Accurate phase mapping of nondiffracting singular beams

We make use of a spatial light modulator to implement a phase-shifting interferometric method to determine the topological charge of multiple singularities embedded in the transverse phase of singular beams. This method allows us to discern between closely spaced singular points and elucidate the dynamics of optical vortices as their charge is increased continually. The transverse phase of beams with a determined phase profile are analyzed used this technique, yielding the precise location of multiple singularities as well as the value of their topological charge. We use apply this method to accurately map the phase and study the transit of vortices across fractional Bessel beams during their continuous order upconversion.