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Pseudo-phase mapping of speckle fields using 2D Hilbert transformation

Zenkova C. Y., Gorsky M. P., Ryabiy P. A.

Optica Applicata

2016

Vol. 46, nr 1

153--162

The use of a "window" 2D Hilbert transform for the 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 change of the position of the kernel of transformation and in the 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.

Different approaches to phase restoration of distant complex optical fields

Zenkova C. Y., Gorsky M P, Ryabiy P A, Gruia I

Optica Applicata

2015

Vol. 45, nr 2

139--150

The paper presents principal approaches to diagnosing the structure forming skeleton of the complex optical field. An analysis of optical field singularity algorithms depending on intensity discretization and image resolution has been carried out. An optimal approach is chosen, which allows to bring much closer the solution of the phase problem of localization of speckle-field special points. A possible approach to diagnosing the signs of zero amplitudes has been offered.

Optimal control and stability of elliptic systems with integral cost functional

Bors D., Skowron A., Walczak S.

Systems Science

2007

Vol. 33, no 4

13-26

We consider a system of resonant elliptic equations and using variational methods derive suffcient conditions for solutions of the system to depend continuously on parameters. This result is employed to obtain existence of solution for some optimal control problem.