Additional approaches to solving the phase problem in optics.

The paper presents principal approaches to diagnosing the structure-forming skeleton of a complex optical field. Analysis of optical field singularity algorithms, depending on intensity discretization and image resolution, has been carried out. An optimal approach is chosen, which allows us to get much closer to the solution of the phase problem of localization speckle-field special points. The use of a "window" 2D Hilbert transform for reconstruction of the phase distribution of the intensity of a speckle field is proposed. It is shown that the advantage of this approach consists in the invariance of a phase map to a position change of the kernel of transformation and in a possibility to reconstruct the structure-forming elements of the skeleton of an optical field, including singular points and saddle points. We demonstrate the possibility to reconstruct the equi-phase lines within a narrow confidence interval and introduce an additional algorithm for solving the phase problem for random 2D intensity distributions.

Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem.

We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution. The core of the algorithm consists in locating the saddle points of the intensity distribution and connecting such points into nets by the lines of intensity gradient that are closely associated with the equi-phase lines of the field. This algorithm provides a new partial solution to the inverse problem in optics commonly referred to as the phase problem.