Abstract

We address an inverse scattering problem using only amplitude information of the scattered field. In particular, we are concerned with the reconstruction of the shape of a metallic planar obstacle, located in a known plane (aperture plane), starting from the knowledge of the intensity of the scattered field over two measurement planes in near zone and parallel to the aperture plane, when a single-frequency incident plane wave is exploited. The formulation of the inverse scattering problem is given under the physical optics approximation, and thus the resulting phase retrieval problem is quadratic. This allows us to apply some phase retrieval techniques already developed for antenna diagnostics. Reconstruction results with synthetic data indicate the feasibility of the proposed approach.

© 2008 Optical Society of America

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References

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    [CrossRef]
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2007

2005

2002

1999

R. Pierri, G. D'Elia, and F. Soldovieri, IEEE Trans. Antennas Propag. 47, 792 (1999).
[CrossRef]

1998

1996

G. Leone, R. Pierri, and F. Soldovieri, J. Opt. Soc. Am. A 13, 1546 (1996).
[CrossRef]

T. Isernia, G. Leone, and R. Pierri, IEEE Trans. Antennas Propag. 44, 701 (1996).
[CrossRef]

1992

A. J. Devaney, IEEE Trans. Image Process. 1, 221 (1992).
[CrossRef]

M. H. Maleki, A. J. Devaney, and A. Schatzberg, J. Opt. Soc. Am. A 10, 1356 (1992).
[CrossRef]

1986

1973

D. L. Misell, J. Phys. D 6, L6 (1973).
[CrossRef]

IEEE Trans. Antennas Propag.

R. Pierri, G. D'Elia, and F. Soldovieri, IEEE Trans. Antennas Propag. 47, 792 (1999).
[CrossRef]

T. Isernia, G. Leone, and R. Pierri, IEEE Trans. Antennas Propag. 44, 701 (1996).
[CrossRef]

F. Soldovieri, A. Liseno, G. D'Elia, and R. Pierri, IEEE Trans. Antennas Propag. 53, 3135 (2005).
[CrossRef]

IEEE Trans. Image Process.

A. J. Devaney, IEEE Trans. Image Process. 1, 221 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

D. L. Misell, J. Phys. D 6, L6 (1973).
[CrossRef]

Opt. Lett.

Other

D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, 1987).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetic Field (Wiley-IEEE, 1996).

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Figures (3)

Fig. 1
Fig. 1

Normalized amplitude of the reconstructed aperture field (decibels) compared with the shape of a metallic square plate (red or gray outline).

Fig. 2
Fig. 2

Normalized amplitude of the reconstructed “aperture field” (decibels) compared with the shape of the metallic square plate (outer red or gray outline) and the shape of the hole (inner green or light gray outline); noise-free data.

Fig. 3
Fig. 3

Same as in Fig. 2; noisy data.

Equations (11)

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E s ( r ¯ o ) = j ω μ 0 Γ G ͇ ( r ¯ o r ¯ ) J PO ( r ¯ ) d r ¯ ,
J PO ( x , y ) = 2 n ̂ × H i z = 0 = ( 2 ζ ) i ̂ z × E 0 i ̂ y = ( 2 ζ ) E 0 i ̂ x
E s ( r ¯ o ) = j ω μ 0 ( 2 ζ ) Γ G x x ( r ¯ o r ¯ ) E 0 d r .
E s ( x , y , z 1 ) = F d u d v v 2 + w 2 w exp [ j u x j v y j w z 1 ] × d x d y E 0 U Γ ( x , y ) exp [ j u x + j v y ] ,
U Γ ( x , y ) = { 1 for r ¯ = ( x , y ) Γ , 0 otherwise } ,
E s ( x , y , z i ) = L i E ̂ s = d u d v E ̂ s ( u , v ) exp [ j u x j v y j w z i ] ,
E ̂ s ( u , v ) = F v 2 + w 2 w d x d y E 0 U Γ ( x , y ) exp [ + j u x + j v y ] ,
( M 1 2 , M 2 2 ) = ( L 1 E ̂ s 2 , L 2 E ̂ s 2 ) .
Φ ( E ̂ s ) = L 1 E ̂ s 2 M ̃ 1 2 2 + L 2 E ̂ s 2 M ̃ 2 2 2 ,
E ̂ s ( u , v ) = n = N N m = M M E ̂ n n sin c ( a u n π ) sin c ( b v m π ) ,
Ψ ( E ̂ s ) = i , j ( L 1 E ̂ s i j 2 M ̃ 1 i j 2 ) 2 M ̃ 1 i j 2 + ( L 2 E ̂ s i j 2 M ̃ 2 i j 2 ) 2 M ̃ 2 i j 2 ,

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