Applications to Real Measured Data - Introduction to Imaging from Scattered Fields - page 128

(a) (b)

300 300

2.8

3

250 250

2.6

2.8

2.4

200 200 2.6

2.2 2.4

150 150

2 2.2

100 100

2

1.8

50 50

1.8

1.6

1.6

0
0

0

50 100 150 200 250 300 0 50 100 150 200 250 300

(c) (d)

300 300

3

2.7

250 250

2.6
2.5
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7

2.5

200 200

150 150

2

100 100

50 50

1.5

0 0

0 50 100 150 200 250 300 0 50 100 150 200 250 300

Figure 9.13 Cepstral reconstruction of FoamDielInt at various frequencies: (a) 3 GHz, (b) 7 GHz, (c) 9 GHz,
and (d) 10 GHz.

for this. The first is that inversion at lower frequencies meets conditions that
increasingly favor the validity of the first Born approximation (i.e. | kVa | ≪ 1)
and for this scatterer at relatively lower frequencies, the sampling rate of the
scattered field is adequate. One might also speculate that at higher frequencies,
as the effective wavelength is reduced, there may be relatively more scatter-
ing from the boundary and less penetration of the field into the target, and so,
less scattering from the higher permittivity internal features. Another impor-
tant factor is that the angular sampling of the scattered field and the number
of incident field directions are identical for all frequencies employed. One

(a) (b)

1800
1600
1400
1200
1000
800
600
400
200

1800
1600
1400
1200
1000
800
600
400
200

-0.06 -0.06

-0.04 -0.04

-0.02
0

-0.02
0

0.02 0.02

0.04
0.06

0.04
0.06

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 -0.06 -0.04 -0.02 0 0.02 0.04 0.06

Figure 9.14 Point spread functions corresponding to the locus of k -space scattered field coverage for the
frequencies of (a) 3 GHz and (b) 10 GHz.