Image Processing Reference

In-Depth Information

3.50

Good

Fair

Bad

Q

3.00

2.50

2.00

1.50

1.00

0.50

0.00

er

Figure 6.5
Graph showing the plot of the Lorenz-Mie scattering efficiency
Q
factor equation for the same

conditions as the images in Table 6.13. Superimposed on this graph is a column for each image which indicates

the relative quality of the Born reconstruction with green indicating good, yellow indicating fair, and red indicating

poor. This graph demonstrates that when
Q
is “high” or increasing, the image reconstruction is good, and when
Q

is “low” or decreasing, the image is poor.

have a larger than expected area and a more uniform appearance. This also

alludes to a new criterion that could be used to help predict the performance

of an image reconstruction from scattered fields

These resonances can be easily predicted for a Mie scatterer, but this may not

always be the case for more complex targets. However, resonances for specific

target sets could be determined experimentally or via simulation and then pos-

sibly characterized by a closed form equation if one uses a structured method

developed like the one used here. One could experimentally determine enough

resonance points and then use some type of curve-fitting algorithm to deter-

mine a resonance relationship much like the
Q
factor for the Mie scatterers.

This is theoretically possible, but for complex structures, a virtual approach

like the one used here is more straightforward. Assuming the pattern of reso-

nant frequencies for any given target could be inferred from measurements,

then this knowledge could be used to predict the Born approximation-based

image reconstruction as well as providing a tool to investigate the properties of

resonant scattering structures. One very special case of the Lorenz-Mie model

and the scattering cross section indicated by
Q
is when the permittivity is

negative. This is recently of special interest for work currently being done in

the meta-material fields as researchers strive to produce materials with nega-

tive index of refraction. While this is a challenge in the physical realm, it can

be simulated rather easily in the virtual realm. Table 6.13 shows the results for

a cylinder as the permittivity is varied from 1 to −4. It should be noted that if

the permittivity is allowed to go negative, it causes problems for the
Q
equation

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