Abstract
It is shown that there is a variety of subsurface objects, the diagnosis of which can be reduced to establishing the shape of the interfaces between media with different refractive indices. An example of this kind of objects are man-made structures created to conduct painful actions, in particular, dugouts, underground tunnel systems, etc. It is shown that the surfaces inherent in such objects can be represented through equivalent circuits built on the basis of a set of paraboloids. It is proven that the characteristics of each of these paraboloids can be determined empirically through the use of analogues of optical systems operating in the radio range. These schemes are aimed at empirically determining the focal length of individual paraboloids included in the equivalent surface scheme by scanning the tunable focal length of the diagnostic system (in the simplest case, a diagnostic lens). It is shown that the application of this approach is closely related to the establishment of singular points of the wave front (singular points of the caustic), which are identified by methods of generalized Fourier optics using the stationary phase method. It is shown that with this approach, the identification of paraboloids that make up the equivalent optical scheme of the surface under study becomes unambiguous.