Development of Numerical Methods for Applications of Coherent Radiation in Studies of the Internal Structure of Objects (Part I)

We consider the problem of finding the spatial distribution of the complex dielectric constant of an object of arbitrary shape. An algorithm for solving this problem is constructed by processing phase diffraction patterns obtained by successive irradiation of the object with Gaussian beams. Formally, we deal with the coefficient inverse problem for the three-dimensional parabolic wave equation or the equivalent inverse problem of quantum scattering theory for a particle moving in a two-dimensional time-dependent potential. To solve the latter, the wave function of the system is expanded in terms of functions of Gaussian beams propagating in free space. The main advantages of the approach are the direct determination of the refractive index along with absorption, as well as the elimination of rotation or movement of the sample and radiation source; its further development can lead to the emergence of a qualitatively new nondestructive method for studying and testing materials and samples.