Revealing the order of a vortex through its intensity record

We show that the intensity distribution of an optical vortex contains information of its order. Specifically, the number of dark rings in the Fourier transform of the intensity is found to be equal to the order of the vortex. Based on this property and the orthogonality of Laguerre polynomials, we demonstrate the feasibility of an experimental technique for determining the order of optical vortices. It shows the beauty of going to complementary spaces, which has been employed earlier also to find the information not available in other domains.