  The optical Talbot interferometer has been used to explore the topological
charges of optical vortices. We recorded the self-imaging of a diffraction
grating in the near-field regime with the optical vortex of several topological
charges. Our twisted light was generated by a spatial light modulator (SLM).
Previous studies showed that interferometric methods can determine the
particular orbital angular momentum (OAM) states, but a large number of OAM
eigenvalues are difficult to distinguish from the interference patterns. Here,
we show that the Talbot patterns can distinguish the charges as well as the OAM
of the vortices with high orders. Owing to high sensitivity and self-imaging of
Talbot effect, several OAM eigenvalues can be distinguished by direct
measurement. We assure the experimental results with our theory. The present
results are useful for classical and quantum metrology as well as future
implementations of quantum communications.
