Abstract

We have developed a reflection tomographic microscope in which the sample is reconstructed from different holograms recorded under various angles and wavelengths of incidence. We present an iterative inversion algorithm based on a rigorous modeling of the wave-sample interaction that processes all the data simultaneously to estimate the sample permittivity distribution. We show that using several wavelengths permits a significant improvement of the reconstruction, especially along the optical axis.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Superresolution in total internal reflection tomography

Kamal Belkebir, Patrick C. Chaumet, and Anne Sentenac
J. Opt. Soc. Am. A 22(9) 1889-1897 (2005)

Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography

Kamal Belkebir, Patrick C. Chaumet, and Anne Sentenac
J. Opt. Soc. Am. A 23(3) 586-595 (2006)

References

  • View by:
  • |
  • |
  • |

  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]
  2. L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an led array microscope,” Optica 2(2), 104–111 (2015).
    [Crossref]
  3. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
    [Crossref]
  4. A. Sentenac and J. Mertz, “Unified description of three-dimensional optical diffraction microscopy: from transmission microscopy to optical coherence tomography: tutorial,” J. Opt. Soc. Am. A 35(5), 748–754 (2018).
    [Crossref]
  5. J. Jung, K. Kim, J. Yoon, and Y. Park, “Hyperspectral optical diffraction tomography,” Opt. Express 24, 2006–2012 (2016)
    [Crossref] [PubMed]
  6. P. Hosseini, Y. Sung, Y. Choi, N. Lue, Z. Yaqoob, and P. So, “Scanning color optical tomography (SCOT),” Opt. Express 23, 19752–19762 (2015).
    [Crossref] [PubMed]
  7. C. Zuo, J. Sun, J. Zhang, Y. Hu, and Q. Chen, “Lensless phase microscopy and diffraction tomography with multi-angle and multi-wavelength illuminations using a led matrix,” Opt. Express 23(11), 14314–14328 (2015).
    [Crossref] [PubMed]
  8. A. C. Akcay, J. P. Rolland, and J. M. Eichenholz, “Spectral shaping to improve the point spread function in optical coherence tomography,” Opt. Lett. 28(20), 1921–1923 (2003).
    [Crossref] [PubMed]
  9. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A 23(5), 1027–1037 (2006).
    [Crossref]
  10. H. Liu, J. Bailleul, B. Simon, M. Debailleul, B. Colicchio, and O. Haeberlé, “Tomographic diffractive microscopy and multiview profilometry with flexible aberration correction,” Appl. Opt. 53, 748–755 (2014).
    [Crossref] [PubMed]
  11. 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]
  12. F. Montfort, T. Colomb, F. Charrière, J. Kühn, P. Marquet, E. Cuche, S. Herminjard, and C. Depeursinge, “Submicrometer optical tomography by multiple-wavelength digital holographic microscopy,” Appl. Opt. 45(32), 8209–8217 (2006).
    [Crossref] [PubMed]
  13. J. Kühn, F. Montfort, T. Colomb, B. Rappaz, C. Moratal, N. Pavillon, P. Marquet, and C. Depeursinge, “Submicrometer tomography of cells by multiple-wavelength digital holographic microscopy in reflection,” Opt. Lett. 34(5), 653–655 (2009).
    [Crossref] [PubMed]
  14. 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(6), 065007 (2012).
    [Crossref]
  15. T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
    [Crossref]
  16. C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
    [Crossref]
  17. T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
    [Crossref]
  18. P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
    [Crossref]
  19. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,”. J. Opt. Soc. Am. A 22, 1889–1897 (2005).
    [Crossref]
  20. T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (2012).
    [Crossref]
  21. A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
    [Crossref]
  22. W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,”. IEEE Microw. Guided Wave Lett. 5(12), 439–441 (1995).
    [Crossref]
  23. A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
    [Crossref]
  24. W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (2009).
    [Crossref]
  25. W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).
  26. S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
    [Crossref]
  27. E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
    [Crossref] [PubMed]
  28. T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
    [Crossref]
  29. B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3(7), 462–467 (2010).
    [Crossref] [PubMed]
  30. B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberlé, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4(4), 460–463 (2017).
    [Crossref]

2018 (1)

2017 (1)

2016 (2)

2015 (4)

2014 (1)

2013 (1)

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

2012 (2)

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (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(6), 065007 (2012).
[Crossref]

2010 (3)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 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(7), 462–467 (2010).
[Crossref] [PubMed]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
[Crossref] [PubMed]

2009 (4)

J. Kühn, F. Montfort, T. Colomb, B. Rappaz, C. Moratal, N. Pavillon, P. Marquet, and C. Depeursinge, “Submicrometer tomography of cells by multiple-wavelength digital holographic microscopy in reflection,” Opt. Lett. 34(5), 653–655 (2009).
[Crossref] [PubMed]

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[Crossref]

W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (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]

2006 (2)

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]

2003 (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]

2001 (1)

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[Crossref]

1999 (1)

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

1995 (2)

T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
[Crossref]

W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,”. IEEE Microw. Guided Wave Lett. 5(12), 439–441 (1995).
[Crossref]

Abubakar, A.

W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (2009).
[Crossref]

Akcay, A. C.

Allain, M.

Bailleul, J.

Beghin, A.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

Belkebir, K.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (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(6), 065007 (2012).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
[Crossref] [PubMed]

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]

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[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]

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[Crossref]

Boppart, S. A.

Carney, P. S.

Catapano, I.

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[Crossref]

Charrière, F.

Chaumet, P. C.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (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(6), 065007 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
[Crossref] [PubMed]

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, “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]

Chen, Q.

Chew, W. C.

W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,”. IEEE Microw. Guided Wave Lett. 5(12), 439–441 (1995).
[Crossref]

Choi, Y.

Chung, S. W.

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

Colicchio, B.

Colomb, T.

Cuche, E.

de Hon, B. P.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[Crossref]

Debailleul, M.

Depeursinge, C.

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]

Dubois, A.

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[Crossref]

Ecoffet, C.

Eichenholz, J. M.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

Giovannini, H.

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]

Godavarthi, C.

Habashy, T. M.

W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (2009).
[Crossref]

Haeberlé, O.

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberlé, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4(4), 460–463 (2017).
[Crossref]

H. Liu, J. Bailleul, B. Simon, M. Debailleul, B. Colicchio, and O. Haeberlé, “Tomographic diffractive microscopy and multiview profilometry with flexible aberration correction,” Appl. Opt. 53, 748–755 (2014).
[Crossref] [PubMed]

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophotonics 3(7), 462–467 (2010).
[Crossref] [PubMed]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

Herminjard, S.

Hosseini, P.

Houkal, M.

Hu, W.

W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (2009).
[Crossref]

Hu, Y.

Jung, J.

Kim, K.

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]

Kühn, J.

Lambert, J.

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, J. H.

W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,”. IEEE Microw. Guided Wave Lett. 5(12), 439–441 (1995).
[Crossref]

Litman, A. C. S.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[Crossref]

Liu, H.

Lue, N.

Maire, G.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[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]

Marks, D. L.

Marquet, P.

Mertz, J.

Montfort, F.

Moratal, C.

Mudry, E.

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(6), 065007 (2012).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
[Crossref] [PubMed]

Park, J.

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

Park, N. H.

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

Park, Y.

Pavillon, N.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).

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]

Ralston, T. S.

Rappaz, B.

Rolland, J. P.

Ruan, Y.

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

Saillard, M.

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[Crossref]

Sentenac, A.

A. Sentenac and J. Mertz, “Unified description of three-dimensional optical diffraction microscopy: from transmission microscopy to optical coherence tomography: tutorial,” J. Opt. Soc. Am. A 35(5), 748–754 (2018).
[Crossref]

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (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(6), 065007 (2012).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, “Mirror-assisted tomographic diffractive microscopy with isotropic resolution,” Opt. Lett. 35(11), 1857–1859 (2010).
[Crossref] [PubMed]

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, “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]

Sentenac, D.

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

Shin, J. H.

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

Simon, B.

So, P.

Soppera, O.

Spangenberg, A.

Sun, J.

Sung, Y.

Talneau, A.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[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]

Teukolski, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).

Tian, L.

Tijhuis, A. G.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[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(7), 462–467 (2010).
[Crossref] [PubMed]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).

Waller, L.

Wedberg, T. C.

T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
[Crossref]

Wedberg, W. C.

T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
[Crossref]

Yaqoob, Z.

Yoon, J.

Zhang, J.

Zhang, T.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, “Superresolution with full-polarized tomographic diffractive microscopy,” J. Opt. Soc. Am. A 32(2), 287–292 (2015).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (2012).
[Crossref]

Zuo, C.

Appl. Opt. (2)

Geophysics (1)

W. Hu, A. Abubakar, and T. M. Habashy, “Simultaneous multifrequency inversion of full-waveform seismic data,” Geophysics 74(2), R1–R14 (2009).
[Crossref]

IEEE Microw. Guided Wave Lett. (1)

W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,”. IEEE Microw. Guided Wave Lett. 5(12), 439–441 (1995).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (1)

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, “Theoretical and computational aspects of 2-D inverse profiling,” IEEE Trans. Geosci. Remote Sens. 39(6), 1316–1330 (2001).
[Crossref]

Inverse Probl. (2)

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, “Electromagnetic wave imaging of targets buried in a cluttered medium u sing a hybrid inversion-dort method,” Inverse Probl. 28(12), 125008 (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(6), 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(7), 462–467 (2010).
[Crossref] [PubMed]

J. Jpn. Appl. Phys. (1)

S. W. Chung, J. H. Shin, N. H. Park, and J. Park, “Dielectric properties of hydrogen silsesquioxane films degraded by heat and plasma treatment,” J. Jpn. Appl. Phys. 38(9A), 5214–5219 (1999).
[Crossref]

J. Microsc. (2)

T. C. Wedberg and W. C. Wedberg, “Tomographic reconstruction of the cross-sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsc. 177(1), 53–67 (1995).
[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. (1)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

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

Opt. Express (3)

Opt. Lett. (3)

Optica (3)

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. (2)

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength,” Phys. Rev. Lett. 111, 243904 (2013).
[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]

Radio Sci. (1)

A. Dubois, K. Belkebir, I. Catapano, and M. Saillard, “Iterative solution of the electromagnetic inverse scattering problem from the transient scattered field,” Radio Sci. 44, 14 (2009).
[Crossref]

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, (Cambridge University, 1996).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 Sketch of the experimental set-up: M, rotating mirror; BE, beam expander; D, diaphragm; OL, objective lens; L1, tube lens; L2,3, relay lenses (f′ = 3.5 cm and 20 cm, respectively); BS1,···,3, beam splitters; P, pinhole; HW1,2, half wave plates.
Fig. 2
Fig. 2 Images of a resin star-sample of 2.08 μm radius for outer ring, 208 nm radius for inner ring, and height 130 nm on a Si substrate. The edge distance between two sectors is 108 nm. (a) Scanning electronic microscope image. (b) Bright field microscopy with NA = 0.95, with five wavelengths.
Fig. 3
Fig. 3 Projections of the 20 unitary incident wavevector kinc/kinc onto the transverse (kx, ky) plane.
Fig. 4
Fig. 4 Reconstruction from monochromatic synthetic data with L = 20 illumination angles. Cut in the transverse plane at z = 100 nm (a,b) cut in the axial plane at y=1 μm (c,d). (a,c) at wavelength 475 nm (b,d) at wavelength 675 nm.
Fig. 5
Fig. 5 Illustration in the kx, kz plane of the support of the Optical Transfer Function (OTF) of a reflection imaging system with numerical aperture NA for the illumination and the observation (a) monochromatic with wavenumber k0 = 2π/λ. (b) polychromatic with 3 different wavelengths.
Fig. 6
Fig. 6 Reconstruction from multi-wavelength multi-illumination synthetic data in the transverse (a,b) and axial plane (c,d). (a,c) with the FH technique, (b,d)with the MF technique.
Fig. 7
Fig. 7 Amplitude and phase of the diffracted field for λ = 475nm, θinc = 49°, ϕinc = 0°. (a,c) experimental data, (b,d) synthetic data.
Fig. 8
Fig. 8 Reconstruction obtained with L = 20 illumination angles at wavelength λ = 475 nm.
Fig. 9
Fig. 9 Reconstruction using the FH method (a) with five wavelengths starting from λ = 675 nm to λ = 475 nm. (b) with four wavelengths, starting from λ = 625 nm to λ = 475 nm
Fig. 10
Fig. 10 Same as Fig. 9 but with the MF method.

Tables (2)

Tables Icon

Table 1 Relative measurement error between the experimental diffracted field and the exact diffracted field obtained with the actual object for the five wavelengths.

Tables Icon

Table 2 Errχ for the different inversion scheme.

Equations (19)

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

E l , p ( r ) = E l , p inc ( r ) + Ω G p ( r , r ) χ ( r ) E l , p ( r ) d r .
E l , p = E l , p inc + A p Ω χ E l , p ,
f l , p diff = B p Γ χ E l , p ,
n ( χ n , E , , n ) = W Γ l = 1 L p = 1 P h l , p , n ( 2 ) Γ 2 + W Ω l = 1 L p = 1 P h l , p , n ( 1 ) Ω 2 ,
W Ω = 1 l = 1 L p = 1 P E l , p inc Ω 2 , and W Γ = 1 l = 1 L p = 1 P f l , p mes Γ 2 .
h l , p , n ( 1 ) = E l , p , n E l , p inc A p Ω χ n E l , p , n ,
h l , p , n ( 2 ) = f l , p mes B p Γ χ n E l , p , n .
E l , p , n = E l , p , n 1 + α l , p , n v l , p , n + β l , p , n w l , p , n ,
χ n = χ n 1 + κ n d n ,
w l , p , n = E ˜ l , p , n 1 E l , p , n 1 ,
E ˜ l , p , n 1 = [ I A p Ω χ n 1 ] 1 E l , p inc ,
ξ n = ξ n 1 + β n ; ξ d n ; ξ .
d n ; ξ = g n ; ξ + γ n ; ξ d n 1 ; ξ with γ n ; ξ = g n ; ξ , g n ; ξ g n 1 ; ξ Ω g n 1 ; ξ Ω 2 ,
g n ; ξ = 2 ξ n 1 Re [ W Ω l = 1 N p = 1 P E ˜ l , p , n 1 ( A p Ω ) h l , p , n 1 ( 1 ) W Γ l = 1 N p = 1 P E ˜ l , p , n 1 ( B p Γ ) h l , p , n 1 ( 2 ) ] ,
v l , p , n = g l , p , n ; E l , p + γ l , p , n ; E l , p v l , p , n 1 ,
γ l , p , n ; E l , p = g l , p , n ; E l , p , g l , p , n ; E l , p g l , p , n 1 ; E l , p Ω g l , p , n 1 ; E l , p Ω 2 ,
g l , p , n ; E l , p = W Ω [ h l , p , n 1 ( 1 ) χ ¯ n 1 ( A p Ω ) h l , p , n 1 ( 1 ) ] W Γ χ ¯ n 1 ( B p Γ ) h l , p , n 1 ( 2 ) .
Err Ep = l | E l , p synth E l , p exp | Γ l | E l , p synth | Γ ,
Err χ = χ actual χ retrieved Ω χ actual Ω .

Metrics