ABSTRACT
The task of 2-D target modeling and image data generation from scattered fields is not a trivial one . The problem lies in that there is no general solution for analytically determining scattered fields for an arbitrary target . There are some analytical solutions only for a few very simple targets, but in general, no solution exists . This means that for the varying case-by-case situations, the analytical solution would have to be derived each time for a new target, if in fact the analytical solution does exist at all in a closed empirical form, which is unlikely . A common numerical solution to this type of problem or modeling is to use the technique of finite element analysis (Jin, 2002; Silvester and Ferrari, 1996) . In this method, the differential equations involved in calculating these scattered fields are solved numerically in an iterative process . The basic model setup for this procedure is similar to the general model shown in Figure 1 .1, with the exception that there is an artificial boundary that defines the extent that the iterative calculations are performed for, since this is a finite method as shown in Figure 5 .4 . At this boundary the properties of the boundary are defined such that there are no reflections and it gives the “appearance” that the model space goes on forever . The general solution for an EZ polarized field in the model space satisfies the scalar Helmholtz equation as follows:
∂ ∂
∂ ∂
+ ∂
∂ ∂ ∂
+ =x E x y
E y
k E jk Z J r
1 1 0 2
0 0µ µ ε (5 .1)
Figure 5.3 The radius of these Ewald circles is specified by the magnitude of the k-vector and so changing the incident frequency and hence, k will change the k-space data mapping as shown.
