Abstract

Optical digital tomographic microscopy can be used for profilometry. The profile of the surface can be estimated from measurements of the complex diffracted far field obtained when the sample is illuminated successively under various incidences. Outside the validity domain of perturbative theories of diffraction, the profile is determined by using an iterative inverse wave scattering numerical method. In this paper we show that, for perfectly conducting surfaces, the two fundamental polarization cases involve different distances of interaction in the multiple scattering phenomenon. The use of both polarization cases in the inversion process leads to a considerable improvement of the lateral resolution. Robustness to noise is also discussed.

© 2012 Optical Society of America

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References

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  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]
  2. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
    [CrossRef]
  3. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
    [CrossRef]
  4. M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
    [CrossRef]
  5. M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
    [CrossRef]
  6. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
    [CrossRef]
  7. 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]
  8. 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]
  9. F. Simonetti, “Multiple scattering: the key to unravel the subwavelength world from the far-field pattern of a scattered wave,” Phys. Rev. E 73, 036619 (2006).
    [CrossRef]
  10. J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (2010).
    [CrossRef]
  11. H. Giovannini, M. Saillard, and A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1191 (1998).
    [CrossRef]
  12. S. Arhab, G. Soriano, K. Belkebir, A. Sentenac, and H. Giovannini, “Full wave optical profilometry,” J. Opt. Soc. Am. A 28, 576–580 (2011).
    [CrossRef]
  13. 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).
  14. T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
    [CrossRef]
  15. M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, 103–137 (2001).
    [CrossRef]
  16. K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).
    [CrossRef]
  17. A. Roger, “Newton–Kantorovitch algorithm applied to an electromagnetic inverse problem,” IEEE Trans. Antennas Propag. 29, 232–238 (1981).
    [CrossRef]
  18. A. Roger, “Reciprocity theorem applied to the computation of functional derivatives of the scattering matrix,” Electromagnetics 2, 69–83 (1982).
    [CrossRef]
  19. A. N. Tikhonov, V. I. A. Arsenin, and F. John, Solutions of Ill-Posed Problems (Winston, 1977).

2011

2010

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
[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]

2008

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

2007

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

2006

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]

F. Simonetti, “Multiple scattering: the key to unravel the subwavelength world from the far-field pattern of a scattered wave,” Phys. Rev. E 73, 036619 (2006).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

2004

T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
[CrossRef]

2002

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]

2001

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, 103–137 (2001).
[CrossRef]

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).
[CrossRef]

1998

1982

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

1981

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

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[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).

Arhab, S.

Arsenin, V. I. A.

A. N. Tikhonov, V. I. A. Arsenin, and F. John, Solutions of Ill-Posed Problems (Winston, 1977).

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Belkebir, K.

S. Arhab, G. Soriano, K. Belkebir, A. Sentenac, and H. Giovannini, “Full wave optical profilometry,” J. Opt. Soc. Am. A 28, 576–580 (2011).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

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]

Chaumet, P. C.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

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]

Chew, W. C.

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).
[CrossRef]

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Debailleul, M.

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
[CrossRef]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

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).

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]

Elfouhaily, T. M.

T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
[CrossRef]

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Georges, V.

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
[CrossRef]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

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.

S. Arhab, G. Soriano, K. Belkebir, A. Sentenac, and H. Giovannini, “Full wave optical profilometry,” J. Opt. Soc. Am. A 28, 576–580 (2011).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

H. Giovannini, M. Saillard, and A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1191 (1998).
[CrossRef]

Girard, J.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

Guérin, C. A.

T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
[CrossRef]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Haeberlé, O.

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

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
[CrossRef]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

John, F.

A. N. Tikhonov, V. I. A. Arsenin, and F. John, Solutions of Ill-Posed Problems (Winston, 1977).

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]

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).

Lauer, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[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]

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Maire, G.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

Morin, R.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

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]

Saillard, M.

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, 103–137 (2001).
[CrossRef]

H. Giovannini, M. Saillard, and A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1191 (1998).
[CrossRef]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Sentenac, A.

S. Arhab, G. Soriano, K. Belkebir, A. Sentenac, and H. Giovannini, “Full wave optical profilometry,” J. Opt. Soc. Am. A 28, 576–580 (2011).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

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]

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, 103–137 (2001).
[CrossRef]

H. Giovannini, M. Saillard, and A. Sentenac, “Numerical study of scattering from rough inhomogeneous films,” J. Opt. Soc. Am. A 15, 1182–1191 (1998).
[CrossRef]

Simon, B.

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett. 34, 79–81 (2009).
[CrossRef]

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

Simonetti, F.

F. Simonetti, “Multiple scattering: the key to unravel the subwavelength world from the far-field pattern of a scattered wave,” Phys. Rev. E 73, 036619 (2006).
[CrossRef]

Soriano, G.

Talneau, A.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (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]

Tikhonov, A. N.

A. N. Tikhonov, V. I. A. Arsenin, and F. John, Solutions of Ill-Posed Problems (Winston, 1977).

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).

Warnick, K. F.

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).
[CrossRef]

Electromagnetics

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.

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

J. Microsc.

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]

J. Mod. Opt.

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

Meas. Sci. Technol.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, “Holographic microscopy and diffractive microtomography of transparent samples,” Meas. Sci. Technol. 19, 074009(2008).
[CrossRef]

Nat. Methods

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007).
[CrossRef]

Opt. Lett.

Phys. Rev. A

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A 82, 061801 (2010).
[CrossRef]

Phys. Rev. E

F. Simonetti, “Multiple scattering: the key to unravel the subwavelength world from the far-field pattern of a scattered wave,” Phys. Rev. E 73, 036619 (2006).
[CrossRef]

Phys. Rev. Lett.

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]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Waves Random Media

T. M. Elfouhaily and C. A. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves Random Media 14, R1–R40 (2004).
[CrossRef]

M. Saillard and A. Sentenac, “Rigorous solutions for electromagnetic scattering from rough surfaces,” Waves Random Media 11, 103–137 (2001).
[CrossRef]

K. F. Warnick and W. C. Chew, “Numerical simulation methods for rough surface scattering,” Waves Random Media 11, R1–R30 (2001).
[CrossRef]

Other

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).

A. N. Tikhonov, V. I. A. Arsenin, and F. John, Solutions of Ill-Posed Problems (Winston, 1977).

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Figures (7)

Fig. 1.
Fig. 1.

Reconstructions of the profile at λ=633nm, using the NK algorithm under TE polarization and starting from plane, for different values of the Tikhonov parameter: (a) μTE2=107, (b) μTE2=108, (c) μTE2=109, and (d) μTE2=1011.

Fig. 2.
Fig. 2.

Reconstructions of the profile at λ=633nm using NK algorithm under TM polarization with Tikhonov parameter fixed to μTM2=109. The initial guess consists in the solution of the NK algorithm under TE polarization and starting from plane, for different values of the Tikhonov parameter: (a) μTE2=107, (b) μTE2=108, (c) μTE2=109, and (d) μTE2=1011.

Fig. 3.
Fig. 3.

Normalized spectral densities of the TE and TM surface currents.

Fig. 4.
Fig. 4.

Field difference over all incidence and scattering angles FD against (a) maximum interaction distance d, (b) cut-off spatial frequency of the filtered profile kc.

Fig. 5.
Fig. 5.

Reconstructions at λ=633nm using NK algorithm under TM polarization with Tikhonov parameter fixed to μTM2=109. Here the reconstructed surface obtained in the TE case with Tikhonov parameter fixed to μTE2=109 is used as a starting solution. Various SNRs are considered. The SNRs are (a) 35, (b) 15, (c) 7, (d) 5.

Fig. 6.
Fig. 6.

Actual and reconstructed profiles using two different polarizations TE (μTE2=109) or TM, and two different initial guesses for the TM case. (a) Central part of the surface, (b) intermediate part, (c) edge part. The best reconstruction (circle line) is obtained in TM (μTM2=1014) polarization when the initial guess is the reconstructed profile obtained in the TE (μTE2=109) case.

Fig. 7.
Fig. 7.

FTs of an actual and the reconstructed profiles using two different polarizations TE (μTE2=109) or TM, and two different initial guesses for the TM case. (a) A bare plane η=0 as initial guess is used. (b) Reconstructed surface using the TM (μTM2=1014) data and with as initial guess the final result of the reconstruction using TE (μTE2=109) case.

Equations (17)

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ψsca(rm,θl)=ψlsca(rm)(1+i)eik|rm|4πk|rm|s(θm,θl).
s(θm,θl)=N(θm,θl)e(x/g)2eiQzη(x)eiQxxdx,
Fηs=Fη.
sml=Γ[nψl(r)+in·kmψl(r)]exp(ikm·r)dc,
12ψl(r1)ΓnG(r1,r2)ψl(r2)dc2+ΓG(r1,r2)nψl(r2)dc2=ψlinc(r1),
z=η(x){ψl(r)=0TEnψl(r)=0TM.
ηn=ηn1+δηn,
Dn1δηn=ssn1,
D:δηδs=Dδη=limt0F(η+tδη)Fηt.
TEδsml=Γnψl(r)nψm(r)δη(x)dc,
TMδsml=Γ{k2ψl(r)ψm(r)tψl(r)tψm(r)}δη(x)dc.
F(δη)=Dδηδs2.
F(δη)=Dδηδs2+μ2Rδη2,
F(δη)=Dδηδs2+μ2[(1α)Iδη2+αSδη2].
[(Dn1)Dn1+μ2(αSS+(1α)I)]δηn=(Dn1)(ssn1),
FD(d)=m,l|smlsml(d)|2m,l|sml|2,
FD(kc)=m,l|smlsml(kc)|2m,l|sml|2.

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