Solving of the inverse diffraction problem in the first Rytov approximation for retrieving the phase object dielectric permittivity

In the study we derive a solution of the inverse diffraction problem aimed at retrieving the dielectric permittivity of a phase object by using the changes in the intensity and phase shift of coherent laser radiation probing the object. The theoretical considerations involve the results of solving the scalar Helmholtz wave equation in the first Rytov approximation. For an axisymmetric phase object probed with a plane wave, both with and without radiation absorption, computationally efficient equations are obtained, which reveal the relationship between the object dielectric permittivity and the Fourier spectra of the diffracted wave characteristics described in terms of the wave intensity and phase shift in free space. The equations provide reliable data when solving the inverse diffraction problem, since they take into account diffraction effects accompanying the wave passage through the object and enhancing in free space. Fundamental properties of the equations obtained are discussed together with their broad applications. The findings can open new perspectives in the diagnostics of various objects in different wavelength ranges.