Characterization of the Vortex Beam by Fermat's Spiral

In this paper, we characterize the helical beam structure through an analysis of the spiral character of the phase distribution inside a light beam. In particular, we show that a line connected with the 2 pi phase jump in the Laguerre-Gauss beam can be described by a Fermat's spiral. We propose a numerical fitting method to determine the parameters of a spiral equation for the phase distribution of the helical beam. Next, we extend the procedure to a vortex beam created by the spiral phase plate and apply it to experimental phase maps, which allows us to recover the phase shift introduced into the object beam in the optical vortex scanning microscope.