We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixelscale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4× FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.

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]. ...

Deep neural networks have emerged as effective tools for computational imaging including quantitative phase microscopy of transparent samples. To reconstruct phase from intensity, current approaches rely on supervised learning with training examples; consequently, their performance is sensitive to a match of training and imaging settings. Here we propose a new approach to phase microscopy by using an untrained deep neural network for measurement formation, encapsulating the image prior and imaging physics. Our approach does not require any training data and simultaneously reconstructs the sought phase and pupil-plane aberrations by fitting the weights of the network to the captured images. To demonstrate experimentally, we reconstruct quantitative phase from through-focus images blindly (i.e. no explicit knowledge of the aberrations).

We propose an accurate and computationally efficient 3D scattering model, multi-layer Born (MLB), and use it to recover the 3D refractive index (RI) of thick biological samples. For inverse problems recovering the complex field of thick samples, weak scattering models (e.g., first Born) may fail or underestimate the RI, especially with a large index contrast. Multi-slice (MS) beam propagation methods model multiple scattering to provide more realistic reconstructions; however, MS does not properly account for highly oblique scattering, nor does it model backward scattering. Our proposed MLB model uses a first Born model at each of many slices, accurately capturing the oblique scattering effects and estimating the backward scattering process. When used in conjunction with an inverse solver, the model provides more accurate RI reconstructions for high-resolution phase tomography. Importantly, MLB retains a reasonable computation time that is critical for practical implementation with iterative inverse algorithms.

We present a new technique for quantitative phase and amplitude microscopy from a single color image with coded illumination. Our system consists of a commercial brightfield microscope with one hardware modification—an inexpensive 3D printed condenser insert. The method, color-multiplexed Differential Phase Contrast (cDPC), is a single-shot variant of Differential Phase Contrast (DPC), which recovers the phase of a sample from images with asymmetric illumination. We employ partially coherent illumination to achieve resolution corresponding to 2× the objective NA. Quantitative phase can then be used to synthesize DIC and phase contrast images or extract shape and density. We demonstrate amplitude and phase recovery at camera-limited frame rates (50 fps) for various in vitro cell samples and c. elegans in a micro-fluidic channel.

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The temporal resolution of quantitative phase imaging with Differential Phase Contrast (DPC) is limited by the requirement for multiple illumination-encoded measurements. This inhibits imaging of fast-moving samples. We present a computational approach to model and correct for non-rigid sample motion during the DPC acquisition in order to improve temporal resolution to that of a single-shot method and enable imaging of motion dynamics at the framerate of the sensor. Our method relies on the addition of a simultaneously-acquired color-multiplexed reference signal to enable non-rigid registration of measurements prior to phase retrieval. We show experimental results where we reduce motion blur from fast-moving live biological samples.