Image Processing Reference
In-Depth Information
used on the data obtained from this modeling method to produce a Fourier
image of various targets so that a reconstructed image can be displayed and
compared to measured real-life data for identical targets. This method is dis-
cussed at length in Ritter (2012) and Shahid et al. (2008).
5.3 tARget ModelIng envIRonMent
The typical model used throughout this text consists of a target area centered
about the origin. Receiver points, which are used to “measure” or obtain the
calculated complex scattered field values at these points, are located on an
imaginary circle centered about the origin with an arbitrarily fixed radius of
760 mm. There are 360 data points equally spaced along this circle, which
basically gives the ability to measure the total field on 1° increments around
the target in the 2-D plane. The illuminating source is “cycled” or rotated
around the target in 36 equally spaced locations, which basically gives the
ability to view the scattered data from a source rotated in 10° increments
around the target. This translates to having the capability of creating 36 sepa-
rate Ewald circles as previously discussed in Wolf (1969). As already men-
tioned, this basic model environment has been successfully implemented,
and data has been successfully gathered from the simulations and formatted
for use in the already developed MATLAB algorithms used in Shahid (2009)
and in this topic. The effectiveness of this modeling method will be demon-
strated in the next section.
The implementation of this environment in the COMSOL software for a
basic cylinder target is shown in Figure 5.5. In this figure, the basic model,
the mesh, the Z component of the E -ield which is orthogonal to the plane
of propagation and the normalized E -ield are shown to illustrate the capa-
bilities of the software and model. It is apparent from these images that this
modeling technique is functioning properly and should provide valid data.
The data obtained from this modeling process is then exported to a Microsoft
Excel spreadsheet and processed to be formatted to be used as a data file in
MATLAB. This processing of the data basically consists of deleting the “i”
terms inserted by COMSOL to designate the imaginary component of the data
pairs. MATLAB does not recognize this format and therefore the data are
formatted such that every other number is the real portion of the data pairs,
while the accompanying every other number is the imaginary component of
the measured data pair. This format will be accounted for the MATLAB code.
5.4 IMAgIng AlgoRIthM IMpleMentAtIonS: exAMple
In order to demonstrate the validity of this modeling process, the data obtained
from the COMSOL model described in the previous section was extracted,
similarly processed, and compared to the measured data obtained from the
Institut Fresnel (Belkebir and Saillard, 2001, 2005; Geffrin et al. 2005) website
for a range of targets. This data was similarly processed using basically the
same algorithm described in Ritter (2012) that maps the data for a given source
frequency onto Ewald circles and then concurrently applies the Born approxi-
mation algorithm to the data to produce a first Born approximation recon-
structed image in MATLAB. To demonstrate that the data from the COMSOL/
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