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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 7 — Jul. 16, 2007

Numerical solution of inverse scattering for near-field optics

Gang Bao and Peijun Li  »View Author Affiliations


Optics Letters, Vol. 32, Issue 11, pp. 1465-1467 (2007)
http://dx.doi.org/10.1364/OL.32.001465


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Abstract

A novel regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium located on a substrate from data accessible through photon scanning tunneling microscopy experiments. Based on multiple frequency scattering data, the method starts from the Born approximation corresponding to weak scattering at a low frequency, and each update is obtained by continuation on the wavenumber from solutions of one forward problem and one adjoint problem of the Helmholtz equation.

© 2007 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(100.3190) Image processing : Inverse problems
(290.3200) Scattering : Inverse scattering

ToC Category:
Image Processing

History
Original Manuscript: February 28, 2007
Manuscript Accepted: March 21, 2007
Published: May 2, 2007

Virtual Issues
Vol. 2, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Gang Bao and Peijun Li, "Numerical solution of inverse scattering for near-field optics," Opt. Lett. 32, 1465-1467 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ol-32-11-1465


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References

  1. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, 1998).
  2. F. Natterer, The Mathematics of Computerized Tomography (Teubner, 1986).
  3. C. Giard and A. Dereux, Rep. Prog. Phys. 59, 657 (1996). [CrossRef]
  4. D. Courjon, Near-field Microscopy and Near-field Optics (Imperial College Press, 2003).
  5. D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989). [CrossRef]
  6. I. Akduman and A. Alkumru, Inverse Probl. 11, 1125 (1995). [CrossRef]
  7. P.-M. Cutzach and C. Hazard, Math. Models Meth. Appl. Sci. 21, 433 (1998).
  8. P. Carney and J. Schotland, J. Opt. A, Pure Appl. Opt. 4, s140 (2002). [CrossRef]
  9. G. Bao and P. Li, J. Comput. Math. 25, 10 (2007).
  10. Y. Chen, Inverse Probl. 13, 253 (1997). [CrossRef]
  11. G. Bao and P. Li, SIAM J. Appl. Math. 65, 2049 (2005). [CrossRef]
  12. G. Bao and J. Liu, SIAM J. Sci. Comput. (USA) 25, 1102 (2003). [CrossRef]
  13. J. Coyle, Inverse Probl. 16, 275 (2000). [CrossRef]
  14. F. Natterer, Inverse Probl. 20, 447 (2004). [CrossRef]
  15. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996). [CrossRef]
  16. E. Turkel and A. Yefet, Appl. Numer. Math. 27, 533 (1998). [CrossRef]

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