Fig. 3: The design of obtaining the complex-amplitude distribution.

a Design strategy of OAM holograms with multiple topological charges l. iFT represents the inverse Fourier transform. b Design principle of the spiral phase for the multiplexing of multiple topological charge l. The topological charges for the incident wavefront and spiral phase plane are lin and lsp respectively. FT represents the Fourier transform. c Intensity distribution of OAM wave in the focal plane. The OAM wave (λ = 633 nm) with topological charge (l = 3) is incident on a lens (diameter is 720 μm and focus distance is 1.36 mm). The subfigure shows the intensity distributions on the 2D focal plane, and the scale bar represents 4 µm. d Numerical characterization of sample distance as a function of topological charge |l|. The subfigure illustrates the definition of the sample distance d. e Flow chart of the complex-amplitude design for the integration of printing images and OAM holograms. \({I}_{j}\) and \({A}_{t}\) are the amplitudes of the OAM holograms and printing images, respectively. FFT and iFFT represent the fast Fourier transform and inverse fast Fourier transform, respectively