Parallel Fourier ptychographic microscopy for high-throughput screening with 96 cameras (96 Eyes)

Long-term imaging of three-dimensional hyphal development using the ePetri dish

Imaging three-dimensional microbial development and behavior over extended periods is crucial for advancing microbiological studies. Here, we introduce an upgraded ePetri dish system specifically designed for extended microbial culturing and 3D imaging, addressing the limitations of existing methods. Our approach includes a sealed growth chamber to enable long-term culturing, and a multi-step reconstruction algorithm that integrates 3D deconvolution, image filtering, ridge, and skeleton detection for detailed visualization of the hyphal network. The system effectively monitored the development of Aspergillus brasiliensis hyphae over a seven-day period, demonstrating the growth medium's stability within the chamber. The system's 3D imaging capability was validated in a volume of 5.5 mm × 4 mm × 0.5 mm, revealing a radial growth pattern of fungal hyphae. Additionally, we show that the system can identify potential filter failures that are undetectable with 2D imaging. With these capabilities, the upgraded ePetri dish represents a significant advancement in long-term 3D microbial imaging, promising new insights into microbial development and behavior across various microbiological research areas.

Depth-of-field extended Fourier ptychographic microscopy without defocus distance priori

Fourier ptychographic microscopy (FPM) provides a solution of high-throughput phase imaging. Thanks to its coherent imaging model, FPM has the capacity of depth-of-field (DOF) extension by simultaneously recovering the sample's transmittance function and pupil aberration, which contains a defocus term. However, existing phase retrieval algorithms (PRs) often struggle in the presence of a significant defocus. In this Letter, different PRs with embedded pupil recovery are compared, and the one based on the alternating direction multiplier method (ADMM-FPM) demonstrates promising potential for reconstructing highly defocused FPM images. Besides, we present a plug-and-play framework that integrates ADMM-FPM and total variation or Hessian denoiser for pupil function enhancement. Both simulations and experiments demonstrate that this framework enables robust reconstruction of defocused FPM images without any prior knowledge of defocus distance or sample characteristics. In experiments involving USAF 1951 targets and pathologic slides, ADMM-FPM combined with the Hessian denoiser successfully corrected the defocus up to approximately 200 µm, i.e., extending the DOF to 400 µm.

Fourier Ptychographic Microscopy 10 Years on: A Review

Fourier ptychographic microscopy (FPM) emerged as a prominent imaging technique in 2013, attracting significant interest due to its remarkable features such as precise phase retrieval, expansive field of view (FOV), and superior resolution. Over the past decade, FPM has become an essential tool in microscopy, with applications in metrology, scientific research, biomedicine, and inspection. This achievement arises from its ability to effectively address the persistent challenge of achieving a trade-off between FOV and resolution in imaging systems. It has a wide range of applications, including label-free imaging, drug screening, and digital pathology. In this comprehensive review, we present a concise overview of the fundamental principles of FPM and compare it with similar imaging techniques. In addition, we present a study on achieving colorization of restored photographs and enhancing the speed of FPM. Subsequently, we showcase several FPM applications utilizing the previously described technologies, with a specific focus on digital pathology, drug screening, and three-dimensional imaging. We thoroughly examine the benefits and challenges associated with integrating deep learning and FPM. To summarize, we express our own viewpoints on the technological progress of FPM and explore prospective avenues for its future developments.

Redundant information model for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a computational optical imaging technique that overcomes the traditional trade-off between resolution and field of view (FOV) by exploiting abundant redundant information in both spatial and frequency domains for high-quality image reconstruction. However, the redundant information in FPM remains ambiguous or abstract, which presents challenges to further enhance imaging capabilities and deepen our understanding of the FPM technique. Inspired by Shannon's information theory and extensive experimental experience in FPM, we defined the specimen complexity and reconstruction algorithm utilization rate and reported a model of redundant information for FPM to predict reconstruction results and guide the optimization of imaging parameters. The model has been validated through extensive simulations and experiments. In addition, it provides a useful tool to evaluate different algorithms, revealing a utilization rate of 24%±1% for the Gauss-Newton algorithm, LED Multiplexing, Wavelength Multiplexing, EPRY-FPM, and GS. In contrast, mPIE exhibits a lower utilization rate of 19%±1%.

ComplexEye: a multi-lens array microscope for high-throughput embedded immune cell migration analysis

Autonomous migration is essential for the function of immune cells such as neutrophils and plays an important role in numerous diseases. The ability to routinely measure or target it would offer a wealth of clinical applications. Video microscopy of live cells is ideal for migration analysis, but cannot be performed at sufficiently high-throughput (HT). Here we introduce ComplexEye, an array microscope with 16 independent aberration-corrected glass lenses spaced at the pitch of a 96-well plate to produce high-resolution movies of migrating cells. With the system, we enable HT migration analysis of immune cells in 96- and 384-well plates with very energy-efficient performance. We demonstrate that the system can measure multiple clinical samples simultaneously. Furthermore, we screen 1000 compounds and identify 17 modifiers of migration in human neutrophils in just 4 days, a task that requires 60-times longer with a conventional video microscope. ComplexEye thus opens the field of phenotypic HT migration screens and enables routine migration analysis for the clinical setting.

Spatial- and Fourier-domain ptychography for high-throughput bio-imaging

First envisioned for determining crystalline structures, ptychography has become a useful imaging tool for microscopists. However, ptychography remains underused by biomedical researchers due to its limited resolution and throughput in the visible light regime. Recent developments of spatial- and Fourier-domain ptychography have successfully addressed these issues and now offer the potential for high-resolution, high-throughput optical imaging with minimal hardware modifications to existing microscopy setups, often providing an excellent trade-off between resolution and field of view inherent to conventional imaging systems, giving biomedical researchers the best of both worlds. Here, we provide extensive information to enable the implementation of ptychography by biomedical researchers in the visible light regime. We first discuss the intrinsic connections between spatial-domain coded ptychography and Fourier ptychography. A step-by-step guide then provides the user instructions for developing both systems with practical examples. In the spatial-domain implementation, we explain how a large-scale, high-performance blood-cell lens can be made at negligible expense. In the Fourier-domain implementation, we explain how adding a low-cost light source to a regular microscope can improve the resolution beyond the limit of the objective lens. The turnkey operation of these setups is suitable for use by professional research laboratories, as well as citizen scientists. Users with basic experience in optics and programming can build the setups within a week. The do-it-yourself nature of the setups also allows these procedures to be implemented in laboratory courses related to Fourier optics, biomedical instrumentation, digital image processing, robotics and capstone projects.

Implementation of miniaturized modular-array fluorescence microscopy for long-term live-cell imaging

Fluorescence microscopy imaging of live cells has provided consistent monitoring of dynamic cellular activities and interactions. However, because current live-cell imaging systems are limited in their adaptability, portable cell imaging systems have been adapted by a variety of strategies, including miniaturized fluorescence microscopy. Here, we provide a protocol for the construction and operational process of miniaturized modular-array fluorescence microscopy (MAM). The MAM system is built in a portable size (15c m×15c m×3c m) and provides in situ cell imaging inside an incubator with a subcellular lateral resolution (∼3µm). We demonstrated the improved stability of the MAM system with fluorescent targets and live HeLa cells, enabling long-term imaging for 12 h without the need for external support or post-processing. We believe the protocol could guide scientists to construct a compact portable fluorescence imaging system and perform time-lapse in situ single-cell imaging and analysis.

Depth-multiplexed ptychographic microscopy for high-throughput imaging of stacked bio-specimens on a chip

Imaging a large number of bio-specimens at high speed is essential for many biomedical applications. The common strategy is to place specimens at different lateral positions and image them sequentially. Here we report a new on-chip imaging strategy, termed depth-multiplexed ptychographic microscopy (DPM), for parallel imaging and sensing at high speed. Different from the common strategy, DPM stacks multiple specimens in the axial direction and images the entire z-stack all at once. In our prototype platform, we modify a low-cost car mirror for programmable steering of the incident laser beam. A blood-coated image sensor is then placed underneath the stacked sample for acquiring the resulting diffraction patterns. With the captured images, we perform blind recovery of the incident beam angle and model different layers of the stacked sample as different coded surfaces for object reconstruction. For in vitro experiment, we demonstrate time-lapse cell culture monitoring by imaging 3 stacked microfluidic channels on the coded sensor. For high-throughput cytometric analysis, we image 5 stacked brain sections with a 205-mm² field of view in ∼50 s. Cytometric analysis is also performed to quantify the cellular proliferation biomarkers on the slides. The DPM approach adds a new degree of freedom for data multiplexing in microscopy, enabling parallel imaging of multiple specimens using a single detector. The demonstrated 6-mm depth of field is among the longest ones in microscopy imaging. The novel depth-multiplexed configuration also complements the miniaturization provided by microfluidics devices, offering a solution for on-chip sensing and imaging with efficient sample handling.

Optical ptychography for biomedical imaging: recent progress and future directions [Invited]

Ptychography is an enabling microscopy technique for both fundamental and applied sciences. In the past decade, it has become an indispensable imaging tool in most X-ray synchrotrons and national laboratories worldwide. However, ptychography's limited resolution and throughput in the visible light regime have prevented its wide adoption in biomedical research. Recent developments in this technique have resolved these issues and offer turnkey solutions for high-throughput optical imaging with minimum hardware modifications. The demonstrated imaging throughput is now greater than that of a high-end whole slide scanner. In this review, we discuss the basic principle of ptychography and summarize the main milestones of its development. Different ptychographic implementations are categorized into four groups based on their lensless/lens-based configurations and coded-illumination/coded-detection operations. We also highlight the related biomedical applications, including digital pathology, drug screening, urinalysis, blood analysis, cytometric analysis, rare cell screening, cell culture monitoring, cell and tissue imaging in 2D and 3D, polarimetric analysis, among others. Ptychography for high-throughput optical imaging, currently in its early stages, will continue to improve in performance and expand in its applications. We conclude this review article by pointing out several directions for its future development.

Parallel Fourier ptychographic microscopy reconstruction method based on FPGA

Fourier ptychographic microscopy (FPM) can bypass the limitation of spatial bandwidth product to get images with large field-of-view and high resolution. The complicated sequential iterative calculation in the FPM reconstruction process reduces the reconstruction efficiency of the FPM. Therefore, we propose a parallel FPM reconstruction method based on field programmable gate array (FPGA) to accelerate the FPM reconstruction process. Using this method, multiple sub-regions in the Fourier domain can be computed in parallel and we customize a dedicated high-performance computational architecture for this approach. We deploy 4 FPM reconstruct computing architectures with a parallelism of 4 in a FPGA to compute the FPM reconstruction process, achieving the speed nearly 180 times faster than traditional methods. The proposed method provides a new perspective of parallel computing for FPM reconstruction.

Automating the High-Throughput Screening of Protein-Based Optical Indicators and Actuators

Over the last 25 years, protein engineers have developed an impressive collection of optical tools to interface with biological systems: indicators to eavesdrop on cellular activity and actuators to poke and prod native processes. To reach the performance level required for their downstream applications, protein-based tools are usually sculpted by iterative rounds of mutagenesis. In each round, libraries of variants are made and evaluated, and the most promising hits are then retrieved, sequenced, and further characterized. Early efforts to engineer protein-based optical tools were largely manual, suffering from low throughput, human error, and tedium. Here, we describe approaches to automating the screening of libraries generated as colonies on agar, multiwell plates, and pooled populations of single-cell variants. We also briefly discuss emerging approaches for screening, including cell-free systems and machine learning.

Embedded parallel Fourier ptychographic microscopy reconstruction system

Fourier ptychographic microscopy (FPM) has attracted a wide range of focus for its ability of large space-bandwidth product and quantitative phase imaging. It is a typical computational imaging technique that jointly optimizes imaging hardware and reconstruction algorithms. The data redundancy and inverse problem algorithms are the sources of FPM's excellent performance. But at the same time, this large amount of data processing and complex algorithms also evidently reduce the imaging speed. To accelerate the FPM reconstruction speed, we proposed a fast FPM reconstruction framework consisting of three levels of parallel computation and implemented it with an embedded computing module. In the conventional FPM framework, the sample image is divided into multiple sub-regions to process separately because the illumination angles and defocus distances for different sub-regions may also be different. Our parallel framework first performs digital refocusing and high-resolution reconstruction for each sub-region separately and then stitches the complex sub-regions together to obtain the final high-resolution complex image. The feasibility of the proposed parallel FPM reconstruction framework is verified with different experimental results acquired with the system we built.

High-speed multi-objective Fourier ptychographic microscopy

The ability of a microscope to rapidly acquire wide-field, high-resolution images is limited by both the optical performance of the microscope objective and the bandwidth of the detector. The use of multiple detectors can increase electronic-acquisition bandwidth, but the use of multiple parallel objectives is problematic since phase coherence is required across the multiple apertures. We report a new synthetic-aperture microscopy technique based on Fourier ptychography, where both the illumination and image-space numerical apertures are synthesized, using a spherical array of low-power microscope objectives that focus images onto mutually incoherent detectors. Phase coherence across apertures is achieved by capturing diffracted fields during angular illumination and using ptychographic reconstruction to synthesize wide-field, high-resolution, amplitude and phase images. Compared to conventional Fourier ptychography, the use of multiple objectives reduces image acquisition times by increasing the area for sampling the diffracted field. We demonstrate the proposed scaleable architecture with a nine-objective microscope that generates an 89-megapixel, 1.1 µm resolution image nine-times faster than can be achieved with a single-objective Fourier-ptychographic microscope. New calibration procedures and reconstruction algorithms enable the use of low-cost 3D-printed components for longitudinal biological sample imaging. Our technique offers a route to high-speed, gigapixel microscopy, for example, imaging the dynamics of large numbers of cells at scales ranging from sub-micron to centimetre, with an enhanced possibility to capture rare phenomena.

Addressing phase-curvature in Fourier ptychography

In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave illumination from various directions is commonly used, to stitch together the captured information into a high synthetic aperture. The underlying far-field (Fraunhofer) diffraction assumption connects the source, sample, and pupil planes by Fourier transforms. While computationally simple, this assumption neglects phase-curvature due to non-planar illumination from point sources as well as phase-curvature from finite-conjugate microscopes (e.g., using a single-lens for image-formation). We describe a simple, efficient, and accurate extension of Fourier ptychography by embedding the effect of phase-curvature into the underlying forward model. With the improved forward model proposed here, quantitative phase reconstruction is possible even for wide fields-of-views and without the need of image segmentation. Lastly, the proposed method is computationally efficient, requiring only two multiplications: prior and following the reconstruction.

Implementation of free-space Fourier Ptychography with near maximum system numerical aperture

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.

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

Fourier ptychographic microscopy (FPM) has risen as a promising computational imaging technique that breaks the trade-off between high resolution and large field of view (FOV). Its reconstruction is normally formulated as a blind phase retrieval problem, where both the object and probe have to be recovered from phaseless measured data. However, the stability and reconstruction quality may dramatically deteriorate in the presence of noise interference. Herein, we utilized the concept of alternating direction method of multipliers (ADMM) to solve this problem (termed ADMM-FPM) by breaking it into multiple subproblems, each of which may be easier to deal with. We compared its performance against existing algorithms in both simulated and practical FPM platform. It is found that ADMM-FPM method belongs to a global optimization algorithm with a high degree of parallelism and thus results in a more stable and robust phase recovery under noisy conditions. We anticipate that ADMM will rekindle interest in FPM as more modifications and innovations are implemented in the future.

Cellular analysis using label-free parallel array microscopy with Fourier ptychography

Quantitative phase imaging (QPI) is an ideal method to non-invasively monitor cell populations and provide label-free imaging and analysis. QPI offers enhanced sample characterization and cell counting compared to conventional label-free techniques. We demonstrate this in the current study through a comparison of cell counting data from digital phase contrast (DPC) imaging and from QPI using a system based on Fourier ptychographic microscopy (FPM). Our FPM system offers multi-well, parallel imaging and a QPI-specific cell segmentation method to establish automated and reliable cell counting. Three cell types were studied and FPM showed improvement in the ability to resolve fine details and thin cells, despite limitations of the FPM system incurred by imaging artifacts. Relative to manually counted fluorescence ground-truth, cell counting results after automated segmentation showed improved accuracy with QPI over DPC.

Robust Fourier ptychographic microscopy via a physics-based defocusing strategy for calibrating angle-varied LED illumination

Fourier ptychographic microscopy (FPM) is a recently developed computational imaging technique for wide-field, high-resolution microscopy with a high space-bandwidth product. It integrates the concepts of synthetic aperture and phase retrieval to surpass the resolution limit imposed by the employed objective lens. In the FPM framework, the position of each sub-spectrum needs to be accurately known to ensure the success of the phase retrieval process. Different from the conventional methods with mechanical adjustment or data-driven optimization strategies, here we report a physics-based defocusing strategy for correcting large-scale positional deviation of the LED illumination in FPM. Based on a subpixel image registration process with a defocused object, we can directly infer the illumination parameters including the lateral offsets of the light source, the in-plane rotation angle of the LED array, and the distance between the sample and the LED board. The feasibility and effectiveness of our method are validated with both simulations and experiments. We show that the reported strategy can obtain high-quality reconstructions of both the complex object and pupil function even the LED array is randomly placed under the sample with both unknown lateral offsets and rotations. As such, it enables the development of robust FPM systems by reducing the requirements on fine mechanical adjustment and data-driven correction in the construction process.

High-performance heterogeneous FPGA data-flow architecture for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed computational imaging technique that can achieve both high-resolution and a wide field-of-view via a sequence of low-resolution images. FPM is a complex iterative process, and it is difficult to meet the needs of rapid reconstruction imaging with the conventional FPM deployed on general purpose processors. In this paper, we propose a high-performance heterogeneous field-programmable gate array (FPGA) architecture based on the principle of full pipeline and the data-flow structure for the iterative reconstruction procedure of FPM. By optimizing the architecture network at gate-level logic circuits, the running time of the FPGA-based FPM reconstruction procedure is nearly 20 times faster than conventional methods. Our proposed architecture can be used to develop FPM imaging equipment that meets resource and performance requirements.

Snapshot ptychography on array cameras

We use convolutional neural networks to recover images optically down-sampled by 6.7 × using coherent aperture synthesis over a 16 camera array. Where conventional ptychography relies on scanning and oversampling, here we apply decompressive neural estimation to recover full resolution image from a single snapshot, although as shown in simulation multiple snapshots can be used to improve signal-to-noise ratio (SNR). In place training on experimental measurements eliminates the need to directly calibrate the measurement system. We also present simulations of diverse array camera sampling strategies to explore how snapshot compressive systems might be optimized.

Review of bio-optical imaging systems with a high space-bandwidth product

Optical imaging has served as a primary method to collect information about biosystems across scales-from functionalities of tissues to morphological structures of cells and even at biomolecular levels. However, to adequately characterize a complex biosystem, an imaging system with a number of resolvable points, referred to as a space-bandwidth product (SBP), in excess of one billion is typically needed. Since a gigapixel-scale far exceeds the capacity of current optical imagers, compromises must be made to obtain either a low spatial resolution or a narrow field-of-view (FOV). The problem originates from constituent refractive optics-the larger the aperture, the more challenging the correction of lens aberrations. Therefore, it is impractical for a conventional optical imaging system to achieve an SBP over hundreds of millions. To address this unmet need, a variety of high-SBP imagers have emerged over the past decade, enabling an unprecedented resolution and FOV beyond the limit of conventional optics. We provide a comprehensive survey of high-SBP imaging techniques, exploring their underlying principles and applications in bioimaging.

Quantitative reconstruction of the complex-valued object based on complementary phase modulations

In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

Optical scanning Fourier ptychographic microscopy

We propose a lower-cost and practical active scanning optical scanning Fourier ptychographic microscopy (OSFPM). Featured is a simple setup of Galvo mirrors capable of scanning large-sized objects. The active scanning laser beam is projected onto the sample in a circular pattern to form multiple lower-resolution images. With multiple lower-resolution images, a higher-resolution image is subsequently reconstructed. The OSFPM is able to more precisely control the overlap of the incident light illumination as compared to that in conventional LED-based or other laser-based scanning FPM systems. The proposed microscope is also suitable for applications where a larger size of the object needs to be imaged with efficient illumination.

Coherent synthetic aperture imaging for visible remote sensing via reflective Fourier ptychography

Synthetic aperture radar can measure the phase of a microwave with an antenna, which cannot be directly extended to visible light imaging due to phase lost. In this Letter, we report an active remote sensing with visible light via reflective Fourier ptychography, termed coherent synthetic aperture imaging (CSAI), achieving high resolution, a wide field-of-view (FOV), and phase recovery. A proof-of-concept experiment is reported with laser scanning and a collimator for the infinite object. Both smooth and rough objects are tested, and the spatial resolution increased from 15.6 to 3.48 µm with a factor of 4.5. The speckle noise can be suppressed obviously, which is important for coherent imaging. Meanwhile, the CSAI method can tackle the aberration induced from the optical system by one-step deconvolution and shows the potential to replace the adaptive optics for aberration removal of atmospheric turbulence.

Miniaturized modular-array fluorescence microscopy

Fluorescence live-cell imaging allows for continuous interrogation of cellular behaviors, and the recent development of portable live-cell imaging platforms has rapidly transformed conventional schemes with high adaptability, cost-effective functionalities and easy accessibility to cell-based assays. However, broader applications remain restrictive due to compatibility with conventional cell culture workflow and biochemical sensors, accessibility to up-right physiological imaging, or parallelization of data acquisition. Here, we introduce miniaturized modular-array fluorescence microscopy (MAM) for compact live-cell imaging in flexible formats. We advance the current miniscopy technology to devise an up-right modular architecture, each combining a gradient-index (GRIN) objective and individually-addressed illumination and acquisition components. Parallelization of an array of such modular devices allows for multi-site data acquisition in situ using conventional off-the-shelf cell chambers. Compared with existing methods, the device offers a high fluorescence sensitivity and efficiency, exquisite spatiotemporal resolution (∼3 µm and up to 60 Hz), a configuration compatible with conventional cell culture assays and physiological imaging, and an effective parallelization of data acquisition. The system has been demonstrated using various calibration and biological samples and experimental conditions, representing a promising solution to time-lapse in situ single-cell imaging and analysis.

High-resolution and large field-of-view Fourier ptychographic microscopy and its applications in biomedicine

Fourier ptychographic microscopy (FPM) is a promising and fast-growing computational imaging technique with high resolution, wide field-of-view (FOV) and quantitative phase recovery, which effectively tackles the problems of phase loss, aberration-introduced artifacts, narrow depth-of-field and the trade-off between resolution and FOV in conventional microscopy simultaneously. In this review, we provide a comprehensive roadmap of microscopy, the fundamental principles, advantages, and drawbacks of existing imaging techniques, and the significant roles that FPM plays in the development of science. Since FPM is an optimization problem in nature, we discuss the framework and related work. We also reveal the connection of Euler's formula between FPM and structured illumination microscopy. We review recent advances in FPM, including the implementation of high-precision quantitative phase imaging, high-throughput imaging, high-speed imaging, three-dimensional imaging, mixed-state decoupling, and introduce the prosperous biomedical applications. We conclude by discussing the challenging problems and future applications. FPM can be extended to a kind of framework to tackle the phase loss and system limits in the imaging system. This insight can be used easily in speckle imaging, incoherent imaging for retina imaging, large-FOV fluorescence imaging, etc.

Fourier ptychography: current applications and future promises

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either "zoom in" and image at high-resolution, or they can "zoom out" to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.