Reconstruction Parameters of Local Scattering Sources of a

Metallic Strip from the Backscattering Pattern

494

ordinates decreases. For

090

ο

ii

y

. (7)

In this case the error of the reconstruction of the longi-

tudinal coordinates in xy system equals to the error of the

reconstruction of the transverse coordinates in x'y' system.

So at the second stage it is better to choose 090

.

3. Numerical Results and Discussion

Later there are the results of the solution of the observing

problem for the metallic strip with the lower edge co-

ordinates (0, −5λ) and upper edge coordinates (0, 5λ)

(Figure 1). The backscattering pattern of the strip was

calculated by the rigorous method of the integral equa-

tions [16] in case of E-polarization (E is directed along z

axis) of the incident plane monochromatic electromag-

netic wave with the amplitude equals 30.

In Figure 3 the dependences of the reconstructed trans-

verse coordinates of two local sources of the strip on the

aspect angle φ are shown. The value of the aspect angles

sector ∆φ = 12˚. In this case two local sources starting

with φ0 = 6˚ are reconstructed when the normal angle to

the strip surface is not thrown into the aspect angles sector

(φ0 = 0˚). Curves 1 and 2, Figure 3 practically equal, so

the first local source is located on the lower edge of the

strip. For the aspect angles φ0 > 48˚ the amplitude of the

first local source is extremely small (Figure 4) and this

local source is not reconstructed. Curves 3 and 4, Figure 3

practically match, so the second local source is located on

the strip upper edge for the aspect angles (6˚, 90˚). The

local scattering sources of the strip are located on its sur-

face, so the reconstruction of its longitudinal coordinates

is obvious.

In Figure 4 the dependences of reconstructed ampli-

tudes of two local sources of the strip are shown on the

Figure 3. The dependence of the reconstructed transverse

coordinates of two local sources of the strip on the aspect

angle φ0 (1) The reconstructed coordinates of the first local

source; (2) Coordinates of the strip lower edge; (3) The re-

constructed coordinates of the second local source; (4) Co-

ordinates of the strip upper edge.

Figure 4. The dependence of the reconstructed amplitudes

of two local sources of the strip on the aspect angle φ0. (1)

The first local source; (2) The second local source.

aspect angle φ0. Their amplitudes are practically equal for

small aspect angles. Increasing the observation angle φ0

the amplitude of the second local source starts over the

amplitude of the first local source. For the aspect angles φ0

> 48˚ the amplitude of the first local source becomes

negligibly small, as the amplitude of the second one at φ0

= 90˚ equals 4.67.

Further as an illustration the results of reconstruction of

the local sources of this metallic strip for case ∆φ = 12˚

and φ0 = 28˚ are shown.

The curve Figure 5 is a fragment of the amplitude

backscattering pattern

Eu of the strip in spatial fre-

quency sector u

[k sin(22˚); k sin(34˚)], (∆φ = 12˚, φ0

= 28˚).

The curve Figure 6 is a fragment of the phase back-

scattering pattern

arg u (let us notice that

exEu Euup argj) of the strip in spatial fre-

quency sector u

[k sin(22˚); k sin(34˚)] (∆φ = 12˚, φ0 =

28˚).

In Figure 7 the modulus of the one-dimensional image

of the strip

for u

[k sin(22˚); k sin(34˚)] (∆φ = 12˚,

φ0 = 28˚) is shown. Two main maxima correspond to two

local sources (N = 2). The reconstructed transverse coor-

dinates of the local sources r (Table 1) equal to a half

of transverse coordinates of the corresponding main maxi-

ma. The transverse coordinates y' (Table 1) correspond to

the transverse coordinates of the strip edges. The modulus

values of the main maxima of the one-dimensional image

y

,Jy

correspond to the modulus of the recon-

structed amplitudes of the local sources r

E (Table 1).

As the result of analysis of the obtained numerical data

(Figure 3) it was found that the absolute error of the re-

construction of the transverse coordinates of the local

sources does not exceed approximately 0.03 λ. The analy-

sis of numerical results (Table 1) affords us to summarize

that in the considered example (∆φ = 12˚, φ0 = 28˚) the

absolute error of the reconstruction of the transverse co-

ordinates of the local sources 0.03y

.

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