Parallel phase-shifting self-interference digital holography with faithful reconstruction using compressive sensing

•A parallel phase-shifting self-interference digital holography is proposed.•Noise introduced by under-sampling is suppressed by compressive reconstruction.•Single-shot 3D imaging method for spatially incoherent object is proposed.

We present a new self-interference digital holographic approach that allows single-shot capturing three-dimensional intensity distribution of the spatially incoherent objects. The Fresnel incoherent correlation holographic microscopy is combined with parallel phase-shifting technique to instantaneously obtain spatially multiplexed phase-shifting holograms. The compressive-sensing-based reconstruction algorithm is implemented to reconstruct the original object from the under sampled demultiplexed holograms. The scheme is verified with simulations. The validity of the proposed method is experimentally demonstrated in an indirectly way by simulating the use of specific parallel phase-shifting recording device.