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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 7 — Jul. 1, 2002
  • pp: 1308–1318

Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity

Angelo Liseno and Rocco Pierri  »View Author Affiliations

JOSA A, Vol. 19, Issue 7, pp. 1308-1318 (2002)

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The problem of determining the shape of perfectly conducting objects from knowledge of the scattered electric field is considered. The formulation of the problem accommodates the nature of the distribution of the induced surface current density. Thus, as the unknown representing the object’s contour, a single layer distribution is chosen so that the contour of the scatterer is described by its support. The nonlinear unknown-data mapping is then linearized by means of the Kirchhoff approximation, and the problem is recast as the inversion of a linear operator acting on a distribution space. An extension of the singular value decomposition approach to solve the linearized problem is provided and numerical results are presented.

© 2002 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: August 13, 2001
Revised Manuscript: January 3, 2002
Manuscript Accepted: January 3, 2002
Published: July 1, 2002

Angelo Liseno and Rocco Pierri, "Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity," J. Opt. Soc. Am. A 19, 1308-1318 (2002)

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  1. B. Borden, “Some issues in inverse synthetic aperture radar image reconstruction,” Inverse Probl. 13, 571–584 (1997). [CrossRef]
  2. A. Sullivan, R. Damarla, N. Geng, Y. Dong, L. Carin, “Ultrawide-band synthetic aperture radar for detection of unexploded ordnance: modeling and measurements,” IEEE Trans. Antennas Propag. 48, 1306–1315 (2000). [CrossRef]
  3. K. J. Langenberg, “Elastic wave inverse scattering as applied to nondestructive evaluation,” in Inverse Problems in Scattering and Imaging, M. Bertero, E. R. Pike eds. (Adam Hilger, Bristol, UK, 1992).
  4. R. Kress, “Numerical methods in inverse obstacle scattering,” Aust. New Zeal. Ind. Appl. Math. J. 42, C44–C67 (2000).
  5. A. Kirsch, “The domain derivative and two applications in inverse scattering theory,” Inverse Probl. 9, 81–96 (1993). [CrossRef]
  6. A. Qing, C. K. Lee, “Electromagnetic inverse scattering of two-dimensional perfectly conducting objects by real-coded genetic algorithm,” IEEE Trans. Geosci. Remote Sens. 39, 665–676 (2001). [CrossRef]
  7. R. D. Marger, N. Bleistein, “An examination of the limited aperture problem of physical optics inverse scattering,” IEEE Trans. Antennas Propag. AP-26, 695–699 (1979).
  8. K. J. Langenberg, M. Brandfass, P. Fellinger, T. Gurke, T. Kreutter, “A unified theory of multidimensional electromagnetic vector inverse scattering within the Kirchoff or Born approximation,” in Radar Target Imaging, W.-M. Boerner, H. Überall eds. (Springer-Verlag, Berlin, 1994).
  9. R. Pierri, A. Liseno, F. Soldovieri, “Shape reconstruction from PO multifrequency scattered fields via the singular value decomposition approach,” IEEE Trans. Antennas Propag. 49, 1333–1343 (2001). [CrossRef]
  10. Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view reconstruction,” IEEE Trans. Antennas Propag. 47, 1323–1329 (1999). [CrossRef]
  11. D. S. Jones, Methods in Electromagnetic Wave Propagation (Oxford U., Press, Oxford, UK, 1994).
  12. V. S. Vladimirov, Generalized Functions in the Mathematical Physics (Mir, Moscow, 1997).
  13. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK1998).
  14. The scattered electric field can be determined by decomposing the total electric field Eas E=Es+Ei,where Eiis the incident field, and by solving for Ethe Helmholtz equation with a Dirichlet boundary condition, which corresponds to perfectly conducting objects. Note that such boundary condition corresponds also to the case of acoustic soft scatterers.4
  15. N. Morita, “The boundary-element method,” in Analysis Methods for Electromagnetic Wave Problems, E. Yamashita ed. (Artech House, Boston, Mass.1990).
  16. L. Schwartz, Mathematics for the Physical Sciences (Addison-Wesley, New York, 1996).
  17. A. D. Yaghjian, T. B. Hansen, A. J. Devaney, “Minimum source region for a given far-field pattern,” IEEE Trans. Antennas Propag. 45, 911–912 (1997). [CrossRef]
  18. I. D. King, T. E. Hodgetts, “An approximate treatment of scattering based on the delta boundary operator technique,” IMA J. Appl. Math. 64, 139–155 (2000). [CrossRef]
  19. L. Kantorovich, G. Akilov, Functional Analysis (Pergamon, New York, 1982).
  20. D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
  21. R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, New York, 1961).
  22. E. Scalas, G. A. Viano, “Resolving power and information theory in signal recovery,” J. Opt. Soc. Am. A 10, 991–996 (1993). [CrossRef]
  23. R. Pierri, F. Soldovieri, “On the information content of the radiated fields in the near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998). [CrossRef]
  24. 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]
  25. R. Pierri, A. Liseno, F. Soldovieri, R. Solimene, “In-depth resolution for a strip source in the Fresnel zone,” J. Opt. Soc. Am. A 18, 352–359 (2001). [CrossRef]
  26. A. Liseno, R. Pierri, F. Soldovieri, “Depth resolving power in near zone: numerical results for a strip source,” Int. J. Electron. Commun. (AEÜ) 55, 100–108 (2001). [CrossRef]
  27. A†denotes the adjoint of A.
  28. N. Kolmogorov, S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, (Nauka, Moscow, 1981).

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