Файл: Ufimtsev P. Fundamentals of the physical theory of diffraction (Wiley 2007)(348s) PEo .pdf

288 Chapter 14 Bistatic Scattering at a Finite-Length Cylinder

Figure 14.1 Cross-section of the cylinder by the y0z-plane. Dots 1, 2, and 3 are the stationary-phase points.

where

The first terms in functions (s,h0), which contain the Bessel function J1( p), relate to the field scattered by the disk, and the second terms describe the scattering at the lateral (cylindrical) surface. These terms were evaluated numerically and their magnitudes are plotted in Figures 14.2 and 14.4.

It follows from the above field expressions that the total scattering cross-section (1.53) is given by

is the area of the shadow beam cross-section.

According to Equations (14.4) and (14.5) the normalized scattering cross-section (13.14) is defined as

This quantity was calculated numerically and the results are presented in Figures 14.2 to 14.5 for the incident wave direction γ = 45◦. Figures 14.2 and 14.4 show the scattering at the individual parts of the cylinder and demonstrate how the total scattered field is formed.

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14.1 Acoustic Waves 289

Figure 14.2 Scattering at the individual parts of a soft cylinder. According to Equation (14.62), this figure also demonstrates the PO approximation for electromagnetic waves (with Ex -polarization) scattered from the parts of a perfectly conducting cylinder.

14.1.2 Shadow Radiation as a Part of the Physical Optics Field

In Section 1.3.4 it was shown that the shadow radiation is the constituent part of the PO field. It was noted there that this field concentrates in the vicinity of the shadow region. Now we can verify this property by numerical investigation of the shadow radiation generated by the finite-length cylinder. The most appropriate procedure for doing this work would be the direct application of the shadow contour theorem demonstrated in Section 1.3.5. However, we can facilitate our work by utilizing the relationship given in Equation (1.73),

and the numerical results obtained in the previous section for the PO fields us(0) and uh(0). Figure 14.6 shows the spatial distribution of the shadow radiation found in this way. The normalized scattering cross-section (14.9) is plotted here in a decibel

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290 Chapter 14 Bistatic Scattering at a Finite-Length Cylinder

Figure 14.3 Scattering at a soft cylinder. According to Equation (14.62), this figure also demonstrates the PO approximation for electromagnetic waves (with Ex -polarization) scattered from a perfectly conducting cylinder.

scale. It is clearly seen that the shadow radiation really represents the nature of the scattered field in the forward sector (0◦ ≤ ≤ 90◦). According to Equations (14.62) and (14.75), this figure also demonstrates the shadow radiation and PO field scattered from a perfectly conducting cylinder.

14.1.3PTD for Bistatic Scattering at a Hard Cylinder

Here we consider the scattering only at a hard cylinder. This problem is more important from a practical point of view. According to PTD the scattered field is generated by the uniform ( jh(0)) and nonuniform ( jh(1)) scattering sources induced by the incident wave on the cylinder. The field created by jh(0) represents the PO field investigated in the previous sections. Now we calculate the field generated by that part of jh(1) that concentrates near the circular edges of the cylinder and which is also called the fringe source. Then we will combine both components of the scattered field and provide the results of numerical calculation.

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14.1 Acoustic Waves 291

Figure 14.4 Scattering at the individual parts of a hard cylinder. According to Equation (14.75), this figure also demonstrates the PO approximation for electromagnetic waves (with Hx -polarization) scattered from the parts of a perfectly conducting cylinder.

The field generated by jh(1) is found by integrating the elementary edge waves introduced in Chapter 7. This field can be written in the following form:

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292 Chapter 14 Bistatic Scattering at a Finite-Length Cylinder

Figure 14.5 Scattering at a hard cylinder. According to Equation (14.75), this figure also demonstrates the PO approximation for electromagnetic waves (with Hx -polarization) scattered from a perfectly conducting cylinder.

to the left and right edges, respectively. Only half of the right edge is illuminated by the incident wave (14.1), which is why the integration limits in Equation (14.13) are

π and 2π .

Functions Fh(1)left,right (ψ , θ , φ) are described by Equations (7.91) and (7.92). Section 13.2.1 shows how one defines the local angles γ0, θ , φ, and φ0 for the backscattering direction ϑ = π − γ . In the same way one can introduce these angles

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