Single-shot incoherent digital holography based on generalised three-step phase-shifting method with 1D phase grating

Incoherent digital holography (IDH) is a passive holographic 3D imaging technique under spatially incoherent light. Single-shot recording with high light-utilization efficiency and high spatial resolution is a challenge in IDH. Herein, we propose a single-shot three-step phase-shifting IDH system with a 1D phase grating that has a line-and-space structure. The 0th and ± 1st diffraction orders of the grating are used for simultaneously creating three self-interference holograms, which are then captured using an image sensor at a single exposure. Three-step phase shifts are introduced into the holograms using the geometric phase of circular polarizations. To compensate the intensity variations between the holograms due to grating fabrication errors, we derive and implement a generalised three-step phase-shifting algorithm. We experimentally performed the single-shot recording of reflective objects as a proof-of-principle demonstration. We further examined the theoretical noise tolerances between three- and four-step phase-shifting methods for grating-assisted space-division phase shifting. The results show that the three-step phase-shifting method is superior to the four-step method when the diffraction efficiency of the 1D phase grating is at least four-thirds higher than that of the 2D phase grating used for the four-step method.