Estimating a Target Cross Section from Forward Scattering Amplitude

Abstract

A conventional sonar detects an echo back scattered from a target to measure its location and other properties. However, the backscatter is not useful for detecting typical dimensions of a target, such as volume and geometrical cross section. For example, a large target with a smooth surface often works as a point target for backscatter, because only a. specular point on the surface scatters the incident beam to the direction of the receiving transducer. In some applications, it is important to measure a typical dimension of a target. To measure the geometrical cross section of the target, this paper proposes a coherent sonar on the basis of the forward scattering theorem: $$\sigma _t = \frac{{4\pi }} {k}\Im [f(\theta ,\phi )|\theta = 0,\phi = 0], $$ (1) where k is the wave number and \( \Im \) denotes the imaginary part. This means that the total scattering cross section σ t of a target is proportional to the imaginary part of the forward scattering amplitude f(0, 0) in the Fraunhofer region[1]. It is also known that, when the typical dimension of a target is much larger than the wavelength, the scattering cross section σ t of the target becomes twice of its geometrical cross section S t : $$ \sigma = 2 \cdot S_{t \cdot } $$ (2) These relations suggest a scheme of a coherent sonar that measures the forward scattering amplitude to estimate the geometrical cross section of a target.