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Thus, the results of our studies lie in developing and implementing the basicprinciples of digital sorting the Laguerre-Gauss modes by radial numbers bothfor a non-degenerate and a degenerate state of a vortex beam subject toperturbations in the form of a hard-edged aperture of variable radius. Thedigital sorting of LG beams by the orthogonal basis involves the use ofhigher-order intensity moments, and subsequent scanning of the modulated beamimages at the focal plane of a spherical lens. As a result, we obtain a systemof linear equations for the squared mode amplitudes and the cross amplitudes ofthe perturbed beam. The solution of the equations allows one to determine theamplitudes of each LG mode and restore both the real mode array and thecombined beam as a whole. First, we developed a digital sorting algorithm, andthen two types of vortex beams were experimentally studied on its basis: asingle LG beam and a composition of single LG beams with the same topologicalcharges(azimuthal numbers) and different radial numbers . The beam wasperturbed by means of a circular hard-edged aperture with different radii R. Asa result of the perturbation, a set of secondary LG modes with different radialnumbers k is appeared that is characterized by an amplitude spectrum . Thespectrum obtained makes it possible to restore both the real array of LG modesand the perturbed beam itself with a degree of correlation not lower than. As ameasure of uncertainty induced by the perturbation we measured theinformational entropy (Shannon's entropy)

Digital sorting perturbed laguerre-gaussian beams by radial numbers via high order intensity moments