Digital sorting of perturbed Laguerre-Gaussian modes by radial index

We have developed a new opto-digital technique for measuring radial Laguerre-Gauss (LG) modes with a fixed topological charge. The technique is based on digital analysis of geometric moments of intensity. To test this technique, we perturbed single LG beams or their composition with a circular diaphragm, while reducing the hole radius. A decrease in the radius of the diaphragm promotes the appearance of secondary LG modes with different radial indices, which are characterized by a spectrum of amplitudes. The sorted spectrum of modes allows one to reconstruct real LG modes and estimate the degree of perturbation using Shannon's Entropy. Measurements have shown that the degree of recovery of the sorted beams lies in the 90% limit.