Methods for determining the orbital angular momentum of a laser beam

We propose and study numerically and experimentally two methods for determining the orbital angular momentum (OAM) of paraxial laser beams. One method is based on registering the intensity in the Fresnel zone, numerically averaging this intensity over the polar angle at discrete radii, and solving a system of linear equations to find squared modules of the coefficients of the light field expansion in terms of basis functions. The other method is based on registering two intensity distributions in the Fourier plane of two cylindrical lenses rotated 90 degrees relative to each other, and calculating the first-order moments of the measured intensities. The experimental error of the OAM determination is about 1% for small fractional OAM (up to 4), and about 8% for large fractional OAM (up to 30).