Modeling of high-frequency wave propagation with application to the double-passage imaging in random media

It is shown that uncertainty considerations play an important role in the construction of high-frequency propagators in randomly fluctuating media. A paired field measure and its spectral transforms known as Wigner and ambiguity functions have been defined in order to account for the uncertainty in the spatial location and the slope of geometrical ray trajectories. The values of these functions at the source plane and the observation plane are related by mixed space-spectral propagators. Writing these propagators in the path integral form and replacing the multiple trajectories by straight ray trajectories leads to solutions that correctly represent intensity correlation characteristics. The fact that the above propagators contain information about the random refractive-index variation along the propagation path allows their application to double-passage analysis when the scattered backward radiation traverses the same random inhomogeneities as the incident one. The resolution effects arising as a result of backward reflection of a spherical wave from a two-point-scatterer target are considered.