Sampling criteria for Fourier ptychographic microscopy in object space and frequency space

Fourier ptychographic microscopy (FPM) is a new computational super-resolution approach, which can obtain not only the correct object function, but also the pupil aberration, the LED misalignment, and beyond. Although many state-mixed FPM techniques have been proposed to achieve higher data acquisition efficiency and recovery accuracy in the past few years, little is known that their reconstruction performance highly depends on the data redundancy in both object and frequency domains. Generally, at least 35% aperture overlapping percentage in the Fourier domain is needed for a successful reconstruction using ordinary FPM method. However, the data redundancy requirements for those state-mixed FPM schemes are largely remained unexplored until now. In this paper, we explore the spatial and spectrum data redundancy requirements for the FPM recovery process to introduce sampling criteria for the conventional and state-mixed FPM techniques in both object and frequency space. Moreover, an upsampled FPM method is proposed to solve the pixel aliasing problem, and an alternative illumination-angle subsampled FPM scheme is introduced to get rid of the complexity of decoherence and achieve the expected recovery quality with reduced data quantity. All the proposed methods and sampling criteria are validated with both simulations and experiments, and our results show that state-mixed techniques cannot provide a significant performance advantage since they are much more sensitive to data redundancy. This paper provides both the guidelines for designing the most suitable FPM platform and the insights for the capabilities and limitations of the FPM approach.