A new computational imaging method to reconstruct the complex wave-field is reported. Due to the existence of zero frequency component, the measured signal by amplitude modulation of pupil has a spectrum similar to the one of off-axis hologram. The mathematical analogy between them is established in this paper. Based on this observation and analyticity of band-limited signal under any diffraction-limited system, an algorithm from Kramers-Kronig (KK) relations is utilized to recover the phase information only from the intensity patterns. From the sensing side, only two measurements are required at least. From the reconstruction algorithm side, our method is iteration-free and parameter-free, also without any assumption on sample characteristics. It owns several advantages over existing phase imaging methods and could provide a unique perspective to understand current computational imaging methods.

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Over the past decade, the research field of Fourier Ptychographic Microscopy (FPM) has seen numerous innovative developments that significantly expands its utility. Here, we report a high numerical aperture (NA) FPM implementation that incorporates some of these innovations to achieve a synthetic NA of 1.9 – close to the maximum possible synthetic NA of 2 for a free space FPM system. At this high synthetic NA, we experimentally found that it is vital to homogenize the illumination field in order to achieve the best resolution. Our FPM implementation has a full pitch resolution of 266 nm for 465 nm light, and depth of field of 3.6 µm. In comparison, a standard transmission microscope (incoherent) with close to maximum possible NA of 0.95 has a full pitch resolution of 318 nm for 465 nm light, and depth of field of 0.65 µm. While it is generally assumed that a free-space coherent imaging system and a free-space incoherent imaging system operating at their respective maximum NA should give comparable resolution, we experimentally find that an FPM system significantly outperforms its incoherent standard microscopy counterpart in resolution by a factor of 20%. Coupled with FPM’s substantially longer effective depth of field (5.5 times longer), our work indicates that, in the near-maximum NA operation regime, the FPM has significant resolution and depth of field advantages over incoherent standard 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 completedin 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. © The Authors.Published by SPIE under a Creative Commons Attribution 4.0 International License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.