Detecting topological charge and phase of the vortex beam embedded into the low coherence background

We propose and experimentally demonstrate a single-path interferometric approach to quantify the higher-order topological charge (TC) and phase structure of a vortex beam embedded into a low-coherence background. The topological charge is determined by an in-line and common path configuration for superposing the fluctuating coherent beams loaded with vortex and non-vortex features. Ensemble average of the intensities of the superimposed fluctuating fields generates petal structure, and the number of petals infers the absolute value of the topological charge of the vortex beam. Furthermore, a three-step phase-shifting method along with a single-path interferometer is utilized to recover the phase and spectra of the TCs in the beams embedded into a low-coherence background. The results of our experiment demonstrate successful measurement of vortex beam with TCs up to 150. We believe that such petal patterns with incoherent light will be useful in sensing the rotation and motion of optically rough objects.