Quantitative phase imaging (QPI) has emerged as a valuable tool for biomedical research thanks to its unique capabilities for quantifying optical thickness variation of living cells and tissues. Among many QPI methods, Fourier ptychographic microscopy (FPM) allows long-term label-free observation and quantitative analysis of large cell populations without compromising spatial and temporal resolution. However, high spatio-temporal resolution imaging over a long-time scale (from hours to days) remains a critical challenge: optically inhomogeneous structure of biological specimens as well as mechanical perturbations and thermal fluctuations of the microscope body all result in time-varying aberration and focus drifts, significantly degrading the imaging performance for long-term study. Moreover, the aberrations are sample- and environment-dependent, and cannot be compensated by a fixed optical design, thus necessitating rapid dynamic correction in the imaging process. Here, we report an adaptive optical QPI method based on annular illumination FPM. In this method, the annular matched illumination configuration (i.e., the illumination numerical aperture (NA) strictly equals to the objective NA), which is the key for recovering low-frequency phase information, is further utilized for the accurate imaging aberration characterization. By using only 6 low-resolution images captured with 6 different illumination angles matching the NA of a 10x, 0.4 NA objective, we recover high-resolution quantitative phase images (synthetic NA of 0.8) and characterize the aberrations in real time, restoring the optimum resolution of the system adaptively. Applying our method to live-cell imaging, we achieve diffraction-limited performance (full-pitch resolution of $$655\,nm$$ 655 n m at a wavelength of $$525\,nm$$ 525 n m ) across a wide field of view ($$1.77\,mm^2$$ 1.77 m m 2 ) over an extended period of time.

Fourier ptychographic microscopy (FPM) is a computational high‐throughput technique for high‐resolution and wide field‐of‐view (FOV) imaging applications such as cell biology, medicine screening, and digital pathology. By integrating angle‐varied illumination, iteration phase retrieval, and synthetic aperture, it achieves a significantly enhanced imaging resolution beyond the diffraction limit of the objective lens while retaining its original large FOV without any mechanical movement. However, sufficient data redundancy is a prerequisite for the convergence of the iteration algorithm, which in turn requires dozens or even hundreds of raw images to get a decent resolution, leaving ample room for further improvement. In this paper, an efficient synthetic aperture scheme for FPM is proposed, termed ESA‐FPM. It employs both coherent and incoherent illuminations to maximize the efficiency of data utilization and achieve high spatial‐bandwidth product (SBP) reconstruction with few acquisitions. The data redundancy requirements are further analyzed, suggesting that ESA‐FPM reaches imaging resolution of 3NAobj$3NA_{\rm obj}$ using only seven images. The experiment with USAF target demonstrates that ESA‐FPM achieves theoretical resolution with only 1.6% of the data of conventional FPM. A customized miniaturized ESA‐FPM system with a high‐numerical‐aperture, low‐magnification objective lens, and a high‐brightness LED array is built, demonstrating its potential for biomedical and pathological applications.

Transport of intensity equation (TIE) is a well-established non-interferometric phase retrieval approach that enables quantitative phase imaging (QPI) by simply measuring intensity images at multiple axially displaced planes. The advantage of a TIE-based QPI system is its compatibility with partially coherent illumination, which provides speckle-free imaging with resolution beyond the coherent diffraction limit. However, TIE is generally implemented with a brightfield (BF) configuration, and the maximum achievable imaging resolution is still limited to the incoherent diffraction limit (twice the coherent diffraction limit). It is desirable that TIE-related approaches can surpass this limit and achieve high-throughput [high-resolution and wide field of view (FOV)] QPI. We propose a hybrid BF and darkfield transport of intensity (HBDTI) approach for highthroughput quantitative phase microscopy. Two through-focus intensity stacks corresponding to BF and darkfield illuminations are acquired through a low-numerical-aperture (NA) objective lens. The high-resolution and large-FOV complex amplitude (both quantitative absorption and phase distributions) can then be synthesized based on an iterative phase retrieval algorithm taking the coherence model decomposition into account. The effectiveness of the proposed method is experimentally verified by the retrieval of the USAF resolution target and different types of biological cells. The experimental results demonstrate that the half-width imaging resolution can be improved from 1230 nm to 488 nm with 2.5× expansion across a 4× FOV of 7.19 mm 2 , corresponding to a 6.25× increase in space-bandwidth product from ∼5 to ∼30.2 megapixels. In contrast to conventional TIE-based QPI methods where only BF illumination is used, the synthetic aperture process of HBDTI further incorporates darkfield illuminations to expand the accessible object frequency, thereby significantly extending the maximum available resolution from 2NA to ∼5NA with a ∼5× promotion of the coherent diffraction limit. Given its capability for high-throughput QPI, the proposed HBDTI approach is expected to be adopted in biomedical fields, such as personalized genomics and cancer diagnostics.

Quantitative phase imaging (QPI) by differential phase contrast (DPC) with partially coherent illumination provides speckle-free imaging and lateral resolution beyond the coherent diffraction limit, demonstrating great potential in biomedical imaging applications. Generally, DPC employs weak object approximation to linearize the phase-to-intensity image formation, simplifying the solution to the phase retrieval as a two-dimensional deconvolution with the corresponding phase transfer function. Despite its widespread adoption, weak object approximation still lacks a precise and clear definition, suggesting that the accuracy of the QPI results, especially for samples with large phase values, is yet to be verified. In this paper, we analyze the weak object approximation condition quantitatively and explicitly give its strict definition that is applicable to arbitrary samples and illumination apertures. Furthermore, an iterative deconvolution QPI technique based on pseudo-weak object approximation is proposed to overcome the difficulty of applying DPC to large-phase samples without additional data acquisition. Experiments with standard microlens arrays and MCF-7 cells demonstrated that the proposed method can effectively extend DPC beyond weak object approximation to high-precision three-dimensional morphological characterization of large-phase technical and biological samples.

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