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.