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

ReConStRuCtIonS

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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