Theory of single scattering by random distributed scatterers

We show that the Fraunhofer diffraction approximation can never be used in the theory of scattering by distributed scatterer (such as turbulence) in the far zone of antenna. We consider the single scattering of waves in a medium containing weak refractive index inhomogeneities using a Fresnel diffraction approximation. We do not introduce scattering volume but consider a transmitting antenna with a Gaussian distribution of current and a receiving antenna with a Gaussian distribution of attenuation across the aperture. The results obtained are valid both in the near and far zones of the antenna. The known contradiction between the applicability of the Fraunhofer diffraction approach and the size of the scattering volume formed by intersection of directivity diagrams is resolved. Similar to the far zone approach, the scattering intensity obtained is proportional to the Bragg component of the inhomogeneities that are averaged in Fourier space using some specific weighting function, depending on antenna size and pulse duration. The concept of a scattering cross section cannot be used for this problem and another more flexible normalization is suggested.