Fundamentals of the Physical Theory of Diffraction, 2nd Edition

14 Bistatic Scattering at a Finite-Length Cylinder

14.1 Acoustic Waves

The geometry of the problem is shown in Figure 14.1. The diameter of the cylinder equals d = 2a, and its length equals L = 2l.

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

The incident wave is given by

(14.1)

The scattered field is evaluated in the plane y0z (φ = π/2 and φ = 3π/2) in the far zone (R ≫ ka², R ≫ kl²). It is convenient to indicate the scattering direction by the angle Θ (0 ⩽ Θ ⩽ 2π):

(14.2)

where ϑ (0 ⩽ ϑ ⩽ π) is the ordinary spherical coordinate of the field point (R,ϑ,φ). One should not confuse this angle Θ with the local angle θ used for description of an EEW diverging from the diffraction point ζ = aψ at the edge. The relevant local coordinates r,θ,ɸ are introduced below by Equations (14.14) to (14.18).

14.1.1 PO Approximation

The incident wave (14.1) generates the uniform component j⁽⁰⁾_{s, h} of the scattering sources only on the left base (disk) and on the lower lateral part (π ⩽ ψ ⩽ 2π) of the cylindrical surface. The scattered field is determined by Equations (1.33) and (1.34). We omit all intermediate calculations ...