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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 10 — Oct. 1, 1999
  • pp: 2392–2399

Information content of the Born field scattered by an embedded slab: multifrequency, multiview, and multifrequency–multiview cases

Rocco Pierri, Raffaele Persico, and Romeo Bernini  »View Author Affiliations

JOSA A, Vol. 16, Issue 10, pp. 2392-2399 (1999)

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The information content of the scattered field in the framework of the linear Born and distorted Born approximations for a one-dimensional lossless dielectric permittivity profile embedded in a lossless homogeneous half-space is analyzed. The number of degrees of freedom of the scattered field and the class of the retrievable profiles from a multifrequency, a multiview, and a multifrequency–multiview configuration are evaluated by analytical considerations and validated by numerical singular-value decomposition. The analysis stresses the effects of the background permittivity value on the degrees of freedom and on the class of retrievable profiles within the distorted Born approximation. In particular, the results show that, for high values of the half-space permittivity, the information content in the multiview approach at a fixed frequency becomes too poor to yield effective reconstructions, whereas a suitable multifrequency or multifrequency–multiview approach can provide better results.

© 1999 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(290.3200) Scattering : Inverse scattering

Original Manuscript: February 16, 1999
Revised Manuscript: May 6, 1999
Manuscript Accepted: May 6, 1999
Published: October 1, 1999

Rocco Pierri, Raffaele Persico, and Romeo Bernini, "Information content of the Born field scattered by an embedded slab: multifrequency, multiview, and multifrequency–multiview cases," J. Opt. Soc. Am. A 16, 2392-2399 (1999)

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  1. D. Lesselier, B. Duchene, “Wavefield inversion of objects in stratified environments: from back-propagation schemes to full solutions,” in Review of Radio Science 1993–1996, R. Stone, ed. (Oxford U. Press, New York, 1996), pp. 235–268.
  2. R. Pierri, G. Leone, R. Bernini, R. Persico, “Tomografic inversion algorithms for permittivity reconstruction in subsurface prospection,” (presented at the 7th International Conference on Ground-Penetrating Radar, Lawrence, Kans., May 27–30, 1998.
  3. A. V. Tikhonravov, M. V. Klibanov, I. V. Zuev, “Numerical study of the phaseless inverse scattering problem in thin-film optics,” Inverse Probl. 11, 251–270 (1995). [CrossRef]
  4. D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
  5. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, New York, 1995).
  6. R. Pierri, A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997). [CrossRef]
  7. I. Akduman, M. Idemen, “On the use of Gaussian beams in one-dimensional profile inversion connected with lossy dielectric slabs,” Inverse Probl. 11, 315–328 (1995). [CrossRef]
  8. T. J. Cui, C. H. Liang, “Direct profile inversion for a half-space weakly lossy medium,” J. Opt. Soc. Am. A 10, 1950–1952 (1993). [CrossRef]
  9. M. A. Fiddy, “Linearized and approximate methods for inversion of scattered field data,” in Inverse Problems in Scattering and Imaging, M. Bertero, E. R. Pike, eds. (Hilger, Bristol, UK, 1992), pp. 23–46.
  10. T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995). [CrossRef]
  11. G. Leone, R. Persico, R. Pierri, “Inverse scattering under the distorted Born approximation for cylindrical geometries,” J. Opt. Soc. Am. A 16, 1779–1787 (1999). [CrossRef]
  12. L. Zeni, R. Bernini, R. Pierri, “Reconstruction of doping profiles in semiconductor materials using optical tomography,” Solid-State Electron. 43, 761–769 (1999). [CrossRef]
  13. T. A. Dickens, G. A. Winbow, “Spatial resolution of diffraction tomography,” J. Acoust. Soc. Am. 101, 77–86 (1997). [CrossRef]
  14. P. M. Van Den Berg, R. E. Kleinman, “Gradient methods in inverse acoustic and electromagnetic scattering,” in Large-Scale Optimization with Applications, L. T. Bigler, T. F. Coleman, A. R. Conn, F. N. Santosa, eds. (Springer-Verlag, New York, 1997), Part I, pp. 173–194.
  15. A. G. Tijhuis, “Born-type reconstruction of material parameters of an inhomogeneous lossy dielectric slab from reflected-field data,” Wave Motion 11, 151–173 (1989). [CrossRef]
  16. M. Bertero, “Linear inverse and ill-posed problems,” in Advances in Electronics and Electronic Physics, P. H. Hawkes, ed. (Academic, New York, 1989), Vol. 75, pp. 1–121.
  17. M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984). [CrossRef]
  18. B. Chen, J. J Stamnes, “Validity of diffraction tomography based on the first Born and first Rytov approximations,” Appl. Opt. 37, 2996–3006 (1998). [CrossRef]
  19. A. Brancaccio, G. Leone, R. Pierri, “Information content of Born scattered fields: results in the circular cylindrical case,” J. Opt. Soc. Am. A 15, 1909–1917 (1998). [CrossRef]
  20. A. J. Devaney, “Current research topics in diffraction tomography,” in Inverse Problems in Scattering and Imaging, M. Bertero, E. R. Pike, eds. (Hilger, Bristol, UK, 1992), pp. 47–58.
  21. M. Idemen, “On different possibilities offered by the Born approximation in inverse scattering problems,” Inverse Probl. 5, 1057–1074 (1989). [CrossRef]
  22. G. Toraldo di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. A 59, 799–804 (1969). [CrossRef]
  23. M. Bertero, G. A. Viano, F. Pasqualetti, L. Ronchi, G. Toraldo di Francia, “The inverse scattering problem in the Born approximation and the number of degrees of freedom,” Opt. Acta 27, 1011–1024 (1980). [CrossRef]
  24. R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998). [CrossRef]
  25. A. G. Tijhuis, Electromagnetic Inverse Profiling: Theory and Numerical Implementation (VNU Science, Utrecht, The Netherlands, 1987).
  26. H. J. Landau, “Sampling, data transmission, and the Nyquist rate,” Proc. IEEE 55, 1701–1706 (1967). [CrossRef]
  27. D. Slepian, H. O. Pollack, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty. I,” Bell Syst. Tech. J. 40, 43–64 (1961). [CrossRef]
  28. H. J. Landau, H. O. Pollack, “Prolate spheroidal wavefunctions, Fourier analysis and uncertainty. III. The dimension of the space of time- and band-limited signals,” Bell Syst. Tech. J. 41, 1295–1336 (1962). [CrossRef]
  29. L. Landau, E. Lifchitz, Electrodynamique des Milieux Continus (Mir, Moscow, 1969).
  30. R. Pierri, F. De Blasio, A. Brancaccio, “Multifrequency approach to inverse scattering: the linear and the quadratic models,” presented at the International Geoscience and Remote Sensing Symposium, Hamburg, Germany, June 28–July 2, 1999.

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