Fig. 1. OAM state measurement of single mode vortex beams through diffraction gratings. (a) Double-slit diffraction^[51]; (b) Triangular aperture diffraction^[53]; (c) Annular triangle aperture diffraction^[56]; (d) Gradually-changing-period diffraction element^[58]; (e) Annular grating^[59]

Fig. 2. OAM spectrum measurement through gray-scale algorithm associated with a Dammann vortex grating^[69]

Fig. 3. OAM mode sorter based on M-Z interferometer. (a) Setup; (b) Three-stage cascaded OAM mode sorter^[71]

Fig. 4. OAM mode sorter from Cartesian to log-polar coordinate transformation. (a) Coordinate transforming grating; (b) Phase-correcting grating; (c) Modeled and observed intensity profiles at before the transforming optical grating, just after the phase-correcting grating, and the modeled and observed images in the detector plane^[76]

Fig. 5. Optimized coordinate transformation based OAM mode sorter. (a) Fan-out scheme^[77]; (b) Radial varying phase scheme^[79]; (c) Spiral transformation scheme^[80]

Fig. 6. [in Chinese]

Fig. 6. Other approaches of OAM spectrum measurement. (a) Rotational Doppler shift scheme^[105]; (b) Time mapping scheme^[107]; (c) Single-pixel imaging scheme^[115]; (d) High-order intensity moments scheme^[122]

Fig. 7. Universal OAM spectrum analyzer based on interference^[124]. (a) Concept; (b) Intensity profiles of muli-ring optical vortices to be measured; (c) Corresponding OAM measurement results of (b)