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

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 2 — Feb. 1, 2008
  • pp: 292–303

Illustration of the role of multiple scattering in subwavelength imaging from far-field measurements

Francesco Simonetti, Matthew Fleming, and Edwin A. Marengo  »View Author Affiliations


JOSA A, Vol. 25, Issue 2, pp. 292-303 (2008)
http://dx.doi.org/10.1364/JOSAA.25.000292


View Full Text Article

Enhanced HTML    Acrobat PDF (610 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Recently it has been proposed that the classical diffraction limit could be overcome by taking into account multiple scattering effects to describe the interaction of a probing wave and the object to be imaged [ Phys. Rev. E 73, 036619 (2006) ]. Here this idea is illustrated by considering two point scatterers spaced much less than a wavelength apart. It is observed that while under the Born approximation the scattered field pattern is similar to that of a monopole source centered between the scatterers, multiple scattering leads to a more complicated pattern. This additional complexity carries information about the subwavelength structure and can lead to superresolution in the presence of large noise levels. Moreover, it is pointed out that the additional information due to multiple scattering is interpreted as a form of coherent noise by inversion algorithms based on the Born approximation.

© 2008 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(040.1240) Detectors : Arrays
(100.3010) Image processing : Image reconstruction techniques
(100.6640) Image processing : Superresolution
(290.4210) Scattering : Multiple scattering

ToC Category:
Image Processing

History
Original Manuscript: September 21, 2007
Revised Manuscript: November 20, 2007
Manuscript Accepted: November 21, 2007
Published: January 10, 2008

Virtual Issues
Vol. 3, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Francesco Simonetti, Matthew Fleming, and Edwin A. Marengo, "Illustration of the role of multiple scattering in subwavelength imaging from far-field measurements," J. Opt. Soc. Am. A 25, 292-303 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-2-292


Sort:  Year  |  Journal  |  Reset  

References

  1. E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Opt. Commun. 1, 153-156 (1969). [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  3. F. Simonetti, "Multiple scattering: The key to unravel the subwavelength world from the far-field pattern of a scattered wave," Phys. Rev. E 73, 036619-1 (2006). [CrossRef]
  4. T. J. Cui, W. C. Chew, X. X. Yin, and W. Hong, "Study of resolution and super resolution in electromagnetic imaging for half-space problems," IEEE Trans. Antennas Propag. 52, 1398-1411 (2004). [CrossRef]
  5. 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]
  6. F. C. Chen and W. C. Chew, "Experimental verifiction of super resolution in nonlinear inverse scattering," Appl. Phys. Lett. 72, 3080-3082 (1998). [CrossRef]
  7. F. Simonetti, "Localization of point-like scatterers in solids with subwavelength resolution," Appl. Phys. Lett. 89, 094105 (2006). [CrossRef]
  8. F. Simonetti, L. Huang, N. Duric, and O. Rama, "Imaging beyond the Born approximation: An experimental investigation with an ultrasonic ring array," Phys. Rev. E 76, 036601 (2007). [CrossRef]
  9. E. A. Marengo and F. K. Gruber, "Subspace-based localization and inverse scattering of multiply scattering point targets," EURASIP J. Adv. Sign. Processing 2007, ID 17324 16 pp. (Hindawi Pub. Corp., 2007).
  10. A. Sentenac, C. A. Guerin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, "Influence of multiple scattering on the resolution of an imaging system: a Cramér-Rao analysis," Opt. Express 15, 1340-1347 (2007). [CrossRef] [PubMed]
  11. F. Simonetti, "Reply to 'comment on "Multiple scattering: the key to unravel the subwavelength world from the far-field pattern of a scattered wave"'," Phys. Rev. E 75, 048602 (2007). [CrossRef]
  12. L. L. Foldy, "The multiple scattering of waves. i. general theory of isotropic scattering by randomly distributed scatterers," Phys. Rev. 67, 107-119 (1945). [CrossRef]
  13. D. Colton and R. Kress, "Using fundamental solutions in inverse scattering," Inverse Probl. 22, R49-66 (2006). [CrossRef]
  14. A. Kirsch, "Characterization of the shape of a scattering obstacle using the spectral data of the far field operator," Inverse Probl. 14, 1489-1512 (1998). [CrossRef]
  15. S. Hou, K. Solna, and H. Zhao, "A direct imaging algorithm for extended targets," Inverse Probl. 22, 1151-1178 (2006). [CrossRef]
  16. E. A. Marengo, F. K. Gruber, and F. Simonetti, "Time-reversal music imaging of extended targets," IEEE Trans. Image Process. 16, 1967-1984 (2007). [CrossRef] [PubMed]
  17. R. Potthast, Point Sources and Multipoles in Inverse Scattering Theory (Chapman & Hall / CRC, 2001). [CrossRef]
  18. J. Hadamard, Lectures on Cauchy's Problems in Linear Partial Differential Equations (Yale U. Press, 1923).
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  20. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty I," Bell Syst. Tech. J. 40, 43-63 (1961).
  21. C. K. Rushforth and R. W. Harris, "Restoration, resolution and noise," J. Opt. Soc. Am. 58, 539-545 (1968). [CrossRef]
  22. G. Toraldo Di Francia, "Degrees of freedom of an image," J. Opt. Soc. Am. 59, 799-804 (1969). [CrossRef] [PubMed]
  23. T. Habashy and E. Wolf, "Reconstruction of scattering potentials from incomplete data," J. Mod. Opt. 41, 1679-1685 (1994). [CrossRef]
  24. M. Bertero and P. Boccacci, "Super-resolution in computational imaging," Micron 34, 265-273 (2003). [CrossRef] [PubMed]
  25. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  26. V. Twersky, "Multiple scattering of waves and optical phenomena," J. Opt. Soc. Am. 52, 145-171 (1961). [CrossRef]
  27. M. Cheney and R. Bonneau, "Imaging that exploits multipath scattering from point scatterers," Inverse Probl. 20, 1691-1711 (2004). [CrossRef]
  28. I. Tolstoy, "Supreresonant systems of scatterers. i," J. Acoust. Soc. Am. 80, 282-294 (1986). [CrossRef]
  29. I. Tolstoy and A. Tolstoy, "Supreresonant systems of scatterers. ii," J. Acoust. Soc. Am. 83, 2086-2096 (1988). [CrossRef]
  30. E. J. Heller, "Quantum proximity resonance," Phys. Rev. Lett. 77, 4122-4125 (1996). [CrossRef] [PubMed]
  31. J. S. Hersch and E. J. Heller, "Observation of proximity resonances in a parallel-plate waveguide," Phys. Rev. Lett. 81, 3059-3062 (1998). [CrossRef]
  32. A. J. Devaney, "Super-resolution processing of multi-static data using time-reversal and music," unpublished; available at www.ece.neu.edu/faculty/devaney/ajd/preprints.htm (2000).
  33. H. Lev-Ari and A. J. Devaney, "The time-reversal technique re-interpreted: subspace-based signal processing for multi-static target location," in Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop (IEEE, 2000), pp. 509-513.
  34. F. K. Gruber, E. A. Marengo, and A. J. Devaney, "Time-reversal imaging with multiple signal classification considering multiple scattering between the targets," J. Acoust. Soc. Am. 115, 3042-3047 (2004). [CrossRef]
  35. G. Shi and A. Nehorai, "Maximum likelihood estimation of point scatterers for computational time-reversal imaging," Commun. Inf. Syst. 5, 227-256 (2005).
  36. M. Rusek, J. Mostowski, and A. Orlowski, "Random Green matrices: From proximity resonance to Anderson localization," Phys. Rev. A 61, 022704 (2000). [CrossRef]
  37. R. K. Snieder and J. A. Scales, "Time-reversed imaging as a diagnostic of wave and particle chaos," Phys. Rev. E 58, 5668-5675 (1998). [CrossRef]

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