An algorithm is proposed for the fast reconstruction of off-axis digital holograms based on a combination of complex encoding (CE) and spatial multiplexing (SM). In this algorithm, every two off-axis holograms recorded in sequence are first assembled into a CE hologram using the CE method, and then four of the CE holograms are again encoded into one complex spatial multiplexing (CSM) hologram based on the SM algorithm. It is demonstrated that the eight holograms encoded into such one CSM hologram can be quickly reconstructed by performing a two-dimensional (2D) Fourier transform (FT) on the CSM hologram. Using this method, the eight 2D FTs required for the reconstruction of the eight holograms in the conventional spatial filtering methods can be simplified to a process with only one 2D FT, which can largely improve the computation efficiency with the resolution of the reconstructed images nearly unchanged.

A setup for the generation of arbitrary vector beams is proposed. The setup mainly consists of a spatial light modulator (SLM), an angle-adjustable polarization beam splitter modulator, and a spatial filtering imaging system. Compared with the system using a birefringent beam splitter with a non-adjustable splitting angle, the polarization splitting angle of the improved setup can be adjusted by slightly rotating the related mirrors, which will bring more convenience when different wavelengths and different pixel sizes of SLMs are involved. The experimental results also demonstrate that the setup possesses a good polarization-selective imaging ability, which reveals that the setup may also be useful in polarization-selective spatial filtering imaging and polarization-encoded encryption.