Abstract

We show that tomographic diffractive microscopy can be used for profilometry applications with high transverse resolution. We present an iterative reconstruction procedure, based on a rigorous wave scattering model, that permits us to retrieve the profile of rough metallic interfaces from the complex scattered field. The transversal resolution is subwavelength, and can even fall below the classical resolution limit if the profile is rough enough for multiple interactions to occur. Large profiles, with tens of wavelength size, can be investigated.

© 2011 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  2. C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
    [CrossRef]
  3. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).
  4. G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
    [CrossRef]
  5. H. J. Tiziani and H. M. Uhde, “Three-dimensional image sensing by chromatic confocal microscopy,” Appl. Opt. 33, 1838–1843(1994).
    [CrossRef] [PubMed]
  6. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
    [CrossRef] [PubMed]
  7. O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
    [CrossRef]
  8. G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
    [CrossRef] [PubMed]
  9. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–595 (2006).
    [CrossRef]
  10. E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
    [CrossRef]
  11. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
    [CrossRef]
  12. J. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  13. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
    [CrossRef]
  14. R. Wombell and J. DeSanto, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
    [CrossRef]
  15. A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propag. 29, 232–238 (1981).
    [CrossRef]
  16. K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
    [CrossRef]
  17. A. Roger, “Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix,” Electromagnetics 2, 69–83 (1982).
    [CrossRef]
  18. A. N. Tikhonov and V. A. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).
  19. O. Haeberlé, A. Sentenac, and H. Giovannini, “An introduction to diffractive tomographic microscopy,” in Modern Research and Educational Topics in Microscopy, A.M.Vilas and J.D.Alvarez, eds. (2007), Vol.  2.

2010 (2)

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

2009 (1)

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

2006 (1)

2002 (1)

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

1997 (1)

K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
[CrossRef]

1994 (1)

1991 (2)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

R. Wombell and J. DeSanto, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
[CrossRef]

1988 (2)

G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

1982 (1)

A. Roger, “Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix,” Electromagnetics 2, 69–83 (1982).
[CrossRef]

1981 (1)

A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propag. 29, 232–238 (1981).
[CrossRef]

1979 (1)

C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Ao, C. O.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
[CrossRef]

Arsenin, V. A.

A. N. Tikhonov and V. A. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

Barends, P.

C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Belkebir, K.

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–595 (2006).
[CrossRef]

K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
[CrossRef]

Blom, P.

C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Brakenhoff, C. J.

C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Chaumet, P. C.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–595 (2006).
[CrossRef]

Corle, T. R.

G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

DeSanto, J.

Ding, K. H.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
[CrossRef]

Drsek, F.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

Giovannini, H.

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

O. Haeberlé, A. Sentenac, and H. Giovannini, “An introduction to diffractive tomographic microscopy,” in Modern Research and Educational Topics in Microscopy, A.M.Vilas and J.D.Alvarez, eds. (2007), Vol.  2.

Girard, J.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Haeberlé, O.

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, A. Sentenac, and H. Giovannini, “An introduction to diffractive tomographic microscopy,” in Modern Research and Educational Topics in Microscopy, A.M.Vilas and J.D.Alvarez, eds. (2007), Vol.  2.

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Kino, G. S.

G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Kleinman, R. E.

K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
[CrossRef]

Konan, D.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Kong, J. A.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
[CrossRef]

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Maire, G.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Pichot, C.

K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Roger, A.

A. Roger, “Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix,” Electromagnetics 2, 69–83 (1982).
[CrossRef]

A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propag. 29, 232–238 (1981).
[CrossRef]

Sentenac, A.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23, 586–595 (2006).
[CrossRef]

O. Haeberlé, A. Sentenac, and H. Giovannini, “An introduction to diffractive tomographic microscopy,” in Modern Research and Educational Topics in Microscopy, A.M.Vilas and J.D.Alvarez, eds. (2007), Vol.  2.

Sheppard, C. J. R.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Shuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Talneau, A.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Thorsos, E.

E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

Tikhonov, A. N.

A. N. Tikhonov and V. A. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

Tiziani, H. J.

Tsang, L.

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
[CrossRef]

Uhde, H. M.

Wilson, T.

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Wombell, R.

Xiao, G. Q.

G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Q. Xiao, T. R. Corle, and G. S. Kino, “Real time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Electromagnetics (1)

A. Roger, “Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix,” Electromagnetics 2, 69–83 (1982).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Roger, “Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propag. 29, 232–238 (1981).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

K. Belkebir, R. E. Kleinman, and C. Pichot, “Microwave imaging—location and shape reconstruction from multifrequency scattering data,” IEEE Trans. Microwave Theory Tech. 45, 469–476 (1997).
[CrossRef]

J. Acoust. Soc. Am. (1)

E. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

J. Microsc. (2)

C. J. Brakenhoff, P. Blom, and P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef] [PubMed]

J. Mod. Opt. (2)

O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
[CrossRef]

J. Opt. Soc. Am. A (2)

Phys. Rev. Lett. (1)

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Shuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (5)

T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations, Wiley Series in Remote Sensing (Wiley-Interscience, 2001).
[CrossRef]

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

A. N. Tikhonov and V. A. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).

O. Haeberlé, A. Sentenac, and H. Giovannini, “An introduction to diffractive tomographic microscopy,” in Modern Research and Educational Topics in Microscopy, A.M.Vilas and J.D.Alvarez, eds. (2007), Vol.  2.

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Figures (5)

Fig. 1
Fig. 1

Geometry of the surface scattering problem.

Fig. 2
Fig. 2

Reconstruction of 60 μm long rough surfaces with Gaussian correlation with rms height of 60 nm and different values of the correlation length . (a) and (b)  = 500 nm , and (c) and (d)  = 100 nm . (a) and (c) Reconstructed profiles using NK, while (b) and (d) are reconstructed profiles using the Fraunhofer approximation. In (c) and (d), only the 20 μm central part is reported.

Fig. 3
Fig. 3

Reconstruction at λ = 633 nm using the NK algorithm of a surface constituted of two bumps of w = 80 nm width and separated by a fixed interdistance d = 200 nm , but with various values of the height h. (a)  h = 50 nm ; (b) h = 100 nm ; (c)  h = 140 nm .

Fig. 4
Fig. 4

Evolution of the cost function against the iteration step for the reconstruction that corresponds to Fig. 3c.

Fig. 5
Fig. 5

Reconstruction, at λ = 633 nm and using the NK algorithm, of a surface constituted of two bumps of w = 80 nm width and height h = 140 nm , separated by a fixed interdistance d = 200 nm from noisy data. The SNRs are (a) 50, (b) 20, and (c) 10.

Equations (13)

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

ψ inc ( r , θ 0 ) = g 2 π | k x | < k exp ( i k x x i k 2 k x 2 z ) × exp [ ( k x k sin θ 0 ) 2 g 2 / 4 ] d k x ,
( r Γ z = η ( x ) ) ψ ( r , θ 0 ) = 0 .
k = k r r = ( k cos θ , k sin θ ) , k = ω c ,
ψ sca ( r , θ 0 ) ( 1 + i ) e i k r 4 π k r s ( θ , θ 0 ) ,
r Γ , Γ G ( r , r ) n ψ ( r , θ 0 ) d r = ψ inc ( r , θ 0 ) ,
s ( θ , θ 0 ) = Γ n ψ ( r , θ 0 ) exp ( i k · r ) d r ,
s ( θ , θ 0 ) = f ˜ ( k sin θ k sin θ 0 ) ,
η ( x ) = λ 4 π arg f ( x ) .
s mes = F η ,
η n = η n 1 + δ η n ,
D δ η n = δ s = ( s mes s n 1 ) ,
δ s ( θ 2 , θ 1 ) = Γ n ψ ( r , θ 1 ) n ψ ( r , θ 2 ) δ η ( r ) d r ,
[ D D + μ 2 I ] δ η n = D ( s mes s n 1 ) ,

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