Analysis of postreconstruction digital refocusing in Fourier ptychographic microscopy

Digital refocusing is a key feature of Fourier ptychographic microscopy (FPM). It is currently performed by determining and removing the defocus aberration during the iterative phase retrieval process. We examine the feasibility of digitally refocusing an FPM image by numerically propagating the recovered complex FPM image after the phase retrieval process has been completed – in effect, disentangling the defocus correction process from the iterative phase retrieval process. If feasible, this type of postreconstruction digital refocusing can significantly reduce the FPM computational load and provide a quick and efficient way for refocusing microscopy images on the fly. We report that such an approach is infeasible for large defocus distances because the raw FPM dataset associated with a defocused sample is illconditioned for the FPM's phase-retrieval process, and it will not output a complex-valued image that corresponds to any physically relevant image wavefront. When the defocus distance is small, the FPM can output an approximately correct image wavefront. However, this wavefront does not contain a global defocus phase term and, therefore, cannot be further focused using the digital refocusing application of a reverse global phase term. In totality, this means that postreconstruction digital refocusing does not serve a meaningful function for any defocus distance. To verify our analysis, we performed a series of experiments, and the results showed that the postreconstruction digital refocusing method is not a viable digital refocusing method.