Calculation of fractional orbital angular momentum of superpositions of optical vortices by intensity moments

Two simple and high-efficiency techniques for measuring the orbital angular momentum (OAM) of paraxial laser beams are proposed and studied numerically and experimentally. One technique relies on measuring the intensity in the Fresnel zone, followed by calculating the intensity that is numerically averaged over angle at discrete radii and deriving squared modules of the light field expansion coefficients via solving a linear set of equations. With the other technique, two intensity distributions are measured in the Fourier plane of a pair of cylindrical lenses positioned perpendicularly, before calculating the first-order moments of the measured intensities. The experimental error grows almost linearly from ~1% for small fractional OAM (up to 4) to ~10% for large fractional OAM (up to 34).