Phase retrieval based on shaped incoherent sources

The current ghost imaging phase reconstruction schemes require either complex optical systems, Fourier transform steps, or iterative algorithms, which may increase the difficulty of system design, cause phase retrieval error or take too much time. To address this problem, we propose a five-step phase-shifting method in which no complex optical systems, Fourier transform steps, or iterative algorithms are needed. With five designed incoherent sources, one can obtain five different corresponding ghost imaging patterns, then the phase information of the object can be calculated from those five speckle patterns. The applicability of this theoretical proposal is demonstrated via numerical simulations with two kinds of complicated objects, and the results illustrate the phase information of the complicated object can be reconstructed successfully and quantitatively.