experiment.

Fig. 2
Fig. 2

Reconstructed relative permittivity distribution with only evanescent-wave illumination: (a), (b) with the extended Born approximation; (c), (d) with the nonlinear inverse scheme.

Fig. 3
Fig. 3

Reconstructed relative permittivity distribution with the nonlinear inverse algorithm from corrupted data with noise: (a), (b) with evanescent waves; (c), (d) with evanescent and propagative waves.

Equations (6)

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

ElriΩ=Elincri+j=1NGri,rjαrjElrj,
EldrmΓ=j=1NGrm,rjαrjElrj.
Eld=G¯¯farαEl,
El=Elinc+G¯¯nearαEl,
Fnαn=l=1Lfl-G¯¯farαnEl,nΓ2l=1LflΓ2
En,l=I¯¯-G¯¯nearαn-1-1Elinc,

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