  We developed a method to characterize arbitrary superpositions of light
orbital angular momentum (OAM) with high fidelity by using astigmatic
tomography and machine learning processing. In order to define each
superposition unequivocally, we combine two intensity measurements. The first
one is the direct image of the input beam, which cannot distinguish between
opposite OAM components. This ambiguity is removed by a second image obtained
after astigmatic transformation of the input beam. Samples of these image pairs
are used to train a convolution neural network and achieve high fidelity
recognition of arbitrary OAM superpositions with dimension up to five.
