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We presented a new method for measuring the squares of the amplitudes and phases of partial vortex-beams in a complex beam array in real time. The method is based on measuring the high-order intensity moments and analyzing the solutions of a system of linear equations. Calibration measurements have shown that the measurement error at least for an array of 10-15 beams does not exceed 4%. When measuring beams with different fractional topological charge of optical vortices, we revealed a sharp decrease in the OAM for small deviations of the topological charge from the integer order which is associated with a sharp increase in the number of integer-order vortices. The application of this approach e.g. for the terabit-information processing in optical fibers provides significant advantages in comparison with the traditional diffraction methods and opens up additional possibilities of information compressor when modulating not only the OAM but also phases of partial beams

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The first simple experiments of self-reconstructing or self-healing Bessel vortex beams after being obscured by symmetric obstacles [1,2] caused a flow of publications, for example, on microscopy with self-reconstructing beams [3], the information transmission and data processing systems [4,5]. Self-healing properties were also found in other types of vortex beams [6][7][8]. However, a more careful analysis of the self-healing showed [9] that Bessel beams do not always self-heal from transparent obstacles, and never self-heal from turbulence. This article caught our attention because it raises the question: what parameters of the beam characterize its selfreconstruction? The answer to this question depends on the use of feature properties of the vortex beam in various optical devices. For example, the sector obstacles inject some measure of uncertainty into the vortex beam [12][13][14] between the orbital angular momentum (OAM) and the angle of the sector obstacle, which, in turn, triggers a chain of vortex birth and annihilation events that increases a number of new vortex states. But such a perturbation although causing irreversible destruction of the wavefront, allows one to determine the topological charge of the optical vortex [10] and the orbital angular momentum [11]. On the other hand, the information properties of the vortex beam as a whole deteriorate significantly. Indeed, the growth of internal uncertainty in the wave structure induced by the sector aperture iindicates significant changes in such physical characteristics as informational entropy [15] and spatial coherence [16]. The fundamental problems of analyzing informational entropy (or Shannon's entropy) in light beams were considered in detail by Francis [15] and applied to vortex beams by the authors of Ref. [17,18]. The authors of Ref.[17] theoretically estimated the informational entropy and pointed out the relationship between entropy and spatial coherence for the 1D case of an unperturbed quasi-monochromatic vortex beam while the authors of Ref.[18] presented experimental confirmation of these theoretical predictions. We paid attention to the fact that, in the general case, informational entropy characterizes the vortex beam as a whole rather than its 1D projection onto the observation plane, as in Ref. [17,18]. Besides, the main contribution to information entropy is made by changes in the number of vortex states in the beam subjected to external perturbations. It is such an approach allowed the authors of Ref.[13] to investigate the relationship between the uncertainty of the angular position inside the vortex beam and the OAM. These studies point out the relationship between the vortex spectrum of the perturbed beam, the OAM, and the information entropy. Thus, the purpose of our letter is both a computer simulation and experimental measurement of informational entropy and the OAM of the perturbed vortex beam on the base of analyzing their vortex spectra.

We found that small perturbations of the optical vortex core in the Laguerre-Gaussian (LG) beams generate a fine structure of the Hermite-Gauss (HG) mode spectrum. Such perturbations can be easily simulated by weak variations of amplitudes and phases of the HG modes in the expansion of the LG beam field. We also theoretically substantiated and experimentally implemented a method for measuring the topological charge of LG beams with an arbitrary number of ring dislocations. Theoretical discussion and experimental studies were accompanied by simple examples of estimating the orbital angular momentum and the topological charge of perturbed LG beams.