Phase shifting to measure the modal composition of the scattered helical beam

We propose and experimentally demonstrate a non-interferometric and highly stable technique to recover the incident orbital angular momentum (OAM) modes from the randomly scattered coherent light. To implement and demonstrate this technique, a non-separable state is generated by encoding spiral and non-spiral modes into the orthogonal polarization bases prior to propagation through a random scattering media. Recovery of the complex OAM mode of the incident light becomes possible by quantitatively measuring the complex Fourier coefficients from the polarization correlation of the random light field along with the three-step phase-shifting method. A detailed theoretical basis of the proposed method is presented and verified by numerical simulation and experimental tests.