Image Processing Reference
In-Depth Information
defining its actual diameter. On the right we see, to the same scale, an image
of a weaker object (permittivity = 1.1) for which the Born approximation is not
good, but not necessarily that bad either. The detrimental effect on the qual-
ity of the reconstructed image is evident by the degree to which the periodic
features arise in the image. This degradation is due to the data truncation
in k -space. As the permittivity of the cylinder increases, we pass through a
series of resonances and for each of these, there is a strong field enhance-
ment inside the cylinder and the measured scattered field in the far field will
reflect this. We see that for those situations, the Born reconstructions are quite
good. This is evident by matching the ε r for maximum scattering in Figures
6.3 and 6.4 with the corresponding reconstructions shown in Tables 6.11 and
6.12, respectively. What is worth noting about these sets of reconstructions is
to see how, at resonance, the far-field measurements seemingly correspond
to a relatively weak scatterer but with a larger diameter. Consider for exam-
ple the reconstructions in Table 6.12 for ε r = 1.4 compared with ε r = 2.1; both
appear reasonably uniform inside the cylinder but neither of them is the cor-
rect diameter. Not unsurprisingly, the relative distortion (increase) in size is
proportional to the increased radar cross section. The problem of nonscatter-
ing and scattering structures and the so-called “bound states” that can store
energy in a scattering object at certain frequencies has long been recognized
as an inherent ambiguity or lack of uniqueness one must accept in inverse
scattering problems. Of course, changing the frequency of illumination can
resolve such ambiguities but not entirely since the material properties such as
permittivity will be wavelength-dependent.
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