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 weaklyscattering 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 non-linear optimization problem to recover the sample's 3D RI distribution. We experimentally demonstrate 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 ≤250 nm and ≤900 nm, respectively. for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved. Fluorescent imaging has enabled stunning visualizations of biological processes at a variety of size scales and resolutions, for studies of gene expression, protein interactions, intracellular dynamics, etc [1][2][3][4]. However, the fluorescent techniques require exogenous biological labels, and so do not directly give endogenous information about a sample's biological structure.Optical diffraction tomography (ODT) also targets 3D biological imaging. In contrast to fluorescent methods, ODT avoids the use of exogenous biological labels, and instead utilizes the intrinsic optical variation within a sample to reconstruct its 3D refractive-index (RI) distribution [5][6][7][8][9][10][11]. Hence, ODT avoids some of fluorescent imaging's main drawbacks, such as photobleaching, slow acquisition speed, low signal-to-noise (SNR) ratio, and complex samplepreparation protocol. Furthermore, RI imaging enables examination of the structural, mechanical, and biochemical properties of a sample, which are important for studies in morphology, mass, shear stiffness, and spectroscopy [9,[12][13][14][15].Standard implementations of ODT use either a rotating sample or a scanning laser beam to capture the angle-specific scattering arising from the sample [5,7,[16][17][18]. Under the assumption of weak scattering (i.e., 1st Born or Rytov approximations), 2D electric-field measurements directly yield information about the sample's 3D scattering potential [19][20][21]. Standard ODT reconstruction algorithms utilize the Fourier diffraction theorem to project the information contained in each electric-field measurement onto spherical shells (i.e., Ewald surfaces) in the 3D Fourier space of the sample's scattering potential [22,23]. ...

Fourier ptychography captures intensity images with varying source patterns (illumination angles) in order to computationally reconstruct large space-bandwidth-product images. Accurate knowledge of the illumination angles is necessary for good image quality; hence, calibration methods are crucial, despite often being impractical or slow. Here, we propose a fast, robust, and accurate self-calibration algorithm that uses only experimentally collected data and general knowledge of the illumination setup. First, our algorithm makes a fast direct estimate of the brightfield illumination angles based on image processing. Then, a more computationally intensive spectral correlation method is used inside the iterative solver to further refine the angle estimates of both brightfield and darkfield images. We demonstrate our method for correcting large and small misalignment artifacts in 2D and 3D Fourier ptychography with different source types: an LED array, a galvo-steered laser, and a high-NA quasi-dome LED illuminator.

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.

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Low-cost, sub-micron resolution, wide-field 1 computational microscopy using opensource 2 hardware 3 4 ABSTRACT 11 The revolution in low-cost consumer photography and computation provides fertile 12 opportunity for a disruptive reduction in the cost of biomedical imaging. Conventional 13 approaches to low-cost microscopy are fundamentally restricted, however, to modest field of 14 view (FOV) and/or resolution. We report a low-cost microscopy technique, implemented with 15a Raspberry Pi single-board computer and color camera combined with Fourier ptychography 16 (FP), to computationally construct 25-megapixel images with sub-micron resolution. New 17 image-construction techniques were developed to enable the use of the low-cost Bayer color 18 sensor, to compensate for the highly aberrated re-used camera lens and to compensate for 19 misalignments associated with the 3D-printed microscope structure. This high ratio of 20 performance to cost is of particular interest to high-throughput microscopy applications, 21 ranging from drug discovery and digital pathology to health screening in low-income countries. 22 3D models and assembly instructions of our microscope are made available for open source 23 use. 24 405 Instructions to build a Raspberry Pi 406 Fourier ptychographic computational 407 microscope 408This document provides instructions to build a low-cost computational microscope reported in 409 the manuscript: "Low-cost, sub-micron resolution, wide-field computational microscopy with 410Raspberry Pi hardware". The CAD files and data acquisition codes can be downloaded from 411

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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.

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