Abstract

A method is provided for reconstruction of the shape of perfectly conducting objects in a homogeneous space starting from knowledge of the scattered far field under the incidence of TE-polarized plane waves. The Kirchhoff model of scattering permits linearization of the inverse problem, which is further simplified by adopting an asymptotic approximation. Thus the problem is tackled with an approach based on singular-value decomposition already developed for the TM case.

© 2003 Optical Society of America

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References

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  1. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK, 1998).
  2. N. Bleistein, “Physical optics far field inverse scattering in the time domain,” J. Acoust. Soc. Am. 60, 1259–1264 (1976).
    [CrossRef]
  3. K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).
  4. Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).
  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, 1308–1319 (2002).
    [CrossRef]
  6. V. S. Vladimirov, Generalized Functions in the Mathematical Physics (Mir, Moscow, 1997).
  7. J. Van Bladel, Singular Electromagnetic Fields and Sources (Wiley–IEEE Press, New York, 1996).
  8. 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]
  9. A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (2002).
    [CrossRef]
  10. N. Morita, “The boundary-element method,” in Analysis Methods for Electromagnetic Wave Problems, E. Yamashita, ed. (Artech House, Boston, 1990), pp. 33–77.
  11. D. S. Jones, Methods in Electromagnetic Wave Propagation, 2nd ed. (Wiley, New York, 1995).

2002 (2)

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1319 (2002).
[CrossRef]

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (2002).
[CrossRef]

2001 (1)

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]

1999 (1)

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

1997 (1)

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

1976 (1)

N. Bleistein, “Physical optics far field inverse scattering in the time domain,” J. Acoust. Soc. Am. 60, 1259–1264 (1976).
[CrossRef]

Bärmann, R.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Bertero, M.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK, 1998).

Bleistein, N.

N. Bleistein, “Physical optics far field inverse scattering in the time domain,” J. Acoust. Soc. Am. 60, 1259–1264 (1976).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK, 1998).

Brancaccio, A.

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (2002).
[CrossRef]

Brandfass, M.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Chen, K. M.

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

Dai, Y.

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

Irmer, S.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Jones, D. S.

D. S. Jones, Methods in Electromagnetic Wave Propagation, 2nd ed. (Wiley, New York, 1995).

Langenberg, K. J.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Leone, G.

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (2002).
[CrossRef]

Liseno, A.

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1319 (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]

Marklein, R.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Morita, N.

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

Müller, H.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Nyquist, D. P.

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

Pierri, R.

A. Liseno, R. Pierri, “Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity,” J. Opt. Soc. Am. A 19, 1308–1319 (2002).
[CrossRef]

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (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]

Potzkai, B.

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Rothwell, E. J.

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

Soldovieri, F.

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (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]

Van Bladel, J.

J. Van Bladel, Singular Electromagnetic Fields and Sources (Wiley–IEEE Press, New York, 1996).

Vladimirov, V. S.

V. S. Vladimirov, Generalized Functions in the Mathematical Physics (Mir, Moscow, 1997).

IEEE Trans. Antennas Propag. (2)

Y. Dai, E. J. Rothwell, K. M. Chen, D. P. Nyquist, “Time-domain imaging of radar targets using sinogram restoration for limited-view restoration,” IEEE Trans. Antennas Propag. AP-47, 1323–1329 (1999).

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]

IEEE Trans. Geosci. Remote Sens. (1)

A. Brancaccio, G. Leone, R. Pierri, F. Soldovieri, “Experimental validation of a PO-based shape reconstruction algorithm,” IEEE Trans. Geosci. Remote Sens. 40, 2093–2099 (2002).
[CrossRef]

J. Acoust. Soc. Am. (1)

N. Bleistein, “Physical optics far field inverse scattering in the time domain,” J. Acoust. Soc. Am. 60, 1259–1264 (1976).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nondestr. Test. Eval. (1)

K. J. Langenberg, R. Bärmann, R. Marklein, S. Irmer, H. Müller, M. Brandfass, B. Potzkai, “Electromagnetic and elastic wave scattering and inverse scattering applied to concrete,” Nondestr. Test. Eval. 30, 205–210 (1997).

Other (5)

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK, 1998).

V. S. Vladimirov, Generalized Functions in the Mathematical Physics (Mir, Moscow, 1997).

J. Van Bladel, Singular Electromagnetic Fields and Sources (Wiley–IEEE Press, New York, 1996).

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

D. S. Jones, Methods in Electromagnetic Wave Propagation, 2nd ed. (Wiley, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

Pictorial view of the geometry of the problem.

Fig. 2
Fig. 2

Specular reflection.

Fig. 3
Fig. 3

Reconstruction of a perfectly conducting circular cylinder from only TE data; SNR=10 dB; dotted curve, actual contour.

Equations (19)

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

Hs(r_)=ΓGn (k0R)J(r_)dΓ,
J(r_)=2Hi(r_)+2ΓJ(r_) Gn (k0R)dΓ.
Oϕ(r_)δΓ(r_)dO=Γϕ(r_)dΓ.
Hs(r_)=OJ_G(k0R)dO,
J_=2N_Hi(r_)+2N_OJ_G(k0R)dO,
Hs=AeTE[J_],
J_=2N_Hi+A_iTE[N_, J_],
Hs(k0, θ)=OJ_τ^rexp[jk0rcos(θ-θ)]dO,
JPO=2HionΓi0onΓs,
JPO=2 exp(-jk0x)U(-nx),
Hs(u, v)=O(Dxcos θ+Dysin θ)×exp[-j(ux+vy)]dO,
Hs=cos θ A[Dx]+sin θ A[Dy],
Hs(u, v)=Γinˆτ^rexp[-j(ux+vy)]dΓi.
Ψ_ : t(t0, t1)Ψ_(t)=amax[Ψx(t), Ψy(t)]R2.
Hs(k0, θ)=t0t1nˆτ^rexp{-jk0amax×[(1-cos θ)Ψx(t)-sin θΨy(t)]}dt.
Ψx(t)(1-cos θ)-Ψy(t)sin θ=0.
τˆbˆ=0,
-sinθ2, cosθ2=-cosπ-θ2, -sinπ-θ2
Hs(u, v)-ODxexp[-j(ux+vy)]dO.

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