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Quantitative phase imaging (QPI) plays a key role in many application areas such as Optical elements measuring and unstained biomedical live samples imaging. Therefore, several computational QPI methods have been developed and widely used, like transport-of-intensity equation (TIE) based techniques and differential phase contrast (DPC) based techniques. However, these phase retrieval approaches are fundamentally limited by the space-bandwidth product (SBP) of the optical microscopy system, resulting in a trade-off between the spatial resolution and field of view (FOV). Lately, this problem is effectively solved by a new computational imaging technique named Fourier ptychographic microscopy (FPM), which reconstructs high-resolution complex image from many angle-variable illuminated, low-resolution intensity images captured by a low numerical-aperture (NA) objective. Although FPM has great potential for finding application in digital pathology and cancer research, it still suffers from long acquisition time and low phase measuring accuracy. Due to the large number of low-resolution images (generally larger than 30 images) required in FPM for recovering one phase image, it is more difficult for FPM to realize real-time phase imaging comparing with TIE (at least 2-3 images) or DPC (at least 4 images). Herein, we report a real-time FPM technique based on annular illuminations (AIFPM) for quantitative phase imaging of unstained live samples in vitro. In AIFPM, we only need four low-resolution images, corresponding to four different illumination angles with 0.4NA, which equal to the NAobj. Therefore, using a 10X, 0.4NA objective lens with final effective imaging performance of 0.8 NA, we present the real-time imaging results of in vitro Hela cells mitosis and apoptosis at a frame rate of 25 Hz with a full-pitch resolution of 655 nm at a wavelength of 525 nm across a wide FOV of 1.77 mm2 . Our work reveals an essential capability of FPM towards highspeed high-throughput phase imaging applications, such as biology and medicine screening, for the significant breakthrough in both space and time.
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