| Abstract: | Pulse mode sonar operation is analyzed under the assumption that the scattering object Γ lies in the far fields of both the transmitter and the receiver. It is shown that, in this approximation, the sonar signal is a plane wave s(x · θ0 – t) near Γ, where θ0 is a unit vector directed from the transmitter toward Γ, and similarly the echo is a plane wave e(x · θ – t) near the receiver, where θ is a unit vector directed from Γ toward the receiver. Moreover, if Γ is stationary with respect to the sonar system then it is shown that  where ?(ω) is the Fourier transform of S(τ) and T+(ωθ,ωθ0) is the scattering amplitude in the direction θ due to the scattering by Γ of a time-harmonic plane wave with frequence ω and propagation direction θ0. A generalization of this relation is derived for moving scatterers. |
