OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 9 — Sep. 1, 2005
  • pp: 1889–1897

Superresolution in total internal reflection tomography

Kamal Belkebir, Patrick C. Chaumet, and Anne Sentenac  »View Author Affiliations


JOSA A, Vol. 22, Issue 9, pp. 1889-1897 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001889


View Full Text Article

Acrobat PDF (340 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.

© 2005 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(180.6900) Microscopy : Three-dimensional microscopy
(290.3200) Scattering : Inverse scattering

Citation
Kamal Belkebir, Patrick C. Chaumet, and Anne Sentenac, "Superresolution in total internal reflection tomography," J. Opt. Soc. Am. A 22, 1889-1897 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-9-1889


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. M. Gustafsson, "Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy," J. Microsc. 198, 82-87 (2000).
  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).
  3. 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).
  4. T. Wedberg and J. Stammes, "Experimental examination of the quantitative imaging properties of optical diffraction tomography," J. Opt. Soc. Am. A 12, 493-500 (1995).
  5. D. Fischer, "Subwavelength depth resolution in near-field microscopy," Opt. Lett. 25, 1529-1531 (2000).
  6. P. So, H. Kwon, and C. Dong, "Resolution enhancement in standing-wave total-internal reflection microscopy: a point spread function engineering approach," J. Opt. Soc. Am. A 18, 2833-2845 (2001).
  7. F. de Fornel, Evanescent Waves, Vol. 73 of Springer Series in Optical Sciences (Springer Verlag, 2001).
  8. G. Cragg and P. So, "Standing wave total-internal reflection microscopy," Opt. Lett. 25, 46-48 (2000).
  9. P. S. Carney and J. C. Schotland, "Three-dimensional total-internal reflection microscopy," Opt. Lett. 26, 1072-1074 (2001).
  10. E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Opt. Commun. 1, 153-156 (1969).
  11. K. Belkebir and A. Sentenac, "High resolution optical diffraction microscopy," J. Opt. Soc. Am. A 20, 1223-1229 (2003).
  12. P. C. Chaumet, K. Belkebir, and A. Sentenac, "Superresolution of three-dimensional optical imaging by use of evanescent waves," Opt. Lett. 29, 2740-2742 (2004).
  13. E. M. Purcell and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J. 186, 705-714 (1973).
  14. P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
  15. A. Lakhtakia, "Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields," Int. J. Mod. Phys. C 3, 583-603 (1992).
  16. P. C. Chaumet, A. Sentenac, and A. Rahmani, "Coupled dipole method for scatterers with large permittivity," Phys. Rev. E 70, 036606 (2004). [CrossRef]
  17. S. Kawata, O. Nakamura, and S. Minami, "Optical microscope tomography. I. Support constraint," J. Opt. Soc. Am. A 4, 292-297 (1987).
  18. P. S. Carney and J. C. Schotland, "Theory of total-internal-reflection tomography," J. Opt. Soc. Am. A 20, 542-547 (2003).
  19. 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, 1316-1330 (2001).
  20. R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
  21. K. Belkebir and A. G. Tijhuis, "Modified2 gradient method and modified Born method for solving a two-dimensional inverse scattering problem," Inverse Probl. 17, 1671-1688 (2001).
  22. P. C. Chaumet, K. Belkebir, and A. Sentenac, "Three-dimensional subwavelength optical imaging using the coupled dipole method," Phys. Rev. B 69, 245405 (2004). [CrossRef]
  23. A. Abubakar, P. M. van den Berg, and B. J. Kooij, "A conjugate gradient contrast source technique for 3D profile inversion," IEICE Trans. Electron. E83-C, 1864-1874 (2000).
  24. A. Abubakar and P. M. van den Berg, "The contrast source inversion method for location and shape reconstructions," Inverse Probl. 18, 495-510 (2002).
  25. W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986).
  26. K. Belkebir, S. Bonnard, F. Pezin, P. Sabouroux, and M. Saillard, "Validation of 2D inverse scattering algorithms from multi-frequency experimental data," J. Electromagn. Waves Appl. 14, 1637-1667 (2000).
  27. K. Belkebir, R. E. Kleinman, and C. Pichot, "Microwave imaging--location and shape reconstruction from multifrequency scattering data," IEEE Trans. Microwave Theory Tech. 45, 469-476 (1997).
  28. R. E. Kleinman and P. M. van den Berg, "Two-dimensional location and shape reconstruction," Radio Sci. 29, 1157-1169 (1994).
  29. J. J. Goodman, B. T. Draine, and P. J. Flatau, "Application of fast-Fourier-transform techniques to the discrete-dipole approximation," Opt. Lett. 16, 1198-1200 (1991).
  30. F. Pincemin, A. Sentenac, and J.-J. Greffet, "Near-field scattered by a dielectric rod below a metallic surface," J. Opt. Soc. Am. A 11, 1117-1127 (1994).
  31. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  32. T. M. Habashy, R. W. Groom, and B. R. Spies, "Beyond the Born and Rytov approximations--a nonlinear approach to electromagnetic scattering," J. Geophys. Res. [Solid Earth] 98, 1759-1775 (1993).
  33. A. Rahmani, P. C. Chaumet, F. de Fornel, and C. Girard, "Field propagator of a dressed junction: fluorescence lifetime calculations in a confined geometry," Phys. Rev. A 56, 3245-3254 (1997).
  34. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited