Image Processing Reference
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cross sections rather than their actual physical dimensions. Their actual sizes
can be deduced from size-sensitive estimation techniques like the PDFT that
was described in this topic. Another important observation regarding the res-
olution of the resulting image of a strongly scattering object should be made.
Since, as we described, sub-wavelength-sized scattering features in an object
can generate evanescent waves, the further scattering of these waves back in
to propagating waves can lead to subtle changes in far fields that are mea-
sured. It is not unusual to see apparent super-resolved features in the images
of strongly scattering objects for this reason.
Clearly much more needs to be done to advance the overall state of the art
in imaging from scattered fields The algorithm described here is a step in that
direction. It would be remiss not to end with another application of growing
importance for which this and related inverse scattering algorithms can be
very useful. If one has a method to recover an image of an index or permittivity
distribution from a sufficiently large number of scattered field measurements,
then one can apply the same steps to synthesize objects that may not exist. By
specifying scattered fields as a function of angle, wavelength, incident field
direction, etc., these fields can be inverted to create an object distribution that
can be used to design and create new objects and materials. Constraints on the
index modulation or form factor of the object can be imposed using a method
like the PDFT during the reconstruction (i.e., synthesis) step. We have applied
this approach with some success to the design of low observable objects and
object shape shifting covers. In other words, we can use the imaging method
described to design structures that are very difficult to image because they
scatter very little in selected directions, or scatter like some structure having
a different appearance.
Recent interest in engineered materials or meta-materials and their role in
the interaction of electromagnetic waves can benefit from the inverse meth-
ods presented here. For example, close to a strong resonance, a Mie resonance
associated with a relatively high Q situation, one can expect more extreme
effective values of refractive index (or permittivity or permeability). The first
and dominant Mie resonance for a dielectric particle is associated with a mag-
netic and not electrical resonance. This has led to recent increasing interest
by the meta-material community in getting rid of lossy metals in meta-materi-
als and achieving negative permeability and negative permittivity to achieve a
negative index just by using two different species of dielectric spheres in their
meta-materials. An interesting and important problem worth studying would
be to see if one could design an improved meta-material using inverse scatter-
ing methods based on these observations.
Miller, D. A. 2007. Fundamental limit for optical components. Journal of the
Optical Society of America B , 24(10), A1−A18.
Shahid, U. 2009. Signal Processing Based Method for Solving Inverse Scattering
Problems. PhD Dissertation, Optics. University of North Carolina at
Charlotte, Charlotte: UMI/ProQuest LLC.
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