Fig. 5: \({\mathcal{M}}\)-specific holography.

a Design of a \({\mathcal{M}}\)-specific hologram by adding the correction phase into the OAM channel. b Reconstruction specificity. Experimental results confirm that only the designated operator pathway \({\mathcal{M}}\)(TC = 3/2, n = 2, d = 1 cm) reconstructs the target image (e.g., ''E''), while alternative processes fail. The decoding multiplication modes are listed at the bottom. c Single OAM channel subdivided into operator-defined sub-channels, each acting as an independent information carrier