Abstract

We analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity.

© 2004 Optical Society of America

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  1. Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
    [CrossRef]
  2. R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
    [CrossRef]
  3. X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
    [CrossRef]
  4. 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]
  5. A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1318 (2002).
    [CrossRef]
  6. N. Morita, “The boundary-element method,” in Analysis Methods for Electromagnetic Wave Problems, E. Yamashita, ed. (Artech House, Boston, Mass., 1990), pp. 33–77.
  7. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).
  8. E. Heyman, L. B. Felsen, “High frequency fields in the presence of a curved dielectric interface,” IEEE Trans. Antennas Propag. AP-32, 969–978 (1984).
    [CrossRef]
  9. K. H. Chan, H. L. Bertoni, “Ray representation of longitudinal lateral waves in acoustic microscopy,” IEEE Trans. Ultrason. Ferroel. Freq. Control 38, 27–34 (1991).
    [CrossRef]
  10. This hypothesis allows one to consider transmission inside the void negligible.
  11. A. Liseno, F. Soldovieri, R. Pierri, “Shape identification by physical optics: the two-dimensional TE case,” J. Opt. Soc. Am. A 20, 1827–1830 (2003).
    [CrossRef]
  12. R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
    [CrossRef]
  13. E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
    [CrossRef]
  14. S. Efromovich, V. Koltchinskii, “On inverse problems with unknown operators,” IEEE Trans. Inf. Theory 47, 2876–2894 (2001).
    [CrossRef]
  15. That is, the possibility of expressing the surface fields as space-varying functions having constant amplitude and linear phase, as far as the dependence on the frequency is concerned.
  16. D. M. McCann, M. C. Forde, “Review of NDT methods in the assessment of concrete and masonry structures,” Int. J. Nondestr. Test. 34, 71–84 (2001).
  17. A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).
  18. R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
    [CrossRef]
  19. A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

2004 (1)

A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).

2003 (3)

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
[CrossRef]

A. Liseno, F. Soldovieri, R. Pierri, “Shape identification by physical optics: the two-dimensional TE case,” J. Opt. Soc. Am. A 20, 1827–1830 (2003).
[CrossRef]

2002 (3)

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1318 (2002).
[CrossRef]

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

2001 (3)

S. Efromovich, V. Koltchinskii, “On inverse problems with unknown operators,” IEEE Trans. Inf. Theory 47, 2876–2894 (2001).
[CrossRef]

D. M. McCann, M. C. Forde, “Review of NDT methods in the assessment of concrete and masonry structures,” Int. J. Nondestr. Test. 34, 71–84 (2001).

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]

2000 (2)

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
[CrossRef]

1991 (1)

K. H. Chan, H. L. Bertoni, “Ray representation of longitudinal lateral waves in acoustic microscopy,” IEEE Trans. Ultrason. Ferroel. Freq. Control 38, 27–34 (1991).
[CrossRef]

1984 (1)

E. Heyman, L. B. Felsen, “High frequency fields in the presence of a curved dielectric interface,” IEEE Trans. Antennas Propag. AP-32, 969–978 (1984).
[CrossRef]

Balasubramanian, K.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Bertoni, H. L.

K. H. Chan, H. L. Bertoni, “Ray representation of longitudinal lateral waves in acoustic microscopy,” IEEE Trans. Ultrason. Ferroel. Freq. Control 38, 27–34 (1991).
[CrossRef]

Chan, K. H.

K. H. Chan, H. L. Bertoni, “Ray representation of longitudinal lateral waves in acoustic microscopy,” IEEE Trans. Ultrason. Ferroel. Freq. Control 38, 27–34 (1991).
[CrossRef]

Chapman, S. J.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Colella, N.

A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

De Blasio, F.

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

De Flaviis, F.

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

De Micheli, E.

E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
[CrossRef]

Efromovich, S.

S. Efromovich, V. Koltchinskii, “On inverse problems with unknown operators,” IEEE Trans. Inf. Theory 47, 2876–2894 (2001).
[CrossRef]

Felsen, L. B.

E. Heyman, L. B. Felsen, “High frequency fields in the presence of a curved dielectric interface,” IEEE Trans. Antennas Propag. AP-32, 969–978 (1984).
[CrossRef]

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

Feng, M. Q.

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

Forde, M. C.

D. M. McCann, M. C. Forde, “Review of NDT methods in the assessment of concrete and masonry structures,” Int. J. Nondestr. Test. 34, 71–84 (2001).

Hannemann, R.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Heyman, E.

E. Heyman, L. B. Felsen, “High frequency fields in the presence of a curved dielectric interface,” IEEE Trans. Antennas Propag. AP-32, 969–978 (1984).
[CrossRef]

Jofre, L.

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

Kim, Y. J.

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

King, J. R.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Koltchinskii, V.

S. Efromovich, V. Koltchinskii, “On inverse problems with unknown operators,” IEEE Trans. Inf. Theory 47, 2876–2894 (2001).
[CrossRef]

Krylov, T.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Langenberg, K. J.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Liseno, A.

A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).

A. Liseno, F. Soldovieri, R. Pierri, “Shape identification by physical optics: the two-dimensional TE case,” J. Opt. Soc. Am. A 20, 1827–1830 (2003).
[CrossRef]

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1318 (2002).
[CrossRef]

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

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]

A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

Marklein, R.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Mayer, K.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

McCann, D. M.

D. M. McCann, M. C. Forde, “Review of NDT methods in the assessment of concrete and masonry structures,” Int. J. Nondestr. Test. 34, 71–84 (2001).

Miller, E. L.

X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
[CrossRef]

Monti Bragadin, G.

E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
[CrossRef]

Morita, N.

N. Morita, “The boundary-element method,” in Analysis Methods for Electromagnetic Wave Problems, E. Yamashita, ed. (Artech House, Boston, Mass., 1990), pp. 33–77.

Ockendon, J. R.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Pierri, R.

A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).

A. Liseno, F. Soldovieri, R. Pierri, “Shape identification by physical optics: the two-dimensional TE case,” J. Opt. Soc. Am. A 20, 1827–1830 (2003).
[CrossRef]

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1318 (2002).
[CrossRef]

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

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]

A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

Rappaport, C. M.

X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
[CrossRef]

Schmitz, V.

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

Smith, B. J.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Soldovieri, F.

A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).

A. Liseno, F. Soldovieri, R. Pierri, “Shape identification by physical optics: the two-dimensional TE case,” J. Opt. Soc. Am. A 20, 1827–1830 (2003).
[CrossRef]

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

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]

A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

Tew, R. H.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Viano, G. A.

E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
[CrossRef]

Xu, X.

X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
[CrossRef]

Zafarullah, I.

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

AEÜ Int. J. Electron. Commun. (1)

A. Liseno, F. Soldovieri, R. Pierri, “Improving a shape reconstruction algorithm with thresholds and multi-view data,” AEÜ Int. J. Electron. Commun. 58, 118–124 (2004).

IEEE Trans. Antennas Propag. (3)

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]

Y. J. Kim, L. Jofre, F. De Flaviis, M. Q. Feng, “Microwave reflection tomography array for damage detection in concrete structures,” IEEE Trans. Antennas Propag. 51, 3022–3032 (2003).
[CrossRef]

E. Heyman, L. B. Felsen, “High frequency fields in the presence of a curved dielectric interface,” IEEE Trans. Antennas Propag. AP-32, 969–978 (1984).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

R. Pierri, F. Soldovieri, A. Liseno, F. De Blasio, “Dielectric profiles reconstruction via the quadratic approach in 2-d geometry from multifrequency and multifrequency/multiview data,” IEEE Trans. Geosci. Remote Sens. 40, 2709–2718 (2002).
[CrossRef]

X. Xu, E. L. Miller, C. M. Rappaport, “Minimum entropy regularization in frequency-wave number migration to localize subsurface objects,” IEEE Trans. Geosci. Remote Sens. 41, 1804–1812 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (1)

S. Efromovich, V. Koltchinskii, “On inverse problems with unknown operators,” IEEE Trans. Inf. Theory 47, 2876–2894 (2001).
[CrossRef]

IEEE Trans. Ultrason. Ferroel. Freq. Control (1)

K. H. Chan, H. L. Bertoni, “Ray representation of longitudinal lateral waves in acoustic microscopy,” IEEE Trans. Ultrason. Ferroel. Freq. Control 38, 27–34 (1991).
[CrossRef]

Int. J. Nondestr. Test. (1)

D. M. McCann, M. C. Forde, “Review of NDT methods in the assessment of concrete and masonry structures,” Int. J. Nondestr. Test. 34, 71–84 (2001).

Inverse Probl. (1)

R. Marklein, K. Mayer, R. Hannemann, T. Krylov, K. Balasubramanian, K. J. Langenberg, V. Schmitz, “Linear and nonlinear inversion algorithms applied in nondestructive testing,” Inverse Probl. 18, 1733–1759 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Rev. Math. Phys. (1)

E. De Micheli, G. Monti Bragadin, G. A. Viano, “Riemannian geometrical optics: surface waves in diffractive scattering,” Rev. Math. Phys. 12, 849–872 (2000).
[CrossRef]

Wave Motion (1)

R. H. Tew, S. J. Chapman, J. R. King, J. R. Ockendon, B. J. Smith, I. Zafarullah, “Scalar wave diffraction by tangent rays,” Wave Motion 32, 363–380 (2000).
[CrossRef]

Other (5)

That is, the possibility of expressing the surface fields as space-varying functions having constant amplitude and linear phase, as far as the dependence on the frequency is concerned.

A. Liseno, N. Colella, F. Soldovieri, R. Pierri, “Linear distribution-based retrieval of underground voids,” in Proceedings of IEEE Geoscience and Remote Sensing Symposium (Institute of Electrical and Electronics Engineers, New York, 2003), CD-ROM.

N. Morita, “The boundary-element method,” in Analysis Methods for Electromagnetic Wave Problems, E. Yamashita, ed. (Artech House, Boston, Mass., 1990), pp. 33–77.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (IEEE Press, Piscataway, N.J., 1994).

This hypothesis allows one to consider transmission inside the void negligible.

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Figures (13)

Fig. 1
Fig. 1

Diagram of the geometry of the problem.

Fig. 2
Fig. 2

Illustration of the lateral waves for the half-space case.

Fig. 3
Fig. 3

Illustration of the lateral waves for the circular cylindrical case. Sensor A receives a specular reflected ray. Sensor B receives the specular ray reflected at the critical angle. Sensor C receives a lateral ray.

Fig. 4
Fig. 4

Illustration of the points of refraction of a lateral wave for the cylindrical case.

Fig. 5
Fig. 5

Tangential component of the total electric field over a circular void: comparison of its unwrapped phase and that of the PO field arg[exp(-jk cos θ)]. Solid lines, Eτ(θ); dashed lines, arg[exp(-jk cos θ)]. θ=180°, 180°-35°, and 180°-45° from top to bottom.

Fig. 6
Fig. 6

Tangential component of the total magnetic field on a circular void: comparison of its unwrapped phase and that of the PO field arg[exp(-jk cos θ)]. Solid lines, H(θ); dashed lines, arg[exp(-jk cos θ)]. θ=180°, 180°-35°, and 180°-45° from top to bottom.

Fig. 7
Fig. 7

Amplitude of the tangential component Eτ(θ) of the total electric field over a circular void. θ=180°, 180°-35°, and 180°-45° from top to bottom.

Fig. 8
Fig. 8

Amplitude of the tangential component H(θ) of the total electric field over a circular void. θ=180°, 180°-35°, and 180°-45° from top to bottom.

Fig. 9
Fig. 9

Reconstruction of a circular void for a background relative permittivity b=9. Dotted circle, actual contour.

Fig. 10
Fig. 10

Reconstruction of two circular voids for a background relative permittivity b=9. Dotted circles, actual contours.

Fig. 11
Fig. 11

Reconstruction of a circular void for a background relative permittivity b=3. Dotted circle, actual contour.

Fig. 12
Fig. 12

Reconstruction of a circular void for a background relative permittivity b=15. Dotted circle, actual contour.

Fig. 13
Fig. 13

Reconstruction of circular perfect conductor. Dotted circle, actual contour.

Tables (1)

Tables Icon

Table 1 Summary of Direct Simulations for Different Values of

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Hs(r)=ΓH(r) Gn (r, r)+jωG(r, r)Eτ(r)dΓ,
OδΓ(r)ϕ(r)dO=Γϕ(r)dΓ,ϕcontinuous,
Hs(r)=O{V  G(r, r)+jωG(r, r)W(r)}dO,
H(r)[1+ΓH(r)]exp(-jki r)U(-nˆ  k^i),
Eτ(r)[1+ΓE(r)]ζ(nˆ  k^i)×exp(-jki r)U(-nˆ  k^i),
Hs(u, v)O [(k^i  n^)fE(r)-(kˆ  n^)fH(r)]δΓ(r)U(-n^  k^i)×exp[-j(ux+vy)]dr,
Hs(u, v)O [(k^i  n^)fE(r)-fH(r)]×δΓ(r)U(-n^  k^i)×exp[-j(ux+vy)]dr,
Ni(r)=[(k^i  nˆ)fE(r)-fH(r)]δΓ(r)U(-nˆ  k^i)
ulw(l)ui(l)pDpexp(-jlμp/a)ka2-1/6w1(μ¯p),
μpka+ξpka21/3+j n2n2-1,
H(r)gH(r)exp(-jki r)U(-nˆ  k^i),
Eτ(r)gE(r)exp(-jki r)U(-nˆ  k^i).
Ψ:θ(90°, 270°)Ψ(θ)=a(cos θ, sin θ)R2.
ΔF=Σkm|Fm(θ)-F¯(θ)|2Σkm|Fm(θ)|21/2,

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