Fast measurement of coherence–orbital angular momentum matrices of random light beams using off-axis holography and coordinate transformation

We propose an effective protocol to measure the coherence–orbital angular momentum (COAM) matrix of an arbitrary partially coherent beam. The method is based on an off-axis holography scheme and the Cartesian–polar coordinate transformation, which enables to simultaneously deal with all the COAM matrix elements of interest. The working principle is presented and discussed in detail. A proof-of-principle experiment is carried out to reconstruct the COAM matrices of partially coherent beams with spatially uniform and non-uniform coherence states. We find an excellent agreement between the experimental results and the theoretical predictions. In addition, we show that the OAM spectrum of a partially coherent beam can also be directly acquired from the measured COAM matrix.