Here, we modify and study a method for measuring the orbital angular momentum (OAM) based on angle-averaged intensity in a single transverse plane. We also simulate propagation of a superposition of two Laguerre-Gaussian modes after passing through a diffuser with a random phase. Despite the distortions caused by the diffuser, the modified method allows OAM measurement with an average error less than 10%. The main advantages of the described technique is that (i) simultaneously with the full OAM the OAM spectrum is obtained and (ii) no any optical elements are needed.
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