Abstract

An inverse scattering approach based on the field equivalence principle is developed for reconstructing the parameters of the medium of a scattering object. A problem equivalent to the original scattering problem but internal to the measurement surface is set up. The equivalent surface currents determined by the measured total-field data rigorously yield the incident fields in the region under test, so the approach does not require explicit knowledge of the incident fields. Taking into account the fact that the equivalent surface currents produce a null field external to the surface, a functional of the medium’s parameters is introduced, and a genetic algorithm is applied to minimization of the functional. Numerical simulations for imaging defects in a known dielectric cylinder from only total-field data measured on an observation surface are performed to illustrate the efficacy of the proposed inversion method.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

2011

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
[CrossRef]

T. Moriyama, Z.-Q. Meng, and T. Takenaka, Microwave Opt. Technol. Lett. 53, 438 (2011).
[CrossRef]

2010

2009

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

2008

M. D’Urso, K. Belkebir, L. Crocco, T. Isernia, and A. Litman, J. Opt. Soc. Am. A 25, 271 (2008).
[CrossRef]

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

2007

2003

2000

M. Gustafsson and S. He, Radio Sci. 35, 525 (2000).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, IEEE Trans. Microwave Theory Tech. 48, 1815 (2000).
[CrossRef]

1997

A. Franchois and C. Pichot, IEEE Trans. Antennas Propag. 45, 203 (1997).
[CrossRef]

T. Isernia, V. Pascazio, and R. Pierri, IEEE Trans. Geosci. Remote Sens. 35, 910 (1997).
[CrossRef]

1996

S. He, P. Fuks, and G. W. Larson, IEEE Trans. Antennas Propag. 44, 1277 (1996).
[CrossRef]

1995

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

1993

M. Moghaddam and W. C. Chew, IEEE Trans. Antennas Propag. 41, 177 (1993).
[CrossRef]

1990

W. C. Chew and Y. M. Wang, IEEE Trans. Med. Imaging 9, 218 (1990).
[CrossRef]

Belkebir, K.

Benedetti, M.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

Caorsi, S.

S. Caorsi, A. Massa, and M. Pastorino, IEEE Trans. Microwave Theory Tech. 48, 1815 (2000).
[CrossRef]

Chen, K.-C.

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

Chen, X.

Chew, W. C.

M. Moghaddam and W. C. Chew, IEEE Trans. Antennas Propag. 41, 177 (1993).
[CrossRef]

W. C. Chew and Y. M. Wang, IEEE Trans. Med. Imaging 9, 218 (1990).
[CrossRef]

Chiu, C.-C.

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

Crocco, L.

D’Urso, M.

Donelli, M.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

Franceschini, D.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

Franchois, A.

A. Franchois and C. Pichot, IEEE Trans. Antennas Propag. 45, 203 (1997).
[CrossRef]

Fuks, P.

S. He, P. Fuks, and G. W. Larson, IEEE Trans. Antennas Propag. 44, 1277 (1996).
[CrossRef]

Gustafsson, M.

M. Gustafsson and S. He, Radio Sci. 35, 525 (2000).
[CrossRef]

Harada, T.

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields, 2nd ed. (Wiley, 2001).

He, S.

M. Gustafsson and S. He, Radio Sci. 35, 525 (2000).
[CrossRef]

S. He, P. Fuks, and G. W. Larson, IEEE Trans. Antennas Propag. 44, 1277 (1996).
[CrossRef]

Huang, C.-H.

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

Isernia, T.

Larson, G. W.

S. He, P. Fuks, and G. W. Larson, IEEE Trans. Antennas Propag. 44, 1277 (1996).
[CrossRef]

Li, C.-L.

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

Litman, A.

Massa, A.

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, IEEE Trans. Microwave Theory Tech. 48, 1815 (2000).
[CrossRef]

Meng, Z.-Q.

T. Moriyama, Z.-Q. Meng, and T. Takenaka, Microwave Opt. Technol. Lett. 53, 438 (2011).
[CrossRef]

Moghaddam, M.

M. Moghaddam and W. C. Chew, IEEE Trans. Antennas Propag. 41, 177 (1993).
[CrossRef]

Moriyama, T.

T. Moriyama, Z.-Q. Meng, and T. Takenaka, Microwave Opt. Technol. Lett. 53, 438 (2011).
[CrossRef]

Oliveri, G.

Pan, L.

Pascazio, V.

T. Isernia, V. Pascazio, and R. Pierri, IEEE Trans. Geosci. Remote Sens. 35, 910 (1997).
[CrossRef]

Pastorino, M.

S. Caorsi, A. Massa, and M. Pastorino, IEEE Trans. Microwave Theory Tech. 48, 1815 (2000).
[CrossRef]

M. Pastorino, Microwave Imaging (Wiley, 2010).

Pichot, C.

A. Franchois and C. Pichot, IEEE Trans. Antennas Propag. 45, 203 (1997).
[CrossRef]

Pierri, R.

T. Isernia, V. Pascazio, and R. Pierri, IEEE Trans. Geosci. Remote Sens. 35, 910 (1997).
[CrossRef]

Rekanos, I. T.

I. T. Rekanos, J. Electromagn. Waves Appl. 17, 271 (2003).
[CrossRef]

Rocca, P.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

Takenaka, T.

T. Moriyama, Z.-Q. Meng, and T. Takenaka, Microwave Opt. Technol. Lett. 53, 438 (2011).
[CrossRef]

T. Takenaka, H. Zhou, and T. Tanaka, J. Opt. Soc. Am. A 20, 1867 (2003).
[CrossRef]

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

Tanaka, T.

T. Takenaka, H. Zhou, and T. Tanaka, J. Opt. Soc. Am. A 20, 1867 (2003).
[CrossRef]

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

Wall, D. J. N.

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

Wang, Y. M.

W. C. Chew and Y. M. Wang, IEEE Trans. Med. Imaging 9, 218 (1990).
[CrossRef]

Yeo, S. P.

Zhong, Y.

Zhou, H.

IEEE Trans. Antennas Propag.

T. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, IEEE Trans. Antennas Propag. 43, 784 (1995).
[CrossRef]

A. Franchois and C. Pichot, IEEE Trans. Antennas Propag. 45, 203 (1997).
[CrossRef]

M. Moghaddam and W. C. Chew, IEEE Trans. Antennas Propag. 41, 177 (1993).
[CrossRef]

S. He, P. Fuks, and G. W. Larson, IEEE Trans. Antennas Propag. 44, 1277 (1996).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

T. Isernia, V. Pascazio, and R. Pierri, IEEE Trans. Geosci. Remote Sens. 35, 910 (1997).
[CrossRef]

IEEE Trans. Med. Imaging

W. C. Chew and Y. M. Wang, IEEE Trans. Med. Imaging 9, 218 (1990).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. Caorsi, A. Massa, and M. Pastorino, IEEE Trans. Microwave Theory Tech. 48, 1815 (2000).
[CrossRef]

Inverse Probl.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 123003 (2009).
[CrossRef]

J. Electromagn. Waves Appl.

I. T. Rekanos, J. Electromagn. Waves Appl. 17, 271 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

T. Moriyama, Z.-Q. Meng, and T. Takenaka, Microwave Opt. Technol. Lett. 53, 438 (2011).
[CrossRef]

Opt. Express

Prog. Electromagn. Res.

C.-H. Huang, C.-C. Chiu, C.-L. Li, and K.-C. Chen, Prog. Electromagn. Res. 82, 381 (2008).
[CrossRef]

Radio Sci.

M. Gustafsson and S. He, Radio Sci. 35, 525 (2000).
[CrossRef]

Other

R. F. Harrington, Time-Harmonic Electromagnetic Fields, 2nd ed. (Wiley, 2001).

M. Pastorino, Microwave Imaging (Wiley, 2010).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Original and (b) equivalent problems for the interior region Ω.

Fig. 2.
Fig. 2.

Detection of two defects in a square cylinder.

Equations (14)

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

Lv=j,
v=[Ex,Ey,Ez,ηHx,ηHy,ηHz]T,
j=[ηJx,ηJy,ηJz,0,0,0]T,
v(r,t)=0,t<0.
LA¯x+B¯y+C¯zF¯(ct)G¯,
F¯=[εrI¯00μrI¯],G¯=[ησI¯000],
Lv=s
u(r,t)=0,t<0,
u=[Exeq,Eyeq,Ezeq,ηHxeq,ηHyeq,ηHzeq]T,
s=[s1s2s3s4s5s6]=[nyηHznzηHynzηHxnxηHznxηHynyηHxnyEz+nzEynzEx+nxEznxEy+nyEx]δΩ,
u(r,t)={v(r,t),ifrΩ,0,ifrΩ¯.
Q(p)=n=1N0cTΩ¯|un(p;r,t)|2drd(ct),
jn=I(t)δ(rrn)z^,
I(t)=d3dt3exp[α2(tτ)2],

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