On The Ambiguities Of Phase Retrieval Problem In Fourier Ptychographic Microscopy

Fourier Ptychographic Microscopy (FPM) has achieved large field of view and high-resolution microscopy, which has attracted widespread attention. However, whether FPM can be restored accurately has not been able to provide a theoretical guarantee. The corresponding measurement system of FPM is the phase retrieval problem of the 2-dimensional inverse short-time Fourier transform (2-D ISTFT). In this paper, aiming at the defect that there are multiple global optimal solutions (ambiguities) for the phase retrieval problem, it is proved that FPM has almost the unique global optimal solution in the sense of removing the global phase solution. Based on different overlap ratios (the ratio of the area of the overlapped part to the window area), the upper bound estimation of the number of the ambiguities is given, and it is proved that FPM can eliminate the conjugate flip solution. In the simulations, the sequential Gerchberg-Saxton method is used to update under different overlap ratio conditions. It is verified that under the condition of low overlap ratio, FPM has poor convergence; under the condition of high overlap ratio, FPM reaches the global optimal solution rapidly.