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Unidirectional imagers form images of input objects only in one direction, e.g., from field-of-view (FOV) A to FOV B, while blocking the image formation in the reverse direction, from FOV B to FOV A. Here, we report unidirectional imaging under spatially partially coherent light and demonstrate high-quality imaging only in the forward direction (A->B) with high power efficiency while distorting the image formation in the backward direction (B->A) along with low power efficiency. Our reciprocal design features a set of spatially engineered linear diffractive layers that are statistically optimized for partially coherent illumination with a given phase correlation length. Our analyses reveal that when illuminated by a partially coherent beam with a correlation length of ~1.5 w or larger, where w is the wavelength of light, diffractive unidirectional imagers achieve robust performance, exhibiting asymmetric imaging performance between the forward and backward directions - as desired. A partially coherent unidirectional imager designed with a smaller correlation length of less than 1.5 w still supports unidirectional image transmission, but with a reduced figure of merit. These partially coherent diffractive unidirectional imagers are compact (axially spanning less than 75 w), polarization-independent, and compatible with various types of illumination sources, making them well-suited for applications in asymmetric visual information processing and communication., Comment: 25 Pages, 8 Figures

Optical continuous glucose monitoring (CGM) systems are emerging for personalized glucose management owing to their lower cost and prolonged durability compared to conventional electrochemical CGMs. Here, we report a computational CGM system, which integrates a biocompatible phosphorescence-based insertable biosensor and a custom-designed phosphorescence lifetime imager (PLI). This compact and cost-effective PLI is designed to capture phosphorescence lifetime images of an insertable sensor through the skin, where the lifetime of the emitted phosphorescence signal is modulated by the local concentration of glucose. Because this phosphorescence signal has a very long lifetime compared to tissue autofluorescence or excitation leakage processes, it completely bypasses these noise sources by measuring the sensor emission over several tens of microseconds after the excitation light is turned off. The lifetime images acquired through the skin are processed by neural network-based models for misalignment-tolerant inference of glucose levels, accurately revealing normal, low (hypoglycemia) and high (hyperglycemia) concentration ranges. Using a 1-mm thick skin phantom mimicking the optical properties of human skin, we performed in vitro testing of the PLI using glucose-spiked samples, yielding 88.8% inference accuracy, also showing resilience to random and unknown misalignments within a lateral distance of ~4.7 mm with respect to the position of the insertable sensor underneath the skin phantom. Furthermore, the PLI accurately identified larger lateral misalignments beyond 5 mm, prompting user intervention for re-alignment. The misalignment-resilient glucose concentration inference capability of this compact and cost-effective phosphorescence lifetime imager makes it an appealing wearable diagnostics tool for real-time tracking of glucose and other biomarkers., Comment: 24 Pages, 4 Figures

Human epidermal growth factor receptor 2 (HER2) is a critical protein in cancer cell growth that signifies the aggressiveness of breast cancer (BC) and helps predict its prognosis. Accurate assessment of immunohistochemically (IHC) stained tissue slides for HER2 expression levels is essential for both treatment guidance and understanding of cancer mechanisms. Nevertheless, the traditional workflow of manual examination by board-certified pathologists encounters challenges, including inter- and intra-observer inconsistency and extended turnaround times. Here, we introduce a deep learning-based approach utilizing pyramid sampling for the automated classification of HER2 status in IHC-stained BC tissue images. Our approach analyzes morphological features at various spatial scales, efficiently managing the computational load and facilitating a detailed examination of cellular and larger-scale tissue-level details. This method addresses the tissue heterogeneity of HER2 expression by providing a comprehensive view, leading to a blind testing classification accuracy of 84.70%, on a dataset of 523 core images from tissue microarrays. Our automated system, proving reliable as an adjunct pathology tool, has the potential to enhance diagnostic precision and evaluation speed, and might significantly impact cancer treatment planning., Comment: 21 Pages, 7 Figures

Systemic amyloidosis is a group of diseases characterized by the deposition of misfolded proteins in various organs and tissues, leading to progressive organ dysfunction and failure. Congo red stain is the gold standard chemical stain for the visualization of amyloid deposits in tissue sections, as it forms complexes with the misfolded proteins and shows a birefringence pattern under polarized light microscopy. However, Congo red staining is tedious and costly to perform, and prone to false diagnoses due to variations in the amount of amyloid, staining quality and expert interpretation through manual examination of tissue under a polarization microscope. Here, we report the first demonstration of virtual birefringence imaging and virtual Congo red staining of label-free human tissue to show that a single trained neural network can rapidly transform autofluorescence images of label-free tissue sections into brightfield and polarized light microscopy equivalent images, matching the histochemically stained versions of the same samples. We demonstrate the efficacy of our method with blind testing and pathologist evaluations on cardiac tissue where the virtually stained images agreed well with the histochemically stained ground truth images. Our virtually stained polarization and brightfield images highlight amyloid birefringence patterns in a consistent, reproducible manner while mitigating diagnostic challenges due to variations in the quality of chemical staining and manual imaging processes as part of the clinical workflow., Comment: 20 Pages, 5 Figures

Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing to execute a set of high-dimensional permutation operations between an input and output field-of-view through layer rotations in a diffractive optical network. In this reconfigurable multiplexed material designed by deep learning, every diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each unique combination of these rotatable layers represents a distinct rotation state of the diffractive design tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive material is capable of all-optically performing up to 4^K independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns, while applying other inverse operations will lead to loss of information. We demonstrated the feasibility of this reconfigurable multiplexed diffractive design by approximating 256 randomly selected permutation matrices using K=4 rotatable diffractive layers. We also experimentally validated this reconfigurable diffractive network using terahertz radiation and 3D-printed diffractive layers, providing a decent match to our numerical results. The presented rotation-multiplexed diffractive processor design is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process., Comment: 37 Pages, 10 Figures

Phase imaging is widely used in biomedical imaging, sensing, and material characterization, among other fields. However, direct imaging of phase objects with subwavelength resolution remains a challenge. Here, we demonstrate subwavelength imaging of phase and amplitude objects based on all-optical diffractive encoding and decoding. To resolve subwavelength features of an object, the diffractive imager uses a thin, high-index solid-immersion layer to transmit high-frequency information of the object to a spatially-optimized diffractive encoder, which converts/encodes high-frequency information of the input into low-frequency spatial modes for transmission through air. The subsequent diffractive decoder layers (in air) are jointly designed with the encoder using deep-learning-based optimization, and communicate with the encoder layer to create magnified images of input objects at its output, revealing subwavelength features that would otherwise be washed away due to diffraction limit. We demonstrate that this all-optical collaboration between a diffractive solid-immersion encoder and the following decoder layers in air can resolve subwavelength phase and amplitude features of input objects in a highly compact design. To experimentally demonstrate its proof-of-concept, we used terahertz radiation and developed a fabrication method for creating monolithic multi-layer diffractive processors. Through these monolithically fabricated diffractive encoder-decoder pairs, we demonstrated phase-to-intensity transformations and all-optically reconstructed subwavelength phase features of input objects by directly transforming them into magnified intensity features at the output. This solid-immersion-based diffractive imager, with its compact and cost-effective design, can find wide-ranging applications in bioimaging, endoscopy, sensing and materials characterization., Comment: 32 Pages, 9 Figures

As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees-of-freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are non-negative, acting on diffraction-limited optical intensity patterns at the input field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors., Comment: 16 Pages, 3 Figures

Diffractive deep neural networks (D2NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view (FOV). Here, we present a pyramid-structured diffractive optical network design (which we term P-D2NN), optimized specifically for unidirectional image magnification and demagnification. In this design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. This P-D2NN design creates high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction - achieving the desired unidirectional imaging operation using a much smaller number of diffractive degrees of freedom within the optical processor volume. Furthermore, P-D2NN design maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single wavelength. We also designed a wavelength-multiplexed P-D2NN, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. Furthermore, we demonstrate that by cascading multiple unidirectional P-D2NN modules, we can achieve higher magnification factors. The efficacy of the P-D2NN architecture was also validated experimentally using terahertz illumination, successfully matching our numerical simulations. P-D2NN offers a physics-inspired strategy for designing task-specific visual processors., Comment: 41 Pages, 11 Figures

Under spatially-coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number (N) of optimizable phase-only diffractive features is greater than or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially-incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially-incoherent monochromatic light, the spatially-varying intensity point spread functon(H) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the spatially-coherent point-spread function of the same diffractive network, and (m,n) and (m',n') define the coordinates of the output and input FOVs, respectively. Using deep learning, supervised through examples of input-output profiles, we numerically demonstrate that a spatially-incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N is greater than or equal to ~2 Ni x No. These results constitute the first demonstration of universal linear intensity transformations performed on an input FOV under spatially-incoherent illumination and will be useful for designing all-optical visual processors that can work with incoherent, natural light., Comment: 29 Pages, 10 Figures

Diffractive optical networks provide rich opportunities for visual computing tasks since the spatial information of a scene can be directly accessed by a diffractive processor without requiring any digital pre-processing steps. Here we present data class-specific transformations all-optically performed between the input and output fields-of-view (FOVs) of a diffractive network. The visual information of the objects is encoded into the amplitude (A), phase (P), or intensity (I) of the optical field at the input, which is all-optically processed by a data class-specific diffractive network. At the output, an image sensor-array directly measures the transformed patterns, all-optically encrypted using the transformation matrices pre-assigned to different data classes, i.e., a separate matrix for each data class. The original input images can be recovered by applying the correct decryption key (the inverse transformation) corresponding to the matching data class, while applying any other key will lead to loss of information. The class-specificity of these all-optical diffractive transformations creates opportunities where different keys can be distributed to different users; each user can only decode the acquired images of only one data class, serving multiple users in an all-optically encrypted manner. We numerically demonstrated all-optical class-specific transformations covering A-->A, I-->I, and P-->I transformations using various image datasets. We also experimentally validated the feasibility of this framework by fabricating a class-specific I-->I transformation diffractive network using two-photon polymerization and successfully tested it at 1550 nm wavelength. Data class-specific all-optical transformations provide a fast and energy-efficient method for image and data encryption, enhancing data security and privacy., Comment: 27 Pages, 9 Figures, 1 Table

Histological staining is the gold standard for tissue examination in clinical pathology and life-science research, which visualizes the tissue and cellular structures using chromatic dyes or fluorescence labels to aid the microscopic assessment of tissue. However, the current histological staining workflow requires tedious sample preparation steps, specialized laboratory infrastructure, and trained histotechnologists, making it expensive, time-consuming, and not accessible in resource-limited settings. Deep learning techniques created new opportunities to revolutionize staining methods by digitally generating histological stains using trained neural networks, providing rapid, cost-effective, and accurate alternatives to standard chemical staining methods. These techniques, broadly referred to as virtual staining, were extensively explored by multiple research groups and demonstrated to be successful in generating various types of histological stains from label-free microscopic images of unstained samples; similar approaches were also used for transforming images of an already stained tissue sample into another type of stain, performing virtual stain-to-stain transformations. In this Review, we provide a comprehensive overview of the recent research advances in deep learning-enabled virtual histological staining techniques. The basic concepts and the typical workflow of virtual staining are introduced, followed by a discussion of representative works and their technical innovations. We also share our perspectives on the future of this emerging field, aiming to inspire readers from diverse scientific fields to further expand the scope of deep learning-enabled virtual histological staining techniques and their applications., Comment: 35 Pages, 7 Figures, 2 Tables

Pathological diagnosis relies on the visual inspection of histologically stained thin tissue specimens, where different types of stains are applied to bring contrast to and highlight various desired histological features. However, the destructive histochemical staining procedures are usually irreversible, making it very difficult to obtain multiple stains on the same tissue section. Here, we demonstrate a virtual stain transfer framework via a cascaded deep neural network (C-DNN) to digitally transform hematoxylin and eosin (H&E) stained tissue images into other types of histological stains. Unlike a single neural network structure which only takes one stain type as input to digitally output images of another stain type, C-DNN first uses virtual staining to transform autofluorescence microscopy images into H&E and then performs stain transfer from H&E to the domain of the other stain in a cascaded manner. This cascaded structure in the training phase allows the model to directly exploit histochemically stained image data on both H&E and the target special stain of interest. This advantage alleviates the challenge of paired data acquisition and improves the image quality and color accuracy of the virtual stain transfer from H&E to another stain. We validated the superior performance of this C-DNN approach using kidney needle core biopsy tissue sections and successfully transferred the H&E-stained tissue images into virtual PAS (periodic acid-Schiff) stain. This method provides high-quality virtual images of special stains using existing, histochemically stained slides and creates new opportunities in digital pathology by performing highly accurate stain-to-stain transformations., Comment: 14 Pages, 4 Figures, 1 Table

Deep learning-based methods in computational microscopy have been shown to be powerful but in general face some challenges due to limited generalization to new types of samples and requirements for large and diverse training data. Here, we demonstrate a few-shot transfer learning method that helps a holographic image reconstruction deep neural network rapidly generalize to new types of samples using small datasets. We pre-trained a convolutional recurrent neural network on a large dataset with diverse types of samples, which serves as the backbone model. By fixing the recurrent blocks and transferring the rest of the convolutional blocks of the pre-trained model, we reduced the number of trainable parameters by ~90% compared with standard transfer learning, while achieving equivalent generalization. We validated the effectiveness of this approach by successfully generalizing to new types of samples using small holographic datasets for training, and achieved (i) ~2.5-fold convergence speed acceleration, (ii) ~20% computation time reduction per epoch, and (iii) improved reconstruction performance over baseline network models trained from scratch. This few-shot transfer learning approach can potentially be applied in other microscopic imaging methods, helping to generalize to new types of samples without the need for extensive training time and data., Comment: 10 Pages, 3 Figures

Structured light with customized complex topological pattern inspires diverse classical and quantum investigations underpinned by accurate detection techniques. However, the current detection schemes are limited to vortex beam with simple phase singularity. The precise recognition of general structured light with multiple singularities remains elusive. Here, we report a deep learning (DL) framework that can unveil multi-singularity phase structures in an end-to-end manner after feeding only two intensity patterns upon beam propagation captured via a camera, thus unleashing intuitive information of twisted photons. The DL toolbox can also acquire phases of Laguerre-Gaussian (LG) modes with single singularity and other general phase objects likewise. Leveraging this DL platform, a phase-based optical secret sharing (OSS) protocol is proposed, which is based on a more general class of multi-singularity modes than conventional LG beams. The OSS protocol features strong security, wealthy state space and convenient intensity-based measurements. This study opens new avenues for vortex beam communications, laser mode analysis, microscopy, Bose-Einstein condensates characterization, etc.

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

Vectorially structured light has emerged as an enabling tool in many diverse applications, from communication to imaging, exploiting quantum-like correlations courtesy of a non-separable spatially varying polarization structure. Creating these states at the source remains challenging and is presently limited to two-dimensional vectorial states by customized lasers. Here we invoke ray-wave duality in a simple laser cavity to produce polarization marked multi-path modes that are non-separable in three degrees of freedom and in eight dimensions. As a topical example, we use our laser to produce the complete set of Greenberger-Horne-Zeilinger (GHZ) basis states, mimicking high-dimensional multi-partite entanglement with classical light, which we confirm by a new projection approach. We offer a complete theoretical framework for our laser based on SU(2) symmetry groups, revealing a rich parameter space for further exploitation. Our approach requires only a conventional laser with no special optical elements, is easily scaleable to higher dimensions, and offers a simple but elegant solution for at-the-source creation of classically entangled states of structured light, opening new applications in simulating and enhancing high-dimensional quantum systems.