Integral representation of the field of the wave propagating in a medium with large-scale irregularities

Abstract

We consider propagation of waves in a medium with irregularities located at relatively long distances from the source and the observer within the paraxial approximation. The asymptotic approximation, which was obtained earlier by using a double weighted Fourier transform, is reduced to form that is convenient for application under these conditions. By using the stationary-phase method, an integral representation in the form of a single-time weighted Fourier transform (the so-called Fresnel transform) is developed from the obtained integral representation. The conditions of the transition of this representation to the phase-screen method determine the conditions of the applicability of the latter and the criteria for selection of the screen location during higherresolution diagnostics of a non-uniform medium. The results of numerical spatial processing of the signal, which improves the resolution of diagnostics of non-uniform media, are presented.