Phase imaging using single-pixel detection in the spatial spectrum plane

We propose a phase imaging method that combines the Fourier ptychography and compressive sensing theories using single-pixel detection in the spatial spectrum plane. Specifically, the spatial Fourier spectrum is shifted based on the Fourier ptychography theory, and the compressive sensing theory is applied to reduce the amount of acquired data. Further, an algorithm has been developed to reconstruct the phase images and an asymmetric mask introduced to eliminate ghost interference. The feasibility of the proposed method was verified through simulation and evaluated in terms of the compressive sensing theory realized. The results show that a two-dimensional image can be restored at a low sampling rate of 5% using the proposed method.