Sensing azimuthally symmetric objects by a single-pixel detector via COAM matrix

A coherence-orbital angular momentum (COAM) matrix describes the second-order spatial correlations among the pairs of the OAM states in a light beam at two radial positions. It provides a detailed information regarding the azimuthal features of the light beam itself or of the objects interacting with it. In this Letter, we reveal a close relationship existing between the COAM matrix's elements of a partially coherent light beam and the angular gratings that it passes through. It is demonstrated both in theory and in experiment that all the parameters of the angular gratings can be identified by measuring the COAM matrix elements. While the off-diagonal elements possess information about the angular shifts and the rotation speed of the angular grating, the diagonal elements account for the energy distribution among the OAM modes. The experimental results agree reasonably well with the theoretical analysis. One practically significant capability is that our technique offers the determination of angular shifts of azimuthally symmetric objects and/or their rotational speed, by means of a single-pixel detector.