High-speed Fourier ptychographic microscopy based on programmable annular illuminations

Classifying breast cancer and fibroadenoma tissue biopsies from paraffined stain-free slides by fractal biomarkers in Fourier Ptychographic Microscopy

Breast cancer is one of the most spread and monitored pathologies in high-income countries. After breast biopsy, histological tissue is stored in paraffin, sectioned and mounted. Conventional inspection of tissue slides under benchtop light microscopes involves paraffin removal and staining, typically with H&E. Then, expert pathologists are called to judge the stained slides. However, paraffin removal and staining are operator-dependent, time and resources consuming processes that can generate ambiguities due to non-uniform staining. Here we propose a novel method that can work directly on paraffined stain-free slides. We use Fourier Ptychography as a quantitative phase-contrast microscopy method, which allows accessing a very wide field of view (i.e., mm2) in one single image while guaranteeing high lateral resolution (i.e., 0.5 µm). This imaging method is multi-scale, since it enables looking at the big picture, i.e. the complex tissue structure and connections, with the possibility to zoom-in up to the single-cell level. To handle this informative image content, we introduce elements of fractal geometry as multi-scale analysis method. We show the effectiveness of fractal features in describing and classifying fibroadenoma and breast cancer tissue slides from ten patients with very high accuracy. We reach 94.0 ± 4.2% test accuracy in classifying single images. Above all, we show that combining the decisions of the single images, each patient's slide can be classified with no error. Besides, fractal geometry returns a guide map to help pathologist to judge the different tissue portions based on the likelihood these can be associated to a breast cancer or fibroadenoma biomarker. The proposed automatic method could significantly simplify the steps of tissue analysis and make it independent from the sample preparation, the skills of the lab operator and the pathologist.

Roadmap on computational methods in optical imaging and holography [invited]

Computational methods have been established as cornerstones in optical imaging and holography in recent years. Every year, the dependence of optical imaging and holography on computational methods is increasing significantly to the extent that optical methods and components are being completely and efficiently replaced with computational methods at low cost. This roadmap reviews the current scenario in four major areas namely incoherent digital holography, quantitative phase imaging, imaging through scattering layers, and super-resolution imaging. In addition to registering the perspectives of the modern-day architects of the above research areas, the roadmap also reports some of the latest studies on the topic. Computational codes and pseudocodes are presented for computational methods in a plug-and-play fashion for readers to not only read and understand but also practice the latest algorithms with their data. We believe that this roadmap will be a valuable tool for analyzing the current trends in computational methods to predict and prepare the future of computational methods in optical imaging and holography.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00340-024-08280-3.

Quantitative phase imaging based on holography: trends and new perspectives

In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.

Ultra-high spatio-temporal resolution imaging with parallel acquisition-readout structured illumination microscopy (PAR-SIM)

Structured illumination microscopy (SIM) has emerged as a promising super-resolution fluorescence imaging technique, offering diverse configurations and computational strategies to mitigate phototoxicity during real-time imaging of biological specimens. Traditional efforts to enhance system frame rates have concentrated on processing algorithms, like rolling reconstruction or reduced frame reconstruction, or on investments in costly sCMOS cameras with accelerated row readout rates. In this article, we introduce an approach to elevate SIM frame rates and region of interest (ROI) coverage at the hardware level, without necessitating an upsurge in camera expenses or intricate algorithms. Here, parallel acquisition-readout SIM (PAR-SIM) achieves the highest imaging speed for fluorescence imaging at currently available detector sensitivity. By using the full frame-width of the detector through synchronizing the pattern generation and image exposure-readout process, we have achieved a fundamentally stupendous information spatial-temporal flux of 132.9 MPixels · s-1, 9.6-fold that of the latest techniques, with the lowest SNR of -2.11 dB and 100 nm resolution. PAR-SIM demonstrates its proficiency in successfully reconstructing diverse cellular organelles in dual excitations, even under conditions of low signal due to ultra-short exposure times. Notably, mitochondrial dynamic tubulation and ongoing membrane fusion processes have been captured in live COS-7 cell, recorded with PAR-SIM at an impressive 408 Hz. We posit that this novel parallel exposure-readout mode not only augments SIM pattern modulation for superior frame rates but also holds the potential to benefit other complex imaging systems with a strategic controlling approach.

Multi-scale fractal Fourier Ptychographic microscopy to assess the dose-dependent impact of copper pollution on living diatoms

Accumulation of bioavailable heavy metals in aquatic environment poses a serious threat to marine communities and human health due to possible trophic transfers through the food chain of toxic, non-degradable, exogenous pollutants. Copper (Cu) is one of the most spread heavy metals in water, and can severely affect primary producers at high doses. Here we show a novel imaging test to assay the dose-dependent effects of Cu on live microalgae identifying stress conditions when they are still capable of sustaining a positive growth. The method relies on Fourier Ptychographic Microscopy (FPM), capable to image large field of view in label-free phase-contrast mode attaining submicron lateral resolution. We uniquely combine FPM with a new multi-scale analysis method based on fractal geometry. The system is able to provide ensemble measurements of thousands of diatoms in the liquid sample simultaneously, while ensuring at same time single-cell imaging and analysis for each diatom. Through new image descriptors, we demonstrate that fractal analysis is suitable for handling the complexity and informative power of such multiscale FPM modality. We successfully tested this new approach by measuring how different concentrations of Cu impact on Skeletonema pseudocostatum diatom populations isolated from the Sarno River mouth.

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.

Fast digital refocusing Fourier ptychographic microscopy method based on convolutional neural network

Fourier ptychographic microscopy (FPM) is used to achieve high resolution and a large field of view. However, traditional FPM image reconstruction methods often yield poor image quality when encountering out-of-focus issues during reconstruction. Therefore, this study proposes a defocus-distance regression network based on convolutional neural networks. In an experimental validation, the root-mean-square error calculated from 1000 sets of predicted and true values was approximately 6.2 µm. The experimental results suggest that the proposed method has good generalization, maintains high accuracy in predicting defocus distances even for different biological samples, and extends the imaging depth-of-field of the FPM system by a factor of more than 3.

On the use of deep learning for phase recovery

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing the refractive index distribution or topography of an object and correcting the aberration of an imaging system. In recent years, deep learning (DL), often implemented through deep neural networks, has provided unprecedented support for computational imaging, leading to more efficient solutions for various PR problems. In this review, we first briefly introduce conventional methods for PR. Then, we review how DL provides support for PR from the following three stages, namely, pre-processing, in-processing, and post-processing. We also review how DL is used in phase image processing. Finally, we summarize the work in DL for PR and provide an outlook on how to better use DL to improve the reliability and efficiency of PR. Furthermore, we present a live-updating resource ( https://github.com/kqwang/phase-recovery ) for readers to learn more about PR.

Fast Fourier ptychographic quantitative phase microscopy for in vitro label-free imaging

Quantitative phase microscopy (QPM) is indispensable in biomedical research due to its advantages in unlabeled transparent sample thickness quantification and obtaining refractive index information. Fourier ptychographic microscopy (FPM) is among the most promising QPM methods, incorporating multi-angle illumination and iterative phase recovery for high-resolution quantitative phase imaging (QPI) of large cell populations over a wide field of-view (FOV) in a single pass. However, FPM is limited by data redundancy and sequential acquisition strategies, resulting in low imaging efficiency, which in turn limits its real-time application in in vitro label-free imaging. Here, we report a fast QPM based on Fourier ptychography (FQP-FPM), which uses an optimized annular downsampling and parallel acquisition strategy to minimize the amount of data required in the front end and reduce the iteration time of the back-end algorithm (3.3% and 4.4% of conventional FPM, respectively). Theoretical and data redundancy analyses show that FQP-FPM can realize high-throughput quantitative phase reconstruction at thrice the resolution of the coherent diffraction limit by acquiring only ten raw images, providing a precondition for in vitro label-free real-time imaging. The FQP-FPM application was validated for various in vitro label-free live-cell imaging. Cell morphology and subcellular phenomena in different periods were observed with a synthetic aperture of 0.75 NA at a 10× FOV, demonstrating its advantages and application potential for fast high-throughput QPI.

Fast and robust Fourier ptychographic microscopy with position misalignment correction

Significance

Fourier ptychographic microscopy (FPM) is a new, developing computational imaging technology. It can realize the quantitative phase imaging of a wide field of view and high-resolution (HR) simultaneously by means of multi-angle illumination via a light emitting diode (LED) array, combined with a phase recovery algorithm and the synthetic aperture principle. However, in the FPM reconstruction process, LED position misalignment affects the quality of the reconstructed image, and the reconstruction efficiency of the existing LED position correction algorithms needs to be improved.

Aim

This study aims to improve the FPM correction method based on simulated annealing (SA) and proposes a position misalignment correction method (AA-C algorithm) using an improved phase recovery strategy.

Approach

The spectrum function update strategy was optimized by adding an adaptive control factor, and the reconstruction efficiency of the algorithm was improved.

Results

The experimental results show that the proposed method is effective and robust for position misalignment correction of LED arrays in FPM, and the convergence speed can be improved by 21.2% and 54.9% compared with SC-FPM and PC-FPM, respectively.

Conclusions

These results can reduce the requirement of the FPM system for LED array accuracy and improve robustness.

Investigating the Joint Amplitude and Phase Imaging of Stained Samples in Automatic Diagnosis

The diagnosis of many diseases relies, at least on first intention, on an analysis of blood smears acquired with a microscope. However, image quality is often insufficient for the automation of such processing. A promising improvement concerns the acquisition of enriched information on samples. In particular, Quantitative Phase Imaging (QPI) techniques, which allow the digitization of the phase in complement to the intensity, are attracting growing interest. Such imaging allows the exploration of transparent objects not visible in the intensity image using the phase image only. Another direction proposes using stained images to reveal some characteristics of the cells in the intensity image; in this case, the phase information is not exploited. In this paper, we question the interest of using the bi-modal information brought by intensity and phase in a QPI acquisition when the samples are stained. We consider the problem of detecting parasitized red blood cells for diagnosing malaria from stained blood smears using a Deep Neural Network (DNN). Fourier Ptychographic Microscopy (FPM) is used as the computational microscopy framework to produce QPI images. We show that the bi-modal information enhances the detection performance by 4% compared to the intensity image only when the convolution in the DNN is implemented through a complex-based formalism. This proves that the DNN can benefit from the bi-modal enhanced information. We conjecture that these results should extend to other applications processed through QPI acquisition.

Fourier ptychographic microscopy image enhancement with bi-modal deep learning

Digital pathology based on a whole slide imaging system is about to permit a major breakthrough in automated diagnosis for rapid and highly sensitive disease detection. High-resolution FPM (Fourier ptychographic microscopy) slide scanners delivering rich information on biological samples are becoming available. They allow new effective data exploitation for efficient automated diagnosis. However, when the sample thickness becomes comparable to or greater than the microscope depth of field, we report an observation of undesirable contrast change of sub-cellular compartments in phase images around the optimal focal plane, reducing their usability. In this article, a bi-modal U-Net artificial neural network (i.e., a two channels U-Net fed with intensity and phase images) is trained to reinforce specifically targeted sub-cellular compartments contrast for both intensity and phase images. The procedure used to construct a reference database is detailed. It is obtained by exploiting the FPM reconstruction algorithm to explore images around the optimal focal plane with virtual Z-stacking calculations and selecting those with adequate contrast and focus. By construction and once trained, the U-Net is able to simultaneously reinforce targeted cell compartment visibility and compensate for any focus imprecision. It is efficient over a large field of view at high resolution. The interest of the approach is illustrated considering the use-case of Plasmodium falciparum detection in blood smear where improvement in the detection sensitivity is demonstrated without degradation of the specificity. Post-reconstruction FPM image processing with such U-Net and its training procedure is general and applicable to demanding biological screening applications.

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.

ROCS microscopy with distinct zero-order blocking

Research in modern light microscopy continuously seeks to improve spatial and temporal resolution in combination with user-friendly, cost-effective imaging systems. Among different label-free imaging approaches, Rotating Coherent Scattering (ROCS) microscopy in darkfield mode achieves superior resolution and contrast without image reconstructions, which is especially helpful in life cell experiments. Here we demonstrate how to achieve 145 nm resolution with an amplitude transmission mask for spatial filtering. This mask blocks the reflected 0-th order focus at 12 distinct positions, thereby increasing the effective aperture for the light back-scattered from the object. We further show how angular correlation analysis between coherent raw images helps to estimate the information content from different illumination directions.

Fourier ptychographic microscopy with untrained deep neural network priors

We propose a physics-assisted deep neural network scheme in Fourier ptychographic microscopy (FPM) using untrained deep neural network priors (FPMUP) to achieve a high-resolution image reconstruction from multiple low-resolution images. Unlike the traditional training type of deep neural network that requires a large labelled dataset, this proposed scheme does not require training and instead outputs the high-resolution image by optimizing the parameters of neural networks to fit the experimentally measured low-resolution images. Besides the amplitude and phase of the sample function, another two parallel neural networks that generate the general pupil function and illumination intensity factors are incorporated into the carefully designed neural networks, which effectively improves the image quality and robustness when both the aberration and illumination intensity fluctuation are present in FPM. Reconstructions using simulated and experimental datasets are demonstrated, showing that the FPMUP scheme has better image quality than the traditional iterative algorithms, especially for the phase recovery, but at the expense of increasing computational cost. Most importantly, it is found that the FPMUP scheme can predict the Fourier spectrum of the sample outside synthetic aperture of FPM and thus eliminate the ringing effect of the recovered images due to the spectral truncation. Inspired by deep image prior in the field of image processing, we may impute the expansion of Fourier spectrums to the deep prior rooted in the architecture of the careful designed four parallel deep neural networks. We envisage that the resolution of FPM will be further enhanced if the Fourier spectrum of the sample outside the synthetic aperture of FPM is accurately predicted.

Integration of Fourier ptychography with machine learning: an alternative scheme

As the core task of the reconstruction in conventional ptychography (CP) and Fourier ptychographic microscopy (FPM), the meticulous design of ptychographical iterative engine (PIE) largely affects the performance of reconstruction algorithms. Compared to traditional PIE algorithms, the paradigm of combining with machine learning to cross a local optimum has recently achieved significant progress. Nevertheless, existing designed engines still suffer drawbacks such as excessive hyper-parameters, heavy tuning work and lack of compatibility, which greatly limit their practical applications. In this work, we present a complete set of alternative schemes comprised of a kind of new perspective, a uniform design template, and a fusion framework, to naturally integrate Fourier ptychography (FP) with machine learning concepts. The new perspective, Dynamic Physics, is taken as the preferred tool to analyze a path (algorithm) at the physical level; the uniform design template, T-FP, clarifies the physical significance and optimization part in a path; the fusion framework follows two workable guidelines that are specially designed to keep convergence and make later localized modification for a new path, and further establishes a link between FP iterations and the gradient update in machine learning. Our scheme is compatible with both traditional FP paths and machine learning concepts. By combining ideas in both fields, we offer two design examples, MaFP and AdamFP. Results for both simulations and experiments show that designed algorithms following our scheme obtain better, faster (converge at the early stage after a few iterations) and more stable recovery with only minimal tuning hyper-parameters, demonstrating the effectiveness and superiority of our scheme.

Spectrum sampling optimization for quantitative phase imaging based on Kramers-Kronig relations

Annular-illumination quantitative phase imaging based on space-domain Kramers-Kronig relations (AIKK) is a newly developed technique that is object-independent and non-iterative reconstructed inherently. Only capturing four low-resolution images, the AIKK system gains a resolution enhancement of nearly twofold. Under matching constraints between the illumination wave vector and pupil function aperture, we set a spectrum sampling criterion and establish a spectrum effective utilization model to search for the optimal solution of spectrum distribution for the specific annular structure. In view of the square spectrum structure, a diagonal-expanded sampling based AIKK method (DES-AIKK) is presented to get rid of the pixel aliasing problem. It is worth noting that the space-bandwidth-time product (SBP-T) further increases to 439.51 megapixels (1.8× of AIKK). Our work provides the guidelines and insights for designing the most suitable AIKK platform for high-throughput microscopic applications in pathology and real-time dynamic observation.

Annular illumination in 2D quantitative phase imaging: a systematic evaluation

Quantitative phase imaging (QPI) is an invaluable microscopic technology for definitively imaging phase objects such as biological cells and optical fibers. Traditionally, the condenser lens in QPI produces disk illumination of the object. However, it has been realized by numerous investigators that annular illumination can produce higher-resolution images. Although this performance improvement is impressive and well documented, the evidence presented has invariably been qualitative in nature. Recently, a theoretical basis for annular illumination was presented by Bao et al. [Appl. Opt.58, 137 (2019)APOPAI0003-693510.1364/AO.58.000137]. In our current work, systematic experimental QPI measurements are made with a reference phase mask to rigorously document the performance of annular illumination. In both theory and experiment, three spatial-frequency regions are identified: low, mid, and high. The low spatial-frequency region response is very similar for disk and annular illumination, both theoretically and experimentally. Theoretically, the high spatial-frequency region response is predicted to be much better for the annular illumination compared to the disk illumination--and is experimentally confirmed. In addition, the mid-spatial-frequency region response is theoretically predicted to be less for annular illumination than for disk illumination. This theoretical degradation of the mid-spatial-frequency region is only slightly experimentally observed. This bonus, although not well understood, further elevates the performance of annular illumination over disk illumination.

Synthetic aperture interference light (SAIL) microscopy for high-throughput label-free imaging

Quantitative phase imaging (QPI) is a valuable label-free modality that has gained significant interest due to its wide potentials, from basic biology to clinical applications. Most existing QPI systems measure microscopic objects via interferometry or nonlinear iterative phase reconstructions from intensity measurements. However, all imaging systems compromise spatial resolution for the field of view and vice versa, i.e., suffer from a limited space bandwidth product. Current solutions to this problem involve computational phase retrieval algorithms, which are time-consuming and often suffer from convergence problems. In this article, we presented synthetic aperture interference light (SAIL) microscopy as a solution for high-resolution, wide field of view QPI. The proposed approach employs low-coherence interferometry to directly measure the optical phase delay under different illumination angles and produces large space-bandwidth product label-free imaging. We validate the performance of SAIL on standard samples and illustrate the biomedical applications on various specimens: pathology slides, entire insects, and dynamic live cells in large cultures. The reconstructed images have a synthetic numeric aperture of 0.45 and a field of view of 2.6 × 2.6 mm2. Due to its direct measurement of the phase information, SAIL microscopy does not require long computational time, eliminates data redundancy, and always converges.

High-speed Fourier ptychographic microscopy for quantitative phase imaging

Fourier ptychographic microscopy (FPM), as an emerging computational imaging method, has been applied to quantitative phase imaging with resolution bypassing the physical limit of the detection objective. Due to the weak illumination intensity and long image acquisition time, the achieved imaging speed in current FPM methods is still low, making them unsuitable for real-time imaging applications. We propose and demonstrate a high-speed FPM method based on using laser illumination and digital micro-mirror devices for illumination angle scanning. In this new, to the best of our knowledge, FPM method, we realized quantitative phase imaging and intensity imaging at over 42 frames per second (fps) with around 1 µm lateral resolution. The quantitative phase images have revealed membrane height fluctuations of red blood cells with nanometer-scale sensitivity, while the intensity images have resolved subcellular features in stained cancer tissue slices.

Virtual optics and sensing of the retrieved complex field in the back focal plane using a constrained defocus algorithm

The reflected back focal plane from a microscope objective is known to provide excellent information of material properties and can be used to analyze the generation of surface plasmons and surface waves in a localized region. Most analysis has concentrated on direct measurement of the reflected intensity in the back focal plane. By accessing the phase information, we show that examination in the back focal plane becomes considerably more powerful allowing the reconstructed field to be filtered, propagated and analyzed in different domains. Moreover, the phase often gives a superior measurement that is far easier to use in the assessment of the sample, an example of such cases is examined in the present paper. We discuss how the modified defocus phase retrieval algorithm has the potential for real time measurements with parallel image acquisition since only three images are needed for reliable retrieval of arbitrary distributions.

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.

Digital refocusing and extended depth of field reconstruction in Fourier ptychographic microscopy

Fourier ptychography microscopy (FPM) is a recently developed microscopic imaging method that allows the recovery of a high-resolution complex image by combining a sequence of bright and darkfield images acquired under inclined illumination. The capacity of FPM for high resolution imaging at low magnification makes it particularly attractive for applications in digital pathology which require imaging of large specimens such as tissue sections and blood films. To date most applications of FPM have been limited to imaging thin samples, simplifying both image reconstruction and analysis. In this work we show that, for samples of intermediate thickness (defined here as less than the depth of field of a raw captured image), numerical propagation of the reconstructed complex field allows effective digital refocusing of FPM images. The results are validated by comparison against images obtained with an equivalent high numerical aperture objective lens. We find that post reconstruction refocusing (PRR) yields images comparable in quality to adding a defocus term to the pupil function within the reconstruction algorithm, while reducing computing time by several orders of magnitude. We apply PRR to visualize FPM images of Giemsa-stained peripheral blood films and present a novel image processing pipeline to construct an effective extended depth of field image which optimally displays the 3D sample structure in a 2D image. We also show how digital refocusing allows effective correction of the chromatic focus shifts inherent to the low magnification objective lenses used in FPM setups, improving the overall quality of color FPM images.

Ptychographic imaging of NaD1 induced yeast cell death

Characterising and understanding the mechanisms involved in cell death are especially important to combating threats to human health, particularly for the study of antimicrobial peptides and their effectiveness against pathogenic fungi. However, imaging these processes often relies on the use of synthetic molecules which bind to specific cellular targets to produce contrast. Here we study yeast cell death, induced by the anti-fungal peptide, NaD1. By treating yeast as a model organism we aim to understand anti-fungal cell death processes without relying on sample modification. Using a quantitative phase imaging technique, ptychography, we were able to produce label free images of yeast cells during death and use them to investigate the mode of action of NaD1. Using this technique we were able to identify a significant phase shift which provided a clear signature of yeast cell death. Additionally, ptychography identifies cell death much earlier than a comparative fluorescence study, providing new insights into the cellular changes that occur during cell death. The results indicate ptychography has great potential as a means of providing additional information about cellular processes which otherwise may be masked by indirect labelling approaches.

Optical Imaging Approaches to Monitor Static and Dynamic Cell-on-Chip Platforms: A Tutorial Review

Miniaturized laboratories on chip platforms play an important role in handling life sciences studies. The platforms may contain static or dynamic biological cells. Examples are a fixed medium of an organ-on-a-chip and individual cells moving in a microfluidic channel, respectively. Due to feasibility of control or investigation and ethical implications of live targets, both static and dynamic cell-on-chip platforms promise various applications in biology. To extract necessary information from the experiments, the demand for direct monitoring is rapidly increasing. Among different microscopy methods, optical imaging is a straightforward choice. Considering light interaction with biological agents, imaging signals may be generated as a result of scattering or emission effects from a sample. Thus, optical imaging techniques could be categorized into scattering-based and emission-based techniques. In this review, various optical imaging approaches used in monitoring static and dynamic platforms are introduced along with their optical systems, advantages, challenges, and applications. This review may help biologists to find a suitable imaging technique for different cell-on-chip studies and might also be useful for the people who are going to develop optical imaging systems in life sciences studies.

Weighted-least-squares multi-filter phase imaging with partially coherent light: characteristics of annular illumination

Multi-filter phase imaging with partially coherent light (MFPI-PC) is a promising microscopic quantitative phase imaging (QPI) method that measures the phase of a transparent object. In the present work, a weighted-least-squares version is developed and applied to the important case of annular illumination. The resulting improved algorithms have largely solved the noise magnification problem associated with the original MFPI-PC in annular illumination. Simulation and microlens experiments are used to validate the new QPI method for the case of annular illumination.

Wide-field anti-aliased quantitative differential phase contrast microscopy

Differential phase contrast (DPC) microscopy is a popular methodology to recover quantitative phase information of thin transparent samples under multi-axis asymmetric illumination patterns. Based on spatially partially coherent illuminations, DPC provides high-quality, speckle-free 3D reconstructions with lateral resolution up to twice the coherent diffraction limit, under the precondition that the pixel size of the imaging sensor is small enough to prevent spatial aliasing/undersampling. However, microscope cameras are in general designed to have a large pixel size so that the intensity information transmitted by the optical system cannot be adequately sampled or digitized. On the other hand, using an image sensor with a smaller pixel size or adding a magnification camera adapter to the camera can resolve the undersampling at the expense of a reduced field of view (FOV). To solve this tradeoff, we introduce a new variation of quantitative DPC approach, termed anti-aliased DPC (AADPC), which uses several aliased intensity images under asymmetric illuminations to recover wide-field aliasing-free phase images. Besides, phase transfer functions under different illumination patterns in DPC are analyzed to design an illumination scheme with better phase transfer characteristics. AADPC starts from an initial phase estimate obtained by a DPC-like deconvolution based on the system's weak phase transfer function under discrete half-annular illumination. Then the obtained initial phase map is further refined by the iterative de-multiplexing algorithm to overcome pixel-aliasing and improve the imaging resolution. The data redundancy requirement as well as the optimal illumination scheme of AADPC are analyzed and discussed based on several simulations, suggesting that the spatial undersampling can be mitigated through the iterative algorithm that uses only 4 images, yielding a nearly 4-fold increase in the space-bandwidth product (SBP) compared to the conventional DPC approach. We experimentally verify that AADPC can achieve a half-pitch imaging resolution of 345 nm, corresponding to 1.88× of the theoretical Nyquist-Shannon sampling resolution limit imposed by the sensor pixel size. The high-speed, high-throughput quantitative phase imaging capabilities of AADPC are also demonstrated by imaging HeLa cells mitosis in vitro, achieving a full-pitch lateral resolution of 665 nm across a wide FOV of 1.77mm² at 25 fps.

Near-field ptychographic microscope for quantitative phase imaging

Quantitative phase imaging (QPI) is the name given to a set of microscopy techniques that map out variations in optical path lengths across a sample. These maps are a useful source of contrast for transparent samples such as biological cells, and because they are quantitative they can be used to measure refractive index and thickness variations. Here we detail the setup and operation of a new form of QPI microscope based on near-field ptychography. We test our system using a range of phase objects, and analyse the phase images it produces. Our results show that accurate, high quality images can be obtained from a ptychographical dataset containing as few as four near-field diffraction patterns. We also assess how our system copes with optically thick samples and samples with a wide range of spatial frequencies - two areas where conventional and Fourier ptychography struggle.

Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography

We present a single-shot quantitative phase imaging (QPI) method based on color-multiplexed Fourier ptychographic microscopy (FPM). Three light-emitting diode (LED) elements with respective R/G/B channels in a programmable LED array illuminate the specimen simultaneously, providing triangle oblique illuminations matching the numerical aperture of the objective precisely. A color image sensor records the light transmitted through the specimen, and three monochromatic intensity images at each color channel are then separated and utilized to recover the phase of the specimen. After one-step deconvolution based on the phase contrast transfer function, the obtained initial phase map is further refined by the FPM-based iterative recovery algorithm to overcome pixel-aliasing and improve the phase recovery accuracy. The high-speed, high-throughput QPI capabilities of the proposed approach are demonstrated by imaging HeLa cells mitosis in vitro, achieving a half-pitch resolution of 388 nm across a wide field of view of 1.33  mm² at camera-limited frame rates (50 fps).