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Gram staining has been one of the most frequently used staining protocols in microbiology for over a century, utilized across various fields, including diagnostics, food safety, and environmental monitoring. Its manual procedures make it vulnerable to staining errors and artifacts due to, e.g., operator inexperience and chemical variations. Here, we introduce virtual Gram staining of label-free bacteria using a trained deep neural network that digitally transforms darkfield images of unstained bacteria into their Gram-stained equivalents matching brightfield image contrast. After a one-time training effort, the virtual Gram staining model processes an axial stack of darkfield microscopy images of label-free bacteria (never seen before) to rapidly generate Gram staining, bypassing several chemical steps involved in the conventional staining process. We demonstrated the success of the virtual Gram staining workflow on label-free bacteria samples containing Escherichia coli and Listeria innocua by quantifying the staining accuracy of the virtual Gram staining model and comparing the chromatic and morphological features of the virtually stained bacteria against their chemically stained counterparts. This virtual bacteria staining framework effectively bypasses the traditional Gram staining protocol and its challenges, including stain standardization, operator errors, and sensitivity to chemical variations., Comment: 25 Pages, 5 Figures

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

The immunohistochemical (IHC) staining of the human epidermal growth factor receptor 2 (HER2) biomarker is widely practiced in breast tissue analysis, preclinical studies and diagnostic decisions, guiding cancer treatment and investigation of pathogenesis. HER2 staining demands laborious tissue treatment and chemical processing performed by a histotechnologist, which typically takes one day to prepare in a laboratory, increasing analysis time and associated costs. Here, we describe a deep learning-based virtual HER2 IHC staining method using a conditional generative adversarial network that is trained to rapidly transform autofluorescence microscopic images of unlabeled/label-free breast tissue sections into bright-field equivalent microscopic images, matching the standard HER2 IHC staining that is chemically performed on the same tissue sections. The efficacy of this virtual HER2 staining framework was demonstrated by quantitative analysis, in which three board-certified breast pathologists blindly graded the HER2 scores of virtually stained and immunohistochemically stained HER2 whole slide images (WSIs) to reveal that the HER2 scores determined by inspecting virtual IHC images are as accurate as their immunohistochemically stained counterparts. A second quantitative blinded study performed by the same diagnosticians further revealed that the virtually stained HER2 images exhibit a comparable staining quality in the level of nuclear detail, membrane clearness, and absence of staining artifacts with respect to their immunohistochemically stained counterparts. This virtual HER2 staining framework bypasses the costly, laborious, and time-consuming IHC staining procedures in laboratory, and can be extended to other types of biomarkers to accelerate the IHC tissue staining used in life sciences and biomedical workflow., Comment: 26 Pages, 5 Figures

We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary, nonunitary and noninvertible transforms, (ii) 2D discrete Fourier transformation, (iii) arbitrary 2D permutation operations, and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (N) of spatially-engineered diffractive features/neurons is N_i x N_o or larger, both design methods succeed in all-optical implementation of the target transformation, achieving negligible error. However, compared to data-free designs, deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N < N_i x N_o. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces., Comment: 46 Pages, 12 Figures

Diffractive optical networks unify wave optics and deep learning to all-optically compute a given machine learning or computational imaging task as the light propagates from the input to the output plane. Here, we report the design of diffractive optical networks for the classification and reconstruction of spatially overlapping, phase-encoded objects. When two different phase-only objects spatially overlap, the individual object functions are perturbed since their phase patterns are summed up. The retrieval of the underlying phase images from solely the overlapping phase distribution presents a challenging problem, the solution of which is generally not unique. We show that through a task-specific training process, passive diffractive networks composed of successive transmissive layers can all-optically and simultaneously classify two different randomly-selected, spatially overlapping phase images at the input. After trained with ~550 million unique combinations of phase-encoded handwritten digits from the MNIST dataset, our blind testing results reveal that the diffractive network achieves an accuracy of >85.8% for all-optical classification of two overlapping phase images of new handwritten digits. In addition to all-optical classification of overlapping phase objects, we also demonstrate the reconstruction of these phase images based on a shallow electronic neural network that uses the highly compressed output of the diffractive network as its input (with e.g., ~20-65 times less number of pixels) to rapidly reconstruct both of the phase images, despite their spatial overlap and related phase ambiguity. The presented phase image classification and reconstruction framework might find applications in e.g., computational imaging, microscopy and quantitative phase imaging fields., Comment: 30 Pages, 7 Figures, 2 Tables

Imaging through diffusers presents a challenging problem with various digital image reconstruction solutions demonstrated to date using computers. We present a computer-free, all-optical image reconstruction method to see through random diffusers at the speed of light. Using deep learning, a set of diffractive surfaces are designed/trained to all-optically reconstruct images of objects that are covered by random phase diffusers. We experimentally demonstrated this concept using coherent THz illumination and all-optically reconstructed objects distorted by unknown, random diffusers, never used during training. Unlike digital methods, all-optical diffractive reconstructions do not require power except for the illumination light. This diffractive solution to see through diffusers can be extended to other wavelengths, and might fuel various applications in biomedical imaging, astronomy, atmospheric sciences, oceanography, security, robotics, among others., Comment: 35 Pages, 7 Figures

Optical Coherence Tomography (OCT) is a widely used non-invasive biomedical imaging modality that can rapidly provide volumetric images of samples. Here, we present a deep learning-based image reconstruction framework that can generate swept-source OCT (SS-OCT) images using undersampled spectral data, without any spatial aliasing artifacts. This neural network-based image reconstruction does not require any hardware changes to the optical set-up and can be easily integrated with existing swept-source or spectral domain OCT systems to reduce the amount of raw spectral data to be acquired. To show the efficacy of this framework, we trained and blindly tested a deep neural network using mouse embryo samples imaged by an SS-OCT system. Using 2-fold undersampled spectral data (i.e., 640 spectral points per A-line), the trained neural network can blindly reconstruct 512 A-lines in ~6.73 ms using a desktop computer, removing spatial aliasing artifacts due to spectral undersampling, also presenting a very good match to the images of the same samples, reconstructed using the full spectral OCT data (i.e., 1280 spectral points per A-line). We also successfully demonstrate that this framework can be further extended to process 3x undersampled spectral data per A-line, with some performance degradation in the reconstructed image quality compared to 2x spectral undersampling. This deep learning-enabled image reconstruction approach can be broadly used in various forms of spectral domain OCT systems, helping to increase their imaging speed without sacrificing image resolution and signal-to-noise ratio., Comment: 20 Pages, 7 Figures, 1 Table

Digital holography is one of the most widely used label-free microscopy techniques in biomedical imaging. Recovery of the missing phase information of a hologram is an important step in holographic image reconstruction. Here we demonstrate a convolutional recurrent neural network (RNN) based phase recovery approach that uses multiple holograms, captured at different sample-to-sensor distances to rapidly reconstruct the phase and amplitude information of a sample, while also performing autofocusing through the same network. We demonstrated the success of this deep learning-enabled holography method by imaging microscopic features of human tissue samples and Papanicolaou (Pap) smears. These results constitute the first demonstration of the use of recurrent neural networks for holographic imaging and phase recovery, and compared with existing methods, the presented approach improves the reconstructed image quality, while also increasing the depth-of-field and inference speed., Comment: 18 Pages, 7 Figures, 1 Table

We present a virtual image refocusing method over an extended depth of field (DOF) enabled by cascaded neural networks and a double-helix point-spread function (DH-PSF). This network model, referred to as W-Net, is composed of two cascaded generator and discriminator network pairs. The first generator network learns to virtually refocus an input image onto a user-defined plane, while the second generator learns to perform a cross-modality image transformation, improving the lateral resolution of the output image. Using this W-Net model with DH-PSF engineering, we extend the DOF of a fluorescence microscope by ~20-fold. This approach can be applied to develop deep learning-enabled image reconstruction methods for localization microscopy techniques that utilize engineered PSFs to improve their imaging performance, including spatial resolution and volumetric imaging throughput., Comment: 7 Pages, 3 Figures, 1 Table

Conventional spectrometers are limited by trade-offs set by size, cost, signal-to-noise ratio (SNR), and spectral resolution. Here, we demonstrate a deep learning-based spectral reconstruction framework, using a compact and low-cost on-chip sensing scheme that is not constrained by the design trade-offs inherent to grating-based spectroscopy. The system employs a plasmonic spectral encoder chip containing 252 different tiles of nanohole arrays fabricated using a scalable and low-cost imprint lithography method, where each tile has a unique geometry and, thus, a unique optical transmission spectrum. The illumination spectrum of interest directly impinges upon the plasmonic encoder, and a CMOS image sensor captures the transmitted light, without any lenses, gratings, or other optical components in between, making the entire hardware highly compact, light-weight and field-portable. A trained neural network then reconstructs the unknown spectrum using the transmitted intensity information from the spectral encoder in a feed-forward and non-iterative manner. Benefiting from the parallelization of neural networks, the average inference time per spectrum is ~28 microseconds, which is orders of magnitude faster compared to other computational spectroscopy approaches. When blindly tested on unseen new spectra (N = 14,648) with varying complexity, our deep-learning based system identified 96.86% of the spectral peaks with an average peak localization error, bandwidth error, and height error of 0.19 nm, 0.18 nm, and 7.60%, respectively. This system is also highly tolerant to fabrication defects that may arise during the imprint lithography process, which further makes it ideal for applications that demand cost-effective, field-portable and sensitive high-resolution spectroscopy tools., Comment: 18 pages, 6 figures

Recent research efforts in optical computing have gravitated towards developing optical neural networks that aim to benefit from the processing speed and parallelism of optics/photonics in machine learning applications. Among these endeavors, Diffractive Deep Neural Networks (D2NNs) harness light-matter interaction over a series of trainable surfaces, designed using deep learning, to compute a desired statistical inference task as the light waves propagate from the input plane to the output field-of-view. Although, earlier studies have demonstrated the generalization capability of diffractive optical networks to unseen data, achieving e.g., >98% image classification accuracy for handwritten digits, these previous designs are in general sensitive to the spatial scaling, translation and rotation of the input objects. Here, we demonstrate a new training strategy for diffractive networks that introduces input object translation, rotation and/or scaling during the training phase as uniformly distributed random variables to build resilience in their blind inference performance against such object transformations. This training strategy successfully guides the evolution of the diffractive optical network design towards a solution that is scale-, shift- and rotation-invariant, which is especially important and useful for dynamic machine vision applications in e.g., autonomous cars, in-vivo imaging of biomedical specimen, among others., Comment: 28 Pages, 6 Figures, 1 Table

Volumetric imaging of samples using fluorescence microscopy plays an important role in various fields including physical, medical and life sciences. Here we report a deep learning-based volumetric image inference framework that uses 2D images that are sparsely captured by a standard wide-field fluorescence microscope at arbitrary axial positions within the sample volume. Through a recurrent convolutional neural network, which we term as Recurrent-MZ, 2D fluorescence information from a few axial planes within the sample is explicitly incorporated to digitally reconstruct the sample volume over an extended depth-of-field. Using experiments on C. Elegans and nanobead samples, Recurrent-MZ is demonstrated to increase the depth-of-field of a 63x/1.4NA objective lens by approximately 50-fold, also providing a 30-fold reduction in the number of axial scans required to image the same sample volume. We further illustrated the generalization of this recurrent network for 3D imaging by showing its resilience to varying imaging conditions, including e.g., different sequences of input images, covering various axial permutations and unknown axial positioning errors. Recurrent-MZ demonstrates the first application of recurrent neural networks in microscopic image reconstruction and provides a flexible and rapid volumetric imaging framework, overcoming the limitations of current 3D scanning microscopy tools., Comment: 17 pages, 7 figures

A plethora of research advances have emerged in the fields of optics and photonics that benefit from harnessing the power of machine learning. Specifically, there has been a revival of interest in optical computing hardware, due to its potential advantages for machine learning tasks in terms of parallelization, power efficiency and computation speed. Diffractive Deep Neural Networks (D2NNs) form such an optical computing framework, which benefits from deep learning-based design of successive diffractive layers to all-optically process information as the input light diffracts through these passive layers. D2NNs have demonstrated success in various tasks, including e.g., object classification, spectral-encoding of information, optical pulse shaping and imaging, among others. Here, we significantly improve the inference performance of diffractive optical networks using feature engineering and ensemble learning. After independently training a total of 1252 D2NNs that were diversely engineered with a variety of passive input filters, we applied a pruning algorithm to select an optimized ensemble of D2NNs that collectively improve their image classification accuracy. Through this pruning, we numerically demonstrated that ensembles of N=14 and N=30 D2NNs achieve blind testing accuracies of 61.14% and 62.13%, respectively, on the classification of CIFAR-10 test images, providing an inference improvement of >16% compared to the average performance of the individual D2NNs within each ensemble. These results constitute the highest inference accuracies achieved to date by any diffractive optical neural network design on the same dataset and might provide a significant leapfrog to extend the application space of diffractive optical image classification and machine vision systems., Comment: 22 Pages, 4 Figures, 1 Table

Pathology is practiced by visual inspection of histochemically stained slides. Most commonly, the hematoxylin and eosin (H&E) stain is used in the diagnostic workflow and it is the gold standard for cancer diagnosis. However, in many cases, especially for non-neoplastic diseases, additional "special stains" are used to provide different levels of contrast and color to tissue components and allow pathologists to get a clearer diagnostic picture. In this study, we demonstrate the utility of supervised learning-based computational stain transformation from H&E to different special stains (Masson's Trichrome, periodic acid-Schiff and Jones silver stain) using tissue sections from kidney needle core biopsies. Based on evaluation by three renal pathologists, followed by adjudication by a fourth renal pathologist, we show that the generation of virtual special stains from existing H&E images improves the diagnosis in several non-neoplastic kidney diseases sampled from 58 unique subjects. A second study performed by three pathologists found that the quality of the special stains generated by the stain transformation network was statistically equivalent to those generated through standard histochemical staining. As the transformation of H&E images into special stains can be achieved within 1 min or less per patient core specimen slide, this stain-to-stain transformation framework can improve the quality of the preliminary diagnosis when additional special stains are needed, along with significant savings in time and cost, reducing the burden on healthcare system and patients., Comment: 27 Pages, 6 Figures

Precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and photonics. These advances around the engineering of materials with new functionalities have also opened up exciting avenues for designing trainable surfaces that can perform computation and machine learning tasks through light-matter interaction and diffraction. Here, we analyze the information processing capacity of coherent optical networks formed by diffractive surfaces that are trained to perform an all-optical computational task between a given input and output field-of-view. We show that the dimensionality of the all-optical solution space covering the complex-valued transformations between the input and output fields-of-view is linearly proportional to the number of diffractive surfaces within the optical network, up to a limit that is dictated by the extent of the input and output fields-of-view. Deeper diffractive networks that are composed of larger numbers of trainable surfaces can cover a higher dimensional subspace of the complex-valued linear transformations between a larger input field-of-view and a larger output field-of-view, and exhibit depth advantages in terms of their statistical inference, learning and generalization capabilities for different image classification tasks, when compared with a single trainable diffractive surface. These analyses and conclusions are broadly applicable to various forms of diffractive surfaces, including e.g., plasmonic and/or dielectric-based metasurfaces and flat optics that can be used to form all-optical processors., Comment: 31 Pages, 6 Figures, 1 Table

Polarized light microscopy provides high contrast to birefringent specimen and is widely used as a diagnostic tool in pathology. However, polarization microscopy systems typically operate by analyzing images collected from two or more light paths in different states of polarization, which lead to relatively complex optical designs, high system costs or experienced technicians being required. Here, we present a deep learning-based holographic polarization microscope that is capable of obtaining quantitative birefringence retardance and orientation information of specimen from a phase recovered hologram, while only requiring the addition of one polarizer/analyzer pair to an existing holographic imaging system. Using a deep neural network, the reconstructed holographic images from a single state of polarization can be transformed into images equivalent to those captured using a single-shot computational polarized light microscope (SCPLM). Our analysis shows that a trained deep neural network can extract the birefringence information using both the sample specific morphological features as well as the holographic amplitude and phase distribution. To demonstrate the efficacy of this method, we tested it by imaging various birefringent samples including e.g., monosodium urate (MSU) and triamcinolone acetonide (TCA) crystals. Our method achieves similar results to SCPLM both qualitatively and quantitatively, and due to its simpler optical design and significantly larger field-of-view, this method has the potential to expand the access to polarization microscopy and its use for medical diagnosis in resource limited settings., Comment: 20 pages, 8 figures

Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact pulse engineering system. We experimentally demonstrate the synthesis of square pulses with different temporal-widths by manufacturing passive diffractive layers that collectively control both the spectral amplitude and the phase of an input terahertz pulse. Our results constitute the first demonstration of direct pulse shaping in terahertz spectrum, where a complex-valued spectral modulation function directly acts on terahertz frequencies. Furthermore, a Lego-like physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy., Comment: 27 pages, 6 figures

As an optical machine learning framework, Diffractive Deep Neural Networks (D2NN) take advantage of data-driven training methods used in deep learning to devise light-matter interaction in 3D for performing a desired statistical inference task. Multi-layer optical object recognition platforms designed with this diffractive framework have been shown to generalize to unseen image data achieving e.g., >98% blind inference accuracy for hand-written digit classification. The multi-layer structure of diffractive networks offers significant advantages in terms of their diffraction efficiency, inference capability and optical signal contrast. However, the use of multiple diffractive layers also brings practical challenges for the fabrication and alignment of these diffractive systems for accurate optical inference. Here, we introduce and experimentally demonstrate a new training scheme that significantly increases the robustness of diffractive networks against 3D misalignments and fabrication tolerances in the physical implementation of a trained diffractive network. By modeling the undesired layer-to-layer misalignments in 3D as continuous random variables in the optical forward model, diffractive networks are trained to maintain their inference accuracy over a large range of misalignments; we term this diffractive network design as vaccinated D2NN (v-D2NN). We further extend this vaccination strategy to the training of diffractive networks that use differential detectors at the output plane as well as to jointly-trained hybrid (optical-electronic) networks to reveal that all of these diffractive designs improve their resilience to misalignments by taking into account possible 3D fabrication variations and displacements during their training phase., Comment: 15 Pages, 6 Figures

3D engineering of matter has opened up new avenues for designing systems that can perform various computational tasks through light-matter interaction. Here, we demonstrate the design of optical networks in the form of multiple diffractive layers that are trained using deep learning to transform and encode the spatial information of objects into the power spectrum of the diffracted light, which are used to perform optical classification of objects with a single-pixel spectroscopic detector. Using a time-domain spectroscopy setup with a plasmonic nanoantenna-based detector, we experimentally validated this machine vision framework at terahertz spectrum to optically classify the images of handwritten digits by detecting the spectral power of the diffracted light at ten distinct wavelengths, each representing one class/digit. We also report the coupling of this spectral encoding achieved through a diffractive optical network with a shallow electronic neural network, separately trained to reconstruct the images of handwritten digits based on solely the spectral information encoded in these ten distinct wavelengths within the diffracted light. These reconstructed images demonstrate task-specific image decompression and can also be cycled back as new inputs to the same diffractive network to improve its optical object classification. This unique machine vision framework merges the power of deep learning with the spatial and spectral processing capabilities of diffractive networks, and can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with spectrally encoded classification tasks performed through diffractive optical networks., Comment: 21 pages, 5 figures, 1 table

We demonstrate a deep learning-based offline autofocusing method, termed Deep-R, that is trained to rapidly and blindly autofocus a single-shot microscopy image of a specimen that is acquired at an arbitrary out-of-focus plane. We illustrate the efficacy of Deep-R using various tissue sections that were imaged using fluorescence and brightfield microscopy modalities and demonstrate snapshot autofocusing under different scenarios, such as a uniform axial defocus as well as a sample tilt within the field-of-view. Our results reveal that Deep-R is significantly faster when compared with standard online algorithmic autofocusing methods. This deep learning-based blind autofocusing framework opens up new opportunities for rapid microscopic imaging of large sample areas, also reducing the photon dose on the sample., Comment: 27 pages, 8 figures, 9 supplementary figures, 2 supplementary tables

We present a computational live bacteria detection system that periodically captures coherent microscopy images of bacterial growth inside a 60 mm diameter agar-plate and analyzes these time-lapsed holograms using deep neural networks for rapid detection of bacterial growth and classification of the corresponding species. The performance of our system was demonstrated by rapid detection of Escherichia coli and total coliform bacteria (i.e., Klebsiella aerogenes and Klebsiella pneumoniae subsp. pneumoniae) in water samples. These results were confirmed against gold-standard culture-based results, shortening the detection time of bacterial growth by >12 h as compared to the Environmental Protection Agency (EPA)-approved analytical methods. Our experiments further confirmed that this method successfully detects 90% of bacterial colonies within 7-10 h (and >95% within 12 h) with a precision of 99.2-100%, and correctly identifies their species in 7.6-12 h with 80% accuracy. Using pre-incubation of samples in growth media, our system achieved a limit of detection (LOD) of ~1 colony forming unit (CFU)/L within 9 h of total test time. This computational bacteria detection and classification platform is highly cost-effective (~$0.6 per test) and high-throughput with a scanning speed of 24 cm2/min over the entire plate surface, making it highly suitable for integration with the existing analytical methods currently used for bacteria detection on agar plates. Powered by deep learning, this automated and cost-effective live bacteria detection platform can be transformative for a wide range of applications in microbiology by significantly reducing the detection time, also automating the identification of colonies, without labeling or the need for an expert., Comment: 24 pages, 6 figures

Histological staining is a vital step used to diagnose various diseases and has been used for more than a century to provide contrast to tissue sections, rendering the tissue constituents visible for microscopic analysis by medical experts. However, this process is time-consuming, labor-intensive, expensive and destructive to the specimen. Recently, the ability to virtually-stain unlabeled tissue sections, entirely avoiding the histochemical staining step, has been demonstrated using tissue-stain specific deep neural networks. Here, we present a new deep learning-based framework which generates virtually-stained images using label-free tissue, where different stains are merged following a micro-structure map defined by the user. This approach uses a single deep neural network that receives two different sources of information at its input: (1) autofluorescence images of the label-free tissue sample, and (2) a digital staining matrix which represents the desired microscopic map of different stains to be virtually generated at the same tissue section. This digital staining matrix is also used to virtually blend existing stains, digitally synthesizing new histological stains. We trained and blindly tested this virtual-staining network using unlabeled kidney tissue sections to generate micro-structured combinations of Hematoxylin and Eosin (H&E), Jones silver stain, and Masson's Trichrome stain. Using a single network, this approach multiplexes virtual staining of label-free tissue with multiple types of stains and paves the way for synthesizing new digital histological stains that can be created on the same tissue cross-section, which is currently not feasible with standard histochemical staining methods., Comment: 19 pages, 5 figures, 2 tables

Sickle cell disease (SCD) is a major public health priority throughout much of the world, affecting millions of people. In many regions, particularly those in resource-limited settings, SCD is not consistently diagnosed. In Africa, where the majority of SCD patients reside, more than 50% of the 0.2-0.3 million children born with SCD each year will die from it; many of these deaths are in fact preventable with correct diagnosis and treatment. Here we present a deep learning framework which can perform automatic screening of sickle cells in blood smears using a smartphone microscope. This framework uses two distinct, complementary deep neural networks. The first neural network enhances and standardizes the blood smear images captured by the smartphone microscope, spatially and spectrally matching the image quality of a laboratory-grade benchtop microscope. The second network acts on the output of the first image enhancement neural network and is used to perform the semantic segmentation between healthy and sickle cells within a blood smear. These segmented images are then used to rapidly determine the SCD diagnosis per patient. We blindly tested this mobile sickle cell detection method using blood smears from 96 unique patients (including 32 SCD patients) that were imaged by our smartphone microscope, and achieved ~98% accuracy, with an area-under-the-curve (AUC) of 0.998. With its high accuracy, this mobile and cost-effective method has the potential to be used as a screening tool for SCD and other blood cell disorders in resource-limited settings., Comment: 30 pages, 5 figures

We report a broadband diffractive optical neural network design that simultaneously processes a continuum of wavelengths generated by a temporally-incoherent broadband source to all-optically perform a specific task learned using deep learning. We experimentally validated the success of this broadband diffractive neural network architecture by designing, fabricating and testing seven different multi-layer, diffractive optical systems that transform the optical wavefront generated by a broadband THz pulse to realize (1) a series of tunable, single passband as well as dual passband spectral filters, and (2) spatially-controlled wavelength de-multiplexing. Merging the native or engineered dispersion of various material systems with a deep learning-based design strategy, broadband diffractive neural networks help us engineer light-matter interaction in 3D, diverging from intuitive and analytical design methods to create task-specific optical components that can all-optically perform deterministic tasks or statistical inference for optical machine learning., Comment: 36 pages, 5 figures

We report a framework based on a generative adversarial network (GAN) that performs high-fidelity color image reconstruction using a single hologram of a sample that is illuminated simultaneously by light at three different wavelengths. The trained network learns to eliminate missing-phase-related artifacts, and generates an accurate color transformation for the reconstructed image. Our framework is experimentally demonstrated using lung and prostate tissue sections that are labeled with different histological stains. This framework is envisaged to be applicable to point-of-care histopathology, and presents a significant improvement in the throughput of coherent microscopy systems given that only a single hologram of the specimen is required for accurate color imaging., Comment: 25 pages, 8 Figures, 2 Tables

Diffractive deep neural networks have been introduced earlier as an optical machine learning framework that uses task-specific diffractive surfaces designed by deep learning to all-optically perform inference, achieving promising performance for object classification and imaging. Here we demonstrate systematic improvements in diffractive optical neural networks based on a differential measurement technique that mitigates the non-negativity constraint of light intensity. In this scheme, each class is assigned to a separate pair of photodetectors, behind a diffractive network, and the class inference is made by maximizing the normalized signal difference between the detector pairs. Moreover, by utilizing the inherent parallelization capability of optical systems, we reduced the signal coupling between the positive and negative detectors of each class by dividing their optical path into two jointly-trained diffractive neural networks that work in parallel. We further made use of this parallelization approach, and divided individual classes among multiple jointly-trained differential diffractive neural networks. Using this class-specific differential detection in jointly-optimized diffractive networks, our simulations achieved testing accuracies of 98.52%, 91.48% and 50.82% for MNIST, Fashion-MNIST and grayscale CIFAR-10 datasets, respectively. Similar to ensemble methods practiced in machine learning, we also independently-optimized multiple differential diffractive networks that optically project their light onto a common detector plane, and achieved testing accuracies of 98.59%, 91.06% and 51.44% for MNIST, Fashion-MNIST and grayscale CIFAR-10, respectively. Through these systematic advances in designing diffractive neural networks, the reported classification accuracies set the state-of-the-art for an all-optical neural network design., Comment: 21 pages, 6 Figures, 3 Tables

Three-dimensional (3D) fluorescence microscopy in general requires axial scanning to capture images of a sample at different planes. Here we demonstrate that a deep convolutional neural network can be trained to virtually refocus a 2D fluorescence image onto user-defined 3D surfaces within the sample volume. With this data-driven computational microscopy framework, we imaged the neuron activity of a Caenorhabditis elegans worm in 3D using a time-sequence of fluorescence images acquired at a single focal plane, digitally increasing the depth-of-field of the microscope by 20-fold without any axial scanning, additional hardware, or a trade-off of imaging resolution or speed. Furthermore, we demonstrate that this learning-based approach can correct for sample drift, tilt, and other image aberrations, all digitally performed after the acquisition of a single fluorescence image. This unique framework also cross-connects different imaging modalities to each other, enabling 3D refocusing of a single wide-field fluorescence image to match confocal microscopy images acquired at different sample planes. This deep learning-based 3D image refocusing method might be transformative for imaging and tracking of 3D biological samples, especially over extended periods of time, mitigating photo-toxicity, sample drift, aberration and defocusing related challenges associated with standard 3D fluorescence microscopy techniques., Comment: 47 pages, 5 figures (main text)

We report resolution enhancement in scanning electron microscopy (SEM) images using a generative adversarial network. We demonstrate the veracity of this deep learning-based super-resolution technique by inferring unresolved features in low-resolution SEM images and comparing them with the accurately co-registered high-resolution SEM images of the same samples. Through spatial frequency analysis, we also report that our method generates images with frequency spectra matching higher resolution SEM images of the same fields-of-view. By using this technique, higher resolution SEM images can be taken faster, while also reducing both electron charging and damage to the samples., Comment: 8 pages, 4 figures

Deep learning brings bright-field microscopy contrast to holographic images of a sample volume, bridging the volumetric imaging capability of holography with the speckle- and artifact-free image contrast of bright-field incoherent microscopy., Comment: 3 pages

We present a deep learning framework based on a generative adversarial network (GAN) to perform super-resolution in coherent imaging systems. We demonstrate that this framework can enhance the resolution of both pixel size-limited and diffraction-limited coherent imaging systems. We experimentally validated the capabilities of this deep learning-based coherent imaging approach by super-resolving complex images acquired using a lensfree on-chip holographic microscope, the resolution of which was pixel size-limited. Using the same GAN-based approach, we also improved the resolution of a lens-based holographic imaging system that was limited in resolution by the numerical aperture of its objective lens. This deep learning-based super-resolution framework can be broadly applied to enhance the space-bandwidth product of coherent imaging systems using image data and convolutional neural networks, and provides a rapid, non-iterative method for solving inverse image reconstruction or enhancement problems in optics., Comment: 18 pages, 9 figures, 3 tables

In their Comment, Wei et al. (arXiv:1809.08360v1 [cs.LG]) claim that our original interpretation of Diffractive Deep Neural Networks (D2NN) represent a mischaracterization of the system due to linearity and passivity. In this Response, we detail how this mischaracterization claim is unwarranted and oblivious to several sections detailed in our original manuscript (Science, DOI: 10.1126/science.aat8084) that specifically introduced and discussed optical nonlinearities and reconfigurability of D2NNs, as part of our proposed framework to enhance its performance. To further refute the mischaracterization claim of Wei et al., we, once again, demonstrate the depth feature of optical D2NNs by showing that multiple diffractive layers operating collectively within a D2NN present additional degrees-of-freedom compared to a single diffractive layer to achieve better classification accuracy, as well as improved output signal contrast and diffraction efficiency as the number of diffractive layers increase, showing the deepness of a D2NN, and its inherent depth advantage for improved performance. In summary, the Comment by Wei et al. does not provide an amendment to the original teachings of our original manuscript, and all of our results, core conclusions and methodology of research reported in Science (DOI: 10.1126/science.aat8084) remain entirely valid., Comment: Response to arXiv:1809.08360v1 [cs.LG]

Optical machine learning offers advantages in terms of power efficiency, scalability and computation speed. Recently, an optical machine learning method based on Diffractive Deep Neural Networks (D2NNs) has been introduced to execute a function as the input light diffracts through passive layers, designed by deep learning using a computer. Here we introduce improvements to D2NNs by changing the training loss function and reducing the impact of vanishing gradients in the error back-propagation step. Using five phase-only diffractive layers, we numerically achieved a classification accuracy of 97.18% and 89.13% for optical recognition of handwritten digits and fashion products, respectively; using both phase and amplitude modulation (complex-valued) at each layer, our inference performance improved to 97.81% and 89.32%, respectively. Furthermore, we report the integration of D2NNs with electronic neural networks to create hybrid-classifiers that significantly reduce the number of input pixels into an electronic network using an ultra-compact front-end D2NN with a layer-to-layer distance of a few wavelengths, also reducing the complexity of the successive electronic network. Using a 5-layer phase-only D2NN jointly-optimized with a single fully-connected electronic layer, we achieved a classification accuracy of 98.71% and 90.04% for the recognition of handwritten digits and fashion products, respectively. Moreover, the input to the electronic network was compressed by >7.8 times down to 10x10 pixels. Beyond creating low-power and high-frame rate machine learning platforms, D2NN-based hybrid neural networks will find applications in smart optical imager and sensor design., Comment: 22 pages, 5 Figures, 4 Tables, 1 Supplementary Figure, 2 Supplementary Tables

Holographic microscopy presents challenges for color reproduction due to the usage of narrow-band illumination sources, which especially impacts the imaging of stained pathology slides for clinical diagnoses. Here, an accurate color holographic microscopy framework using absorbance spectrum estimation is presented. This method uses multispectral holographic images acquired and reconstructed at a small number (e.g., three to six) of wavelengths, estimates the absorbance spectrum of the sample, and projects it onto a color tristimulus. Using this method, the wavelength selection is optimized to holographically image 25 pathology slide samples with different tissue and stain combinations to significantly reduce color errors in the final reconstructed images. The results can be used as a practical guide for various imaging applications and, in particular, to correct color distortions in holographic imaging of pathology samples spanning different dyes and tissue types.

Using a deep neural network, we demonstrate a digital staining technique, which we term PhaseStain, to transform quantitative phase images (QPI) of labelfree tissue sections into images that are equivalent to brightfield microscopy images of the same samples that are histochemically stained. Through pairs of image data (QPI and the corresponding brightfield images, acquired after staining) we train a generative adversarial network (GAN) and demonstrate the effectiveness of this virtual staining approach using sections of human skin, kidney and liver tissue, matching the brightfield microscopy images of the same samples stained with Hematoxylin and Eosin, Jones' stain, and Masson's trichrome stain, respectively. This digital staining framework might further strengthen various uses of labelfree QPI techniques in pathology applications and biomedical research in general, by eliminating the need for chemical staining, reducing sample preparation related costs and saving time. Our results provide a powerful example of some of the unique opportunities created by data driven image transformations enabled by deep learning.

We discuss recently emerging applications of the state-of-art deep learning methods on optical microscopy and microscopic image reconstruction, which enable new transformations among different modes and modalities of microscopic imaging, driven entirely by image data. We believe that deep learning will fundamentally change both the hardware and image reconstruction methods used in optical microscopy in a holistic manner.

We introduce an all-optical Diffractive Deep Neural Network (D2NN) architecture that can learn to implement various functions after deep learning-based design of passive diffractive layers that work collectively. We experimentally demonstrated the success of this framework by creating 3D-printed D2NNs that learned to implement handwritten digit classification and the function of an imaging lens at terahertz spectrum. With the existing plethora of 3D-printing and other lithographic fabrication methods as well as spatial-light-modulators, this all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can implement, and will find applications in all-optical image analysis, feature detection and object classification, also enabling new camera designs and optical components that can learn to perform unique tasks using D2NNs., Comment: 20 pages, 4 figures

Histological analysis of tissue samples is one of the most widely used methods for disease diagnosis. After taking a sample from a patient, it goes through a lengthy and laborious preparation, which stains the tissue to visualize different histological features under a microscope. Here, we demonstrate a label-free approach to create a virtually-stained microscopic image using a single wide-field auto-fluorescence image of an unlabeled tissue sample, bypassing the standard histochemical staining process, saving time and cost. This method is based on deep learning, and uses a convolutional neural network trained using a generative adversarial network model to transform an auto-fluorescence image of an unlabeled tissue section into an image that is equivalent to the bright-field image of the stained-version of the same sample. We validated this method by successfully creating virtually-stained microscopic images of human tissue samples, including sections of salivary gland, thyroid, kidney, liver and lung tissue, also covering three different stains. This label-free virtual-staining method eliminates cumbersome and costly histochemical staining procedures, and would significantly simplify tissue preparation in pathology and histology fields.

Holography encodes the three dimensional (3D) information of a sample in the form of an intensity-only recording. However, to decode the original sample image from its hologram(s), auto-focusing and phase-recovery are needed, which are in general cumbersome and time-consuming to digitally perform. Here we demonstrate a convolutional neural network (CNN) based approach that simultaneously performs auto-focusing and phase-recovery to significantly extend the depth-of-field (DOF) in holographic image reconstruction. For this, a CNN is trained by using pairs of randomly de-focused back-propagated holograms and their corresponding in-focus phase-recovered images. After this training phase, the CNN takes a single back-propagated hologram of a 3D sample as input to rapidly achieve phase-recovery and reconstruct an in focus image of the sample over a significantly extended DOF. This deep learning based DOF extension method is non-iterative, and significantly improves the algorithm time-complexity of holographic image reconstruction from O(nm) to O(1), where n refers to the number of individual object points or particles within the sample volume, and m represents the focusing search space within which each object point or particle needs to be individually focused. These results highlight some of the unique opportunities created by data-enabled statistical image reconstruction methods powered by machine learning, and we believe that the presented approach can be broadly applicable to computationally extend the DOF of other imaging modalities.

Mobile-phones have facilitated the creation of field-portable, cost-effective imaging and sensing technologies that approach laboratory-grade instrument performance. However, the optical imaging interfaces of mobile-phones are not designed for microscopy and produce spatial and spectral distortions in imaging microscopic specimens. Here, we report on the use of deep learning to correct such distortions introduced by mobile-phone-based microscopes, facilitating the production of high-resolution, denoised and colour-corrected images, matching the performance of benchtop microscopes with high-end objective lenses, also extending their limited depth-of-field. After training a convolutional neural network, we successfully imaged various samples, including blood smears, histopathology tissue sections, and parasites, where the recorded images were highly compressed to ease storage and transmission for telemedicine applications. This method is applicable to other low-cost, aberrated imaging systems, and could offer alternatives for costly and bulky microscopes, while also providing a framework for standardization of optical images for clinical and biomedical applications.

We demonstrate that a deep neural network can significantly improve optical microscopy, enhancing its spatial resolution over a large field-of-view and depth-of-field. After its training, the only input to this network is an image acquired using a regular optical microscope, without any changes to its design. We blindly tested this deep learning approach using various tissue samples that are imaged with low-resolution and wide-field systems, where the network rapidly outputs an image with remarkably better resolution, matching the performance of higher numerical aperture lenses, also significantly surpassing their limited field-of-view and depth-of-field. These results are transformative for various fields that use microscopy tools, including e.g., life sciences, where optical microscopy is considered as one of the most widely used and deployed techniques. Beyond such applications, our presented approach is broadly applicable to other imaging modalities, also spanning different parts of the electromagnetic spectrum, and can be used to design computational imagers that get better and better as they continue to image specimen and establish new transformations among different modes of imaging.

Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. Here we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training. This deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference related spatial artifacts. Compared to existing approaches, this neural network based method is significantly faster to compute, and reconstructs improved phase and amplitude images of the objects using only one hologram, i.e., requires less number of measurements in addition to being computationally faster. We validated this method by reconstructing phase and amplitude images of various samples, including blood and Pap smears, and tissue sections. These results are broadly applicable to any phase recovery problem, and highlight that through machine learning challenging problems in imaging science can be overcome, providing new avenues to design powerful computational imaging systems.