Vector Diffraction Integrals for Solving Inverse Problems of Radio-Holographic Sensing of the Earth's Surface and Atmosphere

Vector relationships between the fields on a certain surface confining an inhomogeneous three-dimensional volume and the fields inside this volume are obtained by the Stratton–Chu method developed for the case of homogeneous media. The vector relationships allow us to solve the direct and inverse problems of determining the fields inside an inhomogeneous medium given the field on its boundary. The vector equations take into acount the polarization changes of direct and inverse waves propagated in an inhomogeneous medium. In the case of a two-dimensional homogeneous medium, the vector equations reduce to the previously obtained scalar equations used in the approximation of spherical symmetry to describe the process of backward wave propagation during the atmospheric and ionospheric radio-occultation monitoring. It is shown that the Green's function of the scalar wave equation in an inhomogeneous medium should be used as the reference signal for solving the inverse problem of radio-occultation monitoring. This validates the method of focused synthetic aperture previously used for high-accuracy retrieval of the vertical refractive-index profiles in the ionosphere and atmosphere. In this method, the reference-signal phase was determined from a model which describes with sufficient accuracy the radiophysical parameters of a refracting medium in the region of radio-occultation sensing. The obtained equations can be used for the high-accuracy solving of inverse problems of radio-holographic sensing of the Earth's atmosphere and surface by precision signals from radio-navigation satellites.