Image Processing Reference

In-Depth Information

(a)

(b)

60 mm

20 mm

80 mm

ε
r
= 1.45

ε
r
= 1.45

ε
r
= 3

ε
r
= 3

30 mm

30 mm

(c)

(d)

20 mm

60 mm

80 mm

ε
r
= 1.45

ε
r
= 3

ε
r
= 3

ε
r
= 1.45

Metal

30 mm

30 mm

28.5 mm

Figure 9.9
Shape and relative permittivity of Institut Fresnel targets: (a) FoamDielInt, (b) FoamDielExt, (c)

FoamTwinDiel, and (d) FoamMetExt.

the scattered field by subtracting the complex incident field from the complex

total field The inverse Fourier transform of the scattered field data gives a first

Born approximation reconstruction.

9.2.1 FoamdielInt

The FoamDielInt consists of two cylinders: a “foam” of relative permittivity

ε
r
≈ 1.45 and inside the “foam” there is another circular dielectric of relative

permittivity ε
r
≈ 3.0. Figure 9.8 shows the reconstruction from the inverse

Fourier transform of scattered field data, that is, the first Born reconstruction

of FoamDielInt. The Born reconstruction is computed at 6 GHz operating fre-

quency for which the scattering strength of the object is |
kVa
| ≈ 22. The object

represents a fairly strong scatterer, |
kVa
| ≫ 1, as a result of which we see that

the first Born reconstruction is not all that good.

Figure 9.10b shows the reconstructed image of FoamDielInt using the Born

approximation method. The reconstruction shows several undesirable arti-

facts and it also fails to give any meaningful (i.e., quantitative) values for

relative permittivity. The homomorphic filtering method was then applied to

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