Abstract

Tomographic diffractive microscopy (TDM) is a label-free imaging technique that reconstructs the 3D refractive index map of the probed object with an improved resolution compared to confocal microscopy. In this work, we consider a TDM implementation in which the sample is deposited on a reflective substrate. We show that this configuration requires calibration and inversion procedures that account for the presence of the substrate for getting highly resolved quantitative reconstructions.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
    [CrossRef]
  4. M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, R. R. Dasari, M. S. Feld, and W. Choi, “High-speed synthetic aperture microscopy for live cell imaging,” Opt. Lett. 36, 148–150 (2011).
    [CrossRef]
  5. M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
    [CrossRef]
  6. Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
    [CrossRef]
  7. N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
    [CrossRef]
  8. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57, 686–699 (2010).
    [CrossRef]
  9. E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
    [CrossRef]
  10. E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
    [CrossRef]
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    [CrossRef]
  14. M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
    [CrossRef]
  15. 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]
  16. 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]
  17. S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
    [CrossRef]
  18. Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  20. O. Haeberlé, A. Sentenac, and H. Giovannini, An Introduction to Diffractive Tomographic Microscopy, A. M. Vilas and J. D. Alvarez, eds., Modern Research and Educational Topics in Microscopy, Vol. II (Formatex, 2007).
  21. 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]
  22. P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (2009).
    [CrossRef]
  23. P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
    [CrossRef]
  24. E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
    [CrossRef]
  25. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  26. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
    [CrossRef]
  27. The experiment was automatized using the free software OpticsBenchUI.
  28. G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
    [CrossRef]

2013 (2)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

2012 (3)

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

2011 (1)

2010 (7)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (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]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[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]

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[CrossRef]

2009 (3)

P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (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]

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef]

2006 (3)

2005 (1)

2004 (1)

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

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]

2001 (1)

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[CrossRef]

1992 (1)

S. W. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[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]

Arhab, S.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Babacan, S. D.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Bednarz, M.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Beghin, A.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

Belkebir, K.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[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]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (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]

P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (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]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
[CrossRef]

Bon, P.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Chaumet, P.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Chaumet, P. C.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[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]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (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]

P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (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]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Choi, W.

Choi, Y.

Colicchio, B.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Dasari, R. R.

Debailleul, M.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

Delaunay, J.-J.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Destouches, N.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[CrossRef]

Do, M. N.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Drsek, F.

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (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]

Fang-Yen, C.

Feld, M. S.

Ferrand, P.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Garcia, J.

Garcia-Martinez, P.

Georges, V.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[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, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[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, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (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]

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[CrossRef]

O. Haeberlé, A. Sentenac, and H. Giovannini, An Introduction to Diffractive Tomographic Microscopy, A. M. Vilas and J. D. Alvarez, eds., Modern Research and Educational Topics in Microscopy, Vol. II (Formatex, 2007).

Girard, J.

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[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]

Golding, I.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Guérin, C. A.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[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.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (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]

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

O. Haeberlé, A. Sentenac, and H. Giovannini, An Introduction to Diffractive Tomographic Microscopy, A. M. Vilas and J. D. Alvarez, eds., Modern Research and Educational Topics in Microscopy, Vol. II (Formatex, 2007).

Hell, S. W.

S. W. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[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]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Kim, M.

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]

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]

Lequime, M.

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[CrossRef]

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Maire, G.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[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, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (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]

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Mico, V.

Mir, M.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Moal, E. L.

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

Monneret, S.

Mudry, E.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef]

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Popescu, G.

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Ruan, Y.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[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]

Sarmis, M.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

Sentenac, A.

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[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]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35, 1857–1859 (2010).
[CrossRef]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (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]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
[CrossRef]

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

O. Haeberlé, A. Sentenac, and H. Giovannini, An Introduction to Diffractive Tomographic Microscopy, A. M. Vilas and J. D. Alvarez, eds., Modern Research and Educational Topics in Microscopy, Vol. II (Formatex, 2007).

Sentenac, D.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Simon, B.

M. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

Soriano, G.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Stelzer, E. H. K.

S. W. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Sung, Y.

Talneau, A.

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[CrossRef]

Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret, and A. Sentenac, “Tomographic diffractive microscopy with a wavefront sensor,” Opt. Lett. 37, 1631–1633 (2012).
[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, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (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]

Tourneur, Y.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

Toy, F.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Wattellier, B.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

zadegan, K. B.

Zalevsky, Z.

Inverse Probl. (2)

P. C. Chaumet and K. Belkebir, “Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method,” Inverse Probl. 25, 024003 (2009).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method,” Inverse Probl. 28, 065007 (2012).
[CrossRef]

J. Biophotonics (1)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3, 462–467 (2010).
[CrossRef]

J. Microsc. (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]

J. Mod. Opt. (3)

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. Sarmis, B. Simon, M. Debailleul, B. Colicchio, V. Georges, J.-J. Delaunay, and O. Haeberlé, “High resolution reflection tomographic diffractive microscopy,” J. Mod. Opt. 57, 740–745 (2010).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime,” J. Mod. Opt. 57, 746–755 (2010).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nat. Photonics (1)

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[CrossRef]

Opt. Commun. (2)

N. Destouches, C. A. Guérin, M. Lequime, and H. Giovannini, “Determination of the phase of the diffracted field in the optical domain. application to the reconstruction of surface profiles,” Opt. Commun. 198, 233–239 (2001).
[CrossRef]

S. W. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

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 (1)

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. Chaumet, K. Belkebir, and H. Giovannini, “Nanometric resolution with far-field optical profilometry,” Phys. Rev. Lett. 111, 053902 (2013).
[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]

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]

E. Mudry, E. L. Moal, P. Ferrand, P. C. Chaumet, and A. Sentenac, “Isotropic diffraction-limited focusing using a single objective lens,” Phys. Rev. Lett. 105, 203903 (2010).
[CrossRef]

PLoS ONE (1)

M. Mir, S. D. Babacan, M. Bednarz, M. N. Do, I. Golding, and G. Popescu, “Visualizing Escherichia coli sub-cellular structure using sparse deconvolution spatial light interference tomography,” PLoS ONE 7, e39816 (2012).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

O. Haeberlé, A. Sentenac, and H. Giovannini, An Introduction to Diffractive Tomographic Microscopy, A. M. Vilas and J. D. Alvarez, eds., Modern Research and Educational Topics in Microscopy, Vol. II (Formatex, 2007).

The experiment was automatized using the free software OpticsBenchUI.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

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Figures (9)

Fig. 1.
Fig. 1.

Sketch of the experimental setup: M, rotating mirror; BE, beam expander; D, diaphragm; OL, objective lens; L1, tube lens; L2,,5, lenses; BS1,,3, beam splitters; PM, phase modulator; P, pinhole.

Fig. 2.
Fig. 2.

Test sample: subwavelength resin cylinders deposited on a silicon substrate.

Fig. 3.
Fig. 3.

Transverse cut (left) and longitudinal cut (right) of the modulus of the 3D FT1 of the dataset. Cuts are along the white dashed lines.

Fig. 4.
Fig. 4.

Transverse cut (left) and longitudinal cuts (top and bottom) of the 3D permittivity map reconstructed with the nonlinear iterative inversion in a quite large domain. Cuts are along the white dashed lines.

Fig. 5.
Fig. 5.

Same as Fig. 4 with a tightened domain.

Fig. 6.
Fig. 6.

3D permittivity map assuming the sample is surrounded by air (no substrate), with an investigation domain symmetrical with respect to the substrate plane (z=0).

Fig. 7.
Fig. 7.

Same as Fig. 6 when the substrate is taken into account for Eref only.

Fig. 8.
Fig. 8.

Same as Fig. 4 when the substrate is taken into account for Eref and only.

Fig. 9.
Fig. 9.

Same as Fig. 5 when the substrate is taken into account for Eref and only.

Equations (13)

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

Es(k,kl)=Vg(k,r)χ(r)E(r,kl)dr,
Es(k,kl)χ˜(kkl),
E(r)=Eref(r)+VG(r,r)χ(r)E(r)dr,
Els=χEl,
El=Elref+χEl.
Fn(χn,El,n)=l=1Lhl,n(1)Γ2l=1LflΓ2+l=1Lhl,n(2)Ω2l=1LElrefΩ2
=WΓl=1Lhl,n(1)Γ2+WΩl=1Lhl,n(2)Ω2,
hl,n(1)=flχnEl,n,
hl,n(2)=ElrefEl,n+χnEl,n.
Ml=|γl|rlS2πElimS,
φs(k,kl)=φ0(k,kl)+(kkl)·d.
fl=flexp(i[γγl]dz),
G=l=1Lflβ(fl)Γ2,

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