Wave backscattering by point scatterers in the random paraxial regime
Résumé
When waves penetrate a medium without coherent reflectors, but with some fine scale medium heterogeneities, the backscattered wave is incoherent without any specific arrival time or the like. In this paper we consider a distributed field of weak microscatterers, like aerosols in the atmosphere, which coexists with microstructured clutter in the medium, like the fluctuations of the index of refraction of the turbulent atmosphere. We analyze the Wigner transform or the angularly resolved intensity profile of the backscattered wave when the incident wave is a beam in the paraxial regime and when the Born approximation is valid for the microscatterers. An enhanced backscattering phenomenon is proved, and the properties of the enhanced backscattering cone (relative amplitude and profile) are shown to depend on the statistical parameters of the microstructure but not on the microscatterers. These results are based on a multiscale analysis of the fourth-order moment of the fundamental solution of the white-noise paraxial wave equation. They pave the way for an estimation method of the statistical parameters of the microstructure from the observation of the enhanced backscattering cone. In our scaling argument we differentiate the two important canonical scaling regimes, which are the scintillation regime and the spot dancing regime