Efficient illumination angle self-calibration in Fourier ptychography

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.

DMD and microlens array as a switchable module for illumination angle scanning in optical diffraction tomography

Optical diffraction tomography (ODT) enables label-free and morphological 3D imaging of biological samples using refractive-index (RI) contrast. To accomplish this, ODT systems typically capture multiple angular-specific scattering measurements, which are used to computationally reconstruct a sample's 3D RI. Standard ODT systems employ scanning mirrors to generate angular illuminations. However, scanning mirrors are limited to illuminating the sample from only one angle at a time. Furthermore, when operated at high speeds, these mirrors may exhibit mechanical instabilities that compromise image quality and measurement speed. Recently, newer ODT systems have been introduced that utilize digital-micromirror devices (DMD), spatial light modulators (SLMs), or LED arrays to achieve switchable angle-scanning with no physically-scanning components. However, these systems associate with power inefficiencies and/or spurious diffraction orders that can also limit imaging performance. In this work, we developed a novel non-interferometric ODT system that utilizes a fully switchable module for angle scanning composed of a DMD and microlens array (MLA). Compared to other switchable ODT systems, this module enables each illumination angle to be generated fully independently from every other illumination angle (i.e., no spurious diffraction orders) while also optimizing the power efficiency based on the required density of illumination angles. We validate the quantitative imaging capability of this system using calibration microspheres. We also demonstrate its capability for imaging multiple-scattering samples by imaging an early-stage zebrafish embryo.

Transformed pupil-function misalignment calibration strategy for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is an enabling quantitative phase imaging technique with both high-resolution (HR) and wide field-of-view (FOV), which can surpass the diffraction limit of the objective lens by employing an LED array to provide angular-varying illumination. The precise illumination angles are critical to ensure exact reconstruction, while it's difficult to separate actual positional parameters in conventional algorithmic self-calibration approaches due to the mixing of multiple systematic error sources. In this paper, we report a pupil-function-based strategy for independently calibrating the position of LED array. We first deduce the relationship between positional deviation and pupil function in the Fourier domain through a common iterative route. Then, we propose a judgment criterion to determine the misalignment situations, which is based on the arrangement of LED array in the spatial domain. By combining the mapping of complex domains, we can accurately solve the spatial positional parameters concerning the LED array through a boundary-finding scheme. Relevant simulations and experiments demonstrate the proposed method is accessible to precisely correct the positional misalignment of LED array. The approach based on the pupil function is expected to provide valuable insights for precise position correction in the field of microscopy.

LED array microscopy system correction method with comprehensive error parameters optimized by phase smoothing criterion

LED array microscopy is a novel computational imaging technique that can achieve two-dimensional (2D) phase imaging and three-dimensional (3D) refractive index imaging with both high resolution and a large field of view. Although its experimental setup is simple, the errors caused by LED array position and light source central wavelength obviously decrease the quality of reconstructed results. To solve this problem, comprehensive error parameters optimized by the phase smoothing criterion are put forward in this paper. The central wavelength error and 3D misalignment model with six freedom degree errors of LED array are considered as the comprehensive error parameters when the spatial positional and optical features of arbitrarily placed LED array are unknown. Phase smoothing criterion is also introduced to the cost function for optimizing comprehensive error parameters to improve the convergence results. Compared with current system correction methods, the simulation and experimental results show that the proposed method in this paper has the best reconstruction accuracy, which can be well applied to an LED array microscope system with unknown positional and optical features of the LED array.

Three-dimensional refractive index estimation based on deep-inverse non-interferometric optical diffraction tomography (ODT-Deep)

Optical diffraction tomography (ODT) solves an inverse scattering problem to obtain label-free, 3D refractive index (RI) estimation of biological specimens. This work demonstrates 3D RI retrieval methods suitable for partially-coherent ODT systems supported by intensity-only measurements consisting of axial and angular illumination scanning. This framework allows for access to 3D quantitative RI contrast using a simplified non-interferometric technique. We consider a traditional iterative tomographic solver based on a multiple in-plane representation of the optical scattering process and gradient descent optimization adapted for focus-scanning systems, as well as an approach that relies solely on 3D convolutional neural networks (CNNs) to invert the scattering process. The approaches are validated using simulations of the 3D scattering potential for weak phase 3D biological samples.

Hybrid full-pose parameter calibration of a freeform illuminator for Fourier ptychographic microscopy

As a typical computational method, Fourier ptychographic microscopy (FPM) can realize high spatial resolution and quantitative phase imaging while preserving the large field of view with a low numerical aperture (NA) objective. A programmable light-emitting diode (LED) array is used as a typical illuminator in an FPM system, and the illumination parameters of each LED element are crucial to the success of the FPM reconstruction algorithm. Compared with LED arrays arranged in rectangular arrays, LED arrays with special structures such as domes or rings can effectively improve FPM imaging results and imaging efficiency. As a trade-off, their calibration difficulty is greatly increased due to the lack of geometric constraints of rectangular arrays. In this paper, we propose an effective hybrid full-pose parameter calibration method for freeform LED array illuminators, combining stereoscopic 3D imaging techniques and the geometric constraints of the microscopic platform. First, a stereovision system is used to obtain the accurate 3D position of each LED element of the freeform illuminator and to construct a rigid 3D coordinate LED array system. Then, calibration between the coordinate system of the LED array and that of the optical imaging component is realized according to the geometric features of the brightfield-to-darkfield edges. Finally, we verify the feasibility and effectiveness of the proposed method through full-pose parameter calibration of LED arrays with different arrangement rules.

Polarization-sensitive intensity diffraction tomography

Optical anisotropy, which is an intrinsic property of many materials, originates from the structural arrangement of molecular structures, and to date, various polarization-sensitive imaging (PSI) methods have been developed to investigate the nature of anisotropic materials. In particular, the recently developed tomographic PSI technologies enable the investigation of anisotropic materials through volumetric mappings of the anisotropy distribution of these materials. However, these reported methods mostly operate on a single scattering model, and are thus not suitable for three-dimensional (3D) PSI imaging of multiple scattering samples. Here, we present a novel reference-free 3D polarization-sensitive computational imaging technique-polarization-sensitive intensity diffraction tomography (PS-IDT)-that enables the reconstruction of 3D anisotropy distribution of both weakly and multiple scattering specimens from multiple intensity-only measurements. A 3D anisotropic object is illuminated by circularly polarized plane waves at various illumination angles to encode the isotropic and anisotropic structural information into 2D intensity information. These information are then recorded separately through two orthogonal analyzer states, and a 3D Jones matrix is iteratively reconstructed based on the vectorial multi-slice beam propagation model and gradient descent method. We demonstrate the 3D anisotropy imaging capabilities of PS-IDT by presenting 3D anisotropy maps of various samples, including potato starch granules and tardigrade.

Using symmetric illumination and color camera to achieve high throughput Fourier ptychographic microscopy

This study aims to develop a high throughput Fourier ptychographic microscopy (FPM) technique based on symmetric illumination and a color detector, which is able to accelerate image acquisition by up to 12 times. As an emerging technology, the efficiency of FPM is limited by its data acquisition process, especially for color microscope image reconstruction. To overcome this, we built an FPM prototype equipped with a color camera and a 4×/0.13 NA objective lens. During the image acquisition, two symmetric LEDs illuminate the sample simultaneously using white light, which doubles the light intensity and reduces the total captured raw patterns by half. A standard USAF 1951 resolution target was used to measure the system's modulation transfer function (MTF) curve, and the H&E-stained ovarian cancer samples were then imaged to assess the feature qualities depicted on the reconstructed images. The results showed that the measured MTF curves of red, green, and blue channels are generally comparable to the corresponding curves generated by conventional FPM, while symmetric illumination FPM preserves more tissue details, which is superior to the results captured by conventional 20×/0.4 NA objective lens. This investigation initially verified the feasibility of symmetric illumination based color FPM.

PtyLab.m/py/jl: a cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography

Conventional (CP) and Fourier (FP) ptychography have emerged as versatile quantitative phase imaging techniques. While the main application cases for each technique are different, namely lens-less short wavelength imaging for CP and lens-based visible light imaging for FP, both methods share a common algorithmic ground. CP and FP have in part independently evolved to include experimentally robust forward models and inversion techniques. This separation has resulted in a plethora of algorithmic extensions, some of which have not crossed the boundary from one modality to the other. Here, we present an open source, cross-platform software, called PtyLab, enabling both CP and FP data analysis in a unified framework. With this framework, we aim to facilitate and accelerate cross-pollination between the two techniques. Moreover, the availability in Matlab, Python, and Julia will set a low barrier to enter each field.

Fourier ptychographic topography

Topography measurement is essential for surface characterization, semiconductor metrology, and inspection applications. To date, performing high-throughput and accurate topography remains challenging due to the trade-off between field-of-view (FOV) and spatial resolution. Here we demonstrate a novel topography technique based on the reflection-mode Fourier ptychographic microscopy, termed Fourier ptychograhpic topography (FPT). We show that FPT provides both a wide FOV and high resolution, and achieves nanoscale height reconstruction accuracy. Our FPT prototype is based on a custom-built computational microscope consisting of programmable brightfield and darkfield LED arrays. The topography reconstruction is performed by a sequential Gauss-Newton-based Fourier ptychographic phase retrieval algorithm augmented with total variation regularization. We achieve a synthetic numerical aperture (NA) of 0.84 and a diffraction-limited resolution of 750 nm, increasing the native objective NA (0.28) by 3×, across a 1.2 × 1.2 mm² FOV. We experimentally demonstrate the FPT on a variety of reflective samples with different patterned structures. The reconstructed resolution is validated on both amplitude and phase resolution test features. The accuracy of the reconstructed surface profile is benchmarked against high-resolution optical profilometry measurements. In addition, we show that the FPT provides robust surface profile reconstructions even on complex patterns with fine features that cannot be reliably measured by the standard optical profilometer. The spatial and temporal noise of our FPT system is characterized to be 0.529 nm and 0.027 nm, respectively.

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.

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-resolution polarization-sensitive Fourier ptychography microscopy using a high numerical aperture dome illuminator

Polarization-sensitive Fourier-ptychography microscopy (pFPM) allows for high resolution imaging while maintaining a large field of view, and without mechanical movements of optical-setup components. In contrast to ordinary light microscopes, pFPM provides quantitative absorption and phase information, for complex and birefringent specimens, with high resolution across a wide field of view. Using a semi-spherical home-built LED illumination array, a single polarizer, and a 10x /0.28NA objective, we experimentally demonstrate high performance pFPM with a synthesized NA of 1.1. Applying the standard quantitative method, a measured half-pitch resolution of 244 nm is achieved for the 1951 USAF resolution test target. As application examples, the polarimetric properties of a herbaceous flowering plant and the metastatic carcinoma of human liver cells are analyzed and quantitatively imaged.

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.

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.

Robust full-pose-parameter estimation for the LED array in Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) can achieve quantitative phase imaging with a large space-bandwidth product by synthesizing a set of low-resolution intensity images captured under angularly varying illuminations. Determining accurate illumination angles is critical because the consistency between actual systematic parameters and those used in the recovery algorithm is essential for high-quality imaging. This paper presents a full-pose-parameter and physics-based method for calibrating illumination angles. Using a physics-based model constructed with general knowledge of the employed microscope and the brightfield-to-darkfield boundaries inside captured images, we can solve for the full-pose parameters of misplaced LED array, which consist of the distance between the sample and the LED array, two orthogonal lateral shifts, one in-plane rotation angle, and two tilt angles, to correct illumination angles precisely. The feasibility and effectiveness of the proposed method for recovering random or remarkable pose parameters have been demonstrated by both qualitative and quantitative experiments. Due to the completeness of the pose parameters, the clarity of the physical model, and the high robustness for arbitrary misalignments, our method can significantly facilitate the design, implementation, and application of concise and robust FPM platforms.

Automated wide-field malaria parasite infection detection using Fourier ptychography on stain-free thin-smears

Diagnosis of malaria in endemic areas is hampered by the lack of a rapid, stain-free and sensitive method to directly identify parasites in peripheral blood. Herein, we report the use of Fourier ptychography to generate wide-field high-resolution quantitative phase images of erythrocytes infected with malaria parasites, from a whole blood sample. We are able to image thousands of erythrocytes (red blood cells) in a single field of view and make a determination of infection status of the quantitative phase image of each segmented cell based on machine learning (random forest) and deep learning (VGG16) models. Our random forest model makes use of morphology and texture based features of the quantitative phase images. In order to label the quantitative images of the cells as either infected or uninfected before training the models, we make use of a Plasmodium berghei strain expressing GFP (green fluorescent protein) in all life cycle stages. By overlaying the fluorescence image with the quantitative phase image we could identify the infected subpopulation of erythrocytes for labelling purposes. Our machine learning model (random forest) achieved 91% specificity and 72% sensitivity while our deep learning model (VGG16) achieved 98% specificity and 57% sensitivity. These results highlight the potential for quantitative phase imaging coupled with artificial intelligence to develop an easy to use platform for the rapid and sensitive diagnosis of malaria.

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.

Pose correction scheme for camera-scanning Fourier ptychography based on camera calibration and homography transform

Fourier ptychography (FP), as a computational imaging method, is a powerful tool to improve imaging resolution. Camera-scanning Fourier ptychography extends the application of FP from micro to macro creatively. Due to the non-ideal scanning of the camera driven by the mechanical translation stage, the pose error of the camera occurs, greatly degrading the reconstruction quality, while a precise translation stage is expensive and not suitable for wide-range imaging. Here, to improve the imaging performance of camera-scanning Fourier ptychography, we propose a pose correction scheme based on camera calibration and homography transform approaches. The scheme realizes the accurate alignment of data set and location error correction in the frequency domain. Simulation and experimental results demonstrate this method can optimize the reconstruction results and realize high-quality imaging effectively. Combined with the feature recognition algorithm, the scheme provides the possibility for applying FP in remote sensing imaging and space imaging.

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.

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.

Fourier ptychography multi-parameunter neural network with composite physical priori optimization

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

High-resolution 3D Fourier ptychographic reconstruction using a hemispherical illumination source with multiplexed-coded strategy

Fourier ptychography is a promising and flexible imaging technique that can achieve 2D quantitative reconstruction with higher resolution beyond the limitation of the system. Meanwhile, by using different imaging models, the same platform can be applied to achieve 3D refractive index reconstruction. To improve the illumination NA as much as possible while reducing the intensity attenuation problem caused by the LED board used in the traditional FP platform, we apply a hemispherical lighting structure and design a new LED arrangement according to 3D Fourier diffraction theory. Therefore, we could obtain the illumination of 0.98NA using 187 LEDs and achieve imaging half-pitch resolutions of ∼174 nm and ∼524 nm for the lateral and axial directions respectively, using a 40×/0.6NA objective lens. Furthermore, to reduce the number of captured images required and realize real-time data collection, we apply the multiplexed-coded illumination strategy and compare several coded patterns through simulation and experiment. Through comparison, we determined a radial-coded illumination pattern that could achieve more similar results as sequential scanning and increase the acquisition speed to above 1 Hz. Therefore, this paper provides the possibility of this technique in real-time 3D observation of in vitro live samples.

Self-calibrated 3D differential phase contrast microscopy with optimized illumination

3D phase imaging recovers an object's volumetric refractive index from intensity and/or holographic measurements. Partially coherent methods, such as illumination-based differential phase contrast (DPC), are particularly simple to implement in a commercial brightfield microscope. 3D DPC acquires images at multiple focus positions and with different illumination source patterns in order to reconstruct 3D refractive index. Here, we present a practical extension of the 3D DPC method that does not require a precise motion stage for scanning the focus and uses optimized illumination patterns for improved performance. The user scans the focus by hand, using the microscope's focus knob, and the algorithm self-calibrates the axial position to solve for the 3D refractive index of the sample through a computational inverse problem. We further show that the illumination patterns can be optimized by an end-to-end learning procedure. Combining these two, we demonstrate improved 3D DPC with a commercial microscope whose only hardware modification is LED array illumination.

Optical Diffraction Tomography Using Nearly In-Line Holography with a Broadband LED Source

We present optical tomography methods for a 3D refractive index reconstruction of weakly scattering objects using LED light sources. We are able to record holograms by minimizing the optical path difference between the signal and reference beams while separating the scattered field from its twin image. We recorded multiple holograms by illuminating the LEDs sequentially and reconstructed the 3D refractive index reconstruction of the sample. The reconstructions show high signal-to-noise ratio in which the effect of speckle artifacts is highly minimized due to the partially incoherent illumination of the LEDs. Results from combining different illumination wavelengths are also described demonstrating higher acquisition speed.

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.

Accurate and stable two-step LED position calibration method for Fourier ptychographic microscopy

SIGNIFICANCE

Fourier ptychography microscopy (FPM) is a computational optical imaging technology that employs angularly varying illuminations and a phase retrieval algorithm to achieve a wide field of view and high-resolution imaging simultaneously. In the FPM, LED position error will reduce the quality of the reconstructed high-resolution image. To correct the LED positions, current methods consider each of the LED positions as independent and use an optimization algorithm to get each of the positions. When the positional misalignment is large or the search position falls into a local optimal value, the current methods may lack stability and accuracy.

AIM

We improve the model of the LED position and propose an accurate and stable two-step correction scheme (tcFPM) to calibrate the LED position error.

APPROACH

The improved LED positions model combines the overall offset, which represents the relative deviation of the LED array and the optical axis, with the slight deviation of each LED's independent position. In the tcFPM, the overall offset of the LED array is corrected at first, which obtains an approximate value of the overall offset of the LED array. Then the position of each LED is precisely adjusted, which obtains the slight offset of each LED.

RESULTS

This LED position error model is more in line with the actual situation. The simulation and experimental results show that the method has high accuracy in correcting the LED position. Furthermore, the reconstruction process of tcFPM is more stable and significantly improves the quality of the reconstruction results, which is compared with some LED position error correction methods.

CONCLUSIONS

An LED position error correction technology is proposed, which has a stable iterative process and improves the reconstruction accuracy of complex amplitude.

Fast digital refocusing and depth of field extended Fourier ptychography microscopy

Fourier ptychography microscopy (FPM) shares its roots with the synthetic aperture technique and phase retrieval method, and is a recently developed computational microscopic super-resolution technique. By turning on the light-emitting diode (LED) elements sequentially and acquiring the corresponding images that contain different spatial frequencies, FPM can achieve a wide field-of-view (FOV), high-spatial-resolution imaging and phase recovery simultaneously. Conventional FPM assumes that the sample is sufficiently thin and strictly in focus. Nevertheless, even for a relatively thin sample, the non-planar distribution characteristics and the non-ideal position/posture of the sample will cause all or part of FOV to be defocused. In this paper, we proposed a fast digital refocusing and depth-of-field (DOF) extended FPM strategy by taking the advantages of image lateral shift caused by sample defocusing and varied-angle illuminations. The lateral shift amount is proportional to the defocus distance and the tangent of the illumination angle. Instead of searching the optimal defocus distance with the optimization search strategy, which is time consuming, the defocus distance of each subregion of the sample can be precisely and quickly obtained by calculating the relative lateral shift amounts corresponding to different oblique illuminations. And then, digital refocusing strategy rooting in the angular spectrum (AS) method is integrated into FPM framework to achieve the high-resolution and phase information reconstruction for each part of the sample, which means the DOF of the FPM can be effectively extended. The feasibility of the proposed method in fast digital refocusing and DOF extending is verified in the actual experiments with the USAF chart and biological samples.

Double-flow convolutional neural network for rapid large field of view Fourier ptychographic reconstruction

Fourier ptychographic microscopy is a promising imaging technique which can circumvent the space-bandwidth product of the system and achieve a reconstruction result with wide field-of-view (FOV), high-resolution and quantitative phase information. However, traditional iterative-based methods typically require multiple times to get convergence, and due to the wave vector deviation in different areas, the millimeter-level full-FOV cannot be well reconstructed once and typically required to be separated into several portions with sufficient overlaps and reconstructed separately, which makes traditional methods suffer from long reconstruction time for a large-FOV (of the order of minutes) and limits the application in real-time large-FOV monitoring of live sample in vitro. Here we propose a novel deep-learning based method called DFNN which can be used in place of traditional iterative-based methods to increase the quality of single large-FOV reconstruction and reducing the processing time from 167.5 to 0.1125 second. In addition, we demonstrate that by training based on the simulation dataset with high-entropy property (Opt. Express 28, 24 152 [2020]), DFNN could has fine generalizability and little dependence on the morphological features of samples. The superior robustness of DFNN against noise is also demonstrated in both simulation and experiment. Furthermore, our model shows more robustness against the wave vector deviation. Therefore, we could achieve better results at the edge areas of a single large-FOV reconstruction. Our method demonstrates a promising way to perform real-time single large-FOV reconstructions and provides further possibilities for real-time large-FOV monitoring of live samples with sub-cellular resolution.

Dither removing Fourier ptychographic microscope based on a two-axis rotation stage

SIGNIFICANCE

Large space-bandwidth product is highly desirable in many biomedical imaging. Fourier ptychographic microscopy (FPM) is a computational imaging technique that can significantly increase the space-bandwidth product of a standard microscope. The illuminator of a Fourier ptychographic microscope is not flexible at present, and it is inconvenient to meet different imaging needs.

AIM

An illuminator based on a two-axis motorized rotation stage was presented to provide a more flexible illuminating way with the goal of meeting different imaging needs.

APPROACH

The illuminator adopts a concentric illuminating method to provide coherent illumination in any direction on the sample plane. The sampling pattern can be freely designed and changed according to the parameters of the imaging system. A dither removing algorithm was proposed to remove the potential dither influence introduced in the image acquisition process.

RESULTS

The illuminator could be conveniently integrated into different imaging systems. The feasibility and flexibility were demonstrated by applying it to imaging systems with numerical aperture of 0.045 and 0.01. The resolution gain is about 4- and 13-fold, respectively. The effectiveness of the dither removing algorithm was validated in both simulation and experiment.

CONCLUSIONS

A more flexible illuminator for FPM was presented to meet different imaging needs. A dither removing algorithm was proposed to remove dither influence.

Optimizing sample illumination scanning in transmission tomographic diffractive microscopy

Due to the sequential nature of data acquisition, it is preferable to limit the number of illuminations to be used in tomographic diffractive microscopy experiments, especially if fast imaging is foreseen. On the other hand, for high-quality, high-resolution imaging, the Fourier space has to be optimally filled. Up to now, the problem of optimal Fourier space filling has not been investigated in itself. In this paper, we perform a comparative study to analyze the effect of sample scanning patterns on Fourier space filling for a transmission setup. Optical transfer functions for several illumination patterns are studied. Simulation as well as experiments are conducted to compare associated image reconstructions. We found that 3D uniform angular sweeping best fills the Fourier space, leading to better quality images.

Object detection neural network improves Fourier ptychography reconstruction

High resolution microscopy is heavily dependent on superb optical elements and superresolution microscopy even more so. Correcting unavoidable optical aberrations during post-processing is an elegant method to reduce the optical system's complexity. A prime method that promises superresolution, aberration correction, and quantitative phase imaging is Fourier ptychography. This microscopy technique combines many images of the sample, recorded at differing illumination angles akin to computed tomography and uses error minimisation between the recorded images with those generated by a forward model. The more precise knowledge of those illumination angles is available for the image formation forward model, the better the result. Therefore, illumination estimation from the raw data is an important step and supports correct phase recovery and aberration correction. Here, we derive how illumination estimation can be cast as an object detection problem that permits the use of a fast convolutional neural network (CNN) for this task. We find that faster-RCNN delivers highly robust results and outperforms classical approaches by far with an up to 3-fold reduction in estimation errors. Intriguingly, we find that conventionally beneficial smoothing and filtering of raw data is counterproductive in this type of application. We present a detailed analysis of the network's performance and provide all our developed software openly.

Extreme ultraviolet microscope characterization using photomask surface roughness

We demonstrate a method for characterizing the field-dependent aberrations of a full-field synchrotron-based extreme ultraviolet microscope. The statistical uniformity of the inherent, atomic-scale roughness of readily-available photomask blanks enables a self-calibrating computational procedure using images acquired under standard operation. We characterize the aberrations across a 30-um field-of-view, demonstrating a minimum aberration magnitude of smaller than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda /21 \, {\hbox {rms}}$$\end{document}λ/21rms averaged over the center 5-um area, with a measurement accuracy better than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda /180 \, {\hbox {rms}}$$\end{document}λ/180rms. The measured field variation of aberrations is consistent with system geometry and agrees with prior characterizations of the same system. In certain cases, it may be possible to additionally recover the illumination wavefront from the same images. Our method is general and is easily applied to coherent imaging systems with steerable illumination without requiring invasive hardware or custom test objects; hence, it provides substantial benefits when characterizing microscopes and high-resolution imaging systems in situ.

Single full-FOV reconstruction Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed computational imaging technique that has high-resolution and wide field-of-view (FOV). FPM bypasses the NA limit of the system by stitching a number of variable-illuminated measured images in Fourier space. On the basis of the wide FOV of the low NA objective, the high-resolution image with a wide FOV can be reconstructed through the phase recovery algorithm. However, the high-resolution reconstruction images are affected by the LED array point light source. The results are: (1) the intensities collected by the sample are severely declined when edge LEDs illuminate the sample; (2) the multiple reconstructions are caused by wavevectors inconsistency for the full FOV images. Here, we propose a new lighting scheme termed full FOV Fourier ptychographic microscopy (F³PM). By combining the LED array and telecentric lens, the method can provide plane waves with different angles while maintaining uniform intensity. Benefiting from the telecentric performance and f‒θ property of the telecentric lens, the system stability is improved and the relationship between the position of LED and its illumination angle is simplified. The excellent plane wave provided by the telecentric lens guarantees the same wavevector in the full FOV, and we use this wavevector to reconstruct the full FOV during one time. The area and diameter of the single reconstruction FOV reached 14.6mm ² and 5.4 mm, respectively, and the diameter is very close to the field number (5.5 mm) of the 4× objective. Compared with the traditional FPM, we have increased the diameter of FOV in a single reconstruction by ∼ 10 times, eliminating the complicated steps of computational redundancy and image stitching.

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.

Accurate angle estimation based on moment for multirotation computation imaging

In a multirotation computation imaging system, the fidelity of the reconstructed result is limited by the accuracy of the estimated rotation angles. Here, an accurate angle detection method using image moment is proposed to estimate angles of diffraction images. The second moment of a digital image is adopted as the rotational inertia in order to estimate angles of diffraction images. Compared with previous versions based on Radon/Hough transform, it has higher accuracy and is simultaneously time-saving, which is verified in both simulation and experiment. The angle error of moment method is narrowed down within 0.1°, or even less, and it also can perform well in sample diversity or when slightly out of focus.

Learned sensing: jointly optimized microscope hardware for accurate image classification

Since its invention, the microscope has been optimized for interpretation by a human observer. With the recent development of deep learning algorithms for automated image analysis, there is now a clear need to re-design the microscope's hardware for specific interpretation tasks. To increase the speed and accuracy of automated image classification, this work presents a method to co-optimize how a sample is illuminated in a microscope, along with a pipeline to automatically classify the resulting image, using a deep neural network. By adding a "physical layer" to a deep classification network, we are able to jointly optimize for specific illumination patterns that highlight the most important sample features for the particular learning task at hand, which may not be obvious under standard illumination. We demonstrate how our learned sensing approach for illumination design can automatically identify malaria-infected cells with up to 5-10% greater accuracy than standard and alternative microscope lighting designs. We show that this joint hardware-software design procedure generalizes to offer accurate diagnoses for two different blood smear types, and experimentally show how our new procedure can translate across different experimental setups while maintaining high accuracy.

A Simply Equipped Fourier Ptychography Platform Based on an Industrial Camera and Telecentric Objective

Fourier ptychography microscopy (FPM) is a recently emerged computational imaging method, which combines the advantages of synthetic aperture and phase retrieval to achieve super-resolution microscopic imaging. FPM can bypass the diffraction limit of the numerical aperture (NA) system and achieve complex images with wide field of view and high resolution (HR) on the basis of the existing microscopic platform, which has low resolution and wide field of view. Conventional FPM platforms are constructed based on basic microscopic platform and a scientific complementary metal-oxide-semiconductor (sCMOS) camera, which has ultrahigh dynamic range. However, sCMOS, or even the microscopic platform, is too expensive to afford for some researchers. Furthermore, the fixed microscopic platform limits the space for function expansion and system modification. In this work, we present a simply equipped FPM platform based on an industrial camera and telecentric objective, which is much cheaper than sCMOS camera and microscopic platform and has accurate optical calibration. A corresponding algorithm was embedded into a conventional FP framework to overcome the low dynamic range of industrial cameras. Simulation and experimental results showed the feasibility and good performance of the designed FPM platform and algorithms.

High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images

Optical diffraction tomography (ODT) reconstructs a sample's volumetric refractive index (RI) to create high-contrast, quantitative 3D visualizations of biological samples. However, standard implementations of ODT use interferometric systems, and so are sensitive to phase instabilities, complex mechanical design, and coherent noise. Furthermore, their reconstruction framework is typically limited to weakly scattering samples, and thus excludes a whole class of multiple-scattering samples. Here, we implement a new 3D RI microscopy technique that utilizes a computational multi-slice beam propagation method to invert the optical scattering process and reconstruct high-resolution (NA > 1.0) 3D RI distributions of multiple-scattering samples. The method acquires intensity-only measurements from different illumination angles and then solves a nonlinear optimization problem to recover the sample's 3D RI distribution. We experimentally demonstrate the reconstruction of samples with varying amounts of multiple-scattering: a 3T3 fibroblast cell, a cluster of C. elegans embryos, and a whole C. elegans worm, with lateral and axial resolutions of ≤ 240 nm and ≤ 900 nm, respectively. The results of this work lays groundwork for future studies into using optical wavelengths to probe 3D RI distributions of highly scattering biological organisms.

Low-cost, sub-micron resolution, wide-field computational microscopy using opensource hardware

The revolution in low-cost consumer photography and computation provides fertile opportunity for a disruptive reduction in the cost of biomedical imaging. Conventional approaches to low-cost microscopy are fundamentally restricted, however, to modest field of view (FOV) and/or resolution. We report a low-cost microscopy technique, implemented with a Raspberry Pi single-board computer and color camera combined with Fourier ptychography (FP), to computationally construct 25-megapixel images with sub-micron resolution. New image-construction techniques were developed to enable the use of the low-cost Bayer color sensor, to compensate for the highly aberrated re-used camera lens and to compensate for misalignments associated with the 3D-printed microscope structure. This high ratio of performance to cost is of particular interest to high-throughput microscopy applications, ranging from drug discovery and digital pathology to health screening in low-income countries. 3D models and assembly instructions of our microscope are made available for open source use.

Apodized coherent transfer function constraint for partially coherent Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed computational microscopy approach that produces both wide field-of-view (FOV) and high resolution (HR) intensity and a phase image of the sample. Inspired by the ideas of synthetic aperture and phase retrieval, FPM iteratively stitches multiple low-resolution (LR) images with variable illumination angles in Fourier space to reconstruct an HR complex image. Typically, FPM illuminating the sample with an LED array is approximated as a coherent imaging process, and the coherent transfer function (CTF) is imposed as a support constraint in Fourier space. However, a millimeter-scale LED is inapposite to be treated as a coherent light source. As a result, the quality of reconstructed image is degraded by the inappropriate approximation. In this paper, we analyze the coherence of an FPM system and propose a novel constraint approach termed Apodized CTF (AC) constraint in Fourier space. Results on both simulated data and actual captured data show that this new constraint is more stable and robust than CTF. This approach can also relax the coherence requirement of illumination. In addition, it is simple, does not require additional computations, and is easy to be embedded in almost all the reconstruction algorithms proposed so far.

Measurements on ATP induced cellular fluctuations using real-time dual view transport of intensity phase microscopy

Dual view transport of intensity phase microscopy is adopted to quantitatively study the regulation of adenosine triphosphate (ATP) on cellular mechanics. It extracts cell phases in real time from simultaneously captured under- and over-focus images. By computing the root-mean-square phase and correlation time, it is found that the cellular fluctuation amplitude and speed increased with ATP compared to those with ATP depletion. Besides, when adenylyl-imidodiphosphate (AMP-PNP) was introduced, it competed with ATP to bind to the ATP binding site, and the cellular fluctuation amplitude and speed decreased. The results prove that ATP is a factor in the regulation of cellular mechanics. To our best knowledge, it is the first time that the dual view transport of intensity phase microscopy was used for live cell phase imaging and analysis. Our work not only provides direct measurements on cellular fluctuations to study ATP regulation on cellular mechanics, but it also proves that our proposed dual view transport of intensity phase microscopy can be well used, especially in quantitative phase imaging of live cells in biological and medical applications.

Reliable deep-learning-based phase imaging with uncertainty quantification

Emerging deep-learning (DL)-based techniques have significant potential to revolutionize biomedical imaging. However, one outstanding challenge is the lack of reliability assessment in the DL predictions, whose errors are commonly revealed only in hindsight. Here, we propose a new Bayesian convolutional neural network (BNN)-based framework that overcomes this issue by quantifying the uncertainty of DL predictions. Foremost, we show that BNN-predicted uncertainty maps provide surrogate estimates of the true error from the network model and measurement itself. The uncertainty maps characterize imperfections often unknown in real-world applications, such as noise, model error, incomplete training data, and out-of-distribution testing data. Quantifying this uncertainty provides a per-pixel estimate of the confidence level of the DL prediction as well as the quality of the model and data set. We demonstrate this framework in the application of large space-bandwidth product phase imaging using a physics-guided coded illumination scheme. From only five multiplexed illumination measurements, our BNN predicts gigapixel phase images in both static and dynamic biological samples with quantitative credibility assessment. Furthermore, we show that low-certainty regions can identify spatially and temporally rare biological phenomena. We believe our uncertainty learning framework is widely applicable to many DL-based biomedical imaging techniques for assessing the reliability of DL predictions.

Aberration recovery by imaging a weak diffuser

We present a computational method for field-varying aberration recovery in optical systems by imaging a weak (index-matched) diffuser. Using multiple images acquired under plane wave illumination at distinct angles, the aberrations of the imaging system can be uniquely determined up to a sign. Our method is based on a statistical model for image formation that relates the spectrum of the speckled intensity image to the local aberrations at different locations in the field-of-view. The diffuser is treated as a wide-sense stationary scattering object, eliminating the need for precise knowledge of its surface shape. We validate our method both numerically and experimentally, showing that this relatively simple algorithmic calibration method can be reliably used to recover system aberrations quantitatively.