The problem of single-beam probing of an unknown medium

We propose an algorithm for determining the shadows of unknown bodies inside an arbitrary medium probed by radiation only in one direction. We demonstrate a successful performance of the algorithm in the case that on a direct visualization (a photograph) the bodies under consideration are indistinguishable. We study the problem of overlapping the shadows of some objects by others and conclude that this circumstance can improve or worsen the quality of reconstruction depending on the radiation characteristics of the medium. The presented results of numerical experiments show good agreement between theoretical and computational methods.