Space-time Fourier ptychography for in vivo quantitative phase imaging

Quantitative phase imaging of living biological specimens is challenging due to their continuous movement and complex behavior. Here, we introduce space-time Fourier ptychography (ST-FP), which combines a fast Fourier ptychography (FP) model based on compressive sensing with space-time motion priors for joint reconstruction of quantitative phase, intensity, and motion fields across consecutive frames. Using the same input data as compressive sensing FP, ST-FP increases the space-bandwidth-time product of the reconstructed complex image sequence while leveraging redundant temporal information to achieve robust reconstruction performance. The efficacy of this approach is demonstrated across various applications, particularly in observing living microorganisms undergoing rapid morphological changes and reconstructing amplitude and phase targets in motion. The improved phase retrieval capability of ST-FP enables digital refocusing, facilitating comprehensive three-dimensional analysis of microorganisms. This advancement paves the way for enhanced visualization of cellular processes, developmental biology studies, and investigations into life mechanics at the microscopic level.