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.

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).

Optical diffraction tomography (ODT) reconstructs a samples volumetric refractive index (RI) to create high-contrast, quantitative 3D visualizations of biological samples. However, standard implementations of ODT use interferometric systems, and so are sensitive to phase instabilities, complex mechanical design, and coherent noise. Furthermore, their reconstruction framework is typically limited to weakly-scattering samples, and thus excludes a whole class of multiple-scattering samples. Here, we implement a new 3D RI microscopy technique that utilizes a computational multi-slice beam propagation method to invert the optical scattering process and reconstruct high-resolution (NA>1.0) 3D RI distributions of multiple-scattering samples. The method acquires intensity-only measurements from different illumination angles, and then solves a non-linear optimization problem to recover the sample 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.

3D quantitative phase (refractive index) microscopy reveals volumetric structure of biological specimens. Optical diffraction tomography (ODT) is a common technique for 3D phase imaging. By angularly scanning a spatially coherent light source and measuring scattered fields on the imaging plane, 3D refractive index (RI) is recovered by solving an inverse problem. However, ODT often linearizes the process by using a weakly scattering model, e.g. the first Born approximation or Rytov approximation, which underestimate the RI and fail to reconstruct realistic shape of high RI contrast multiple scattering objects. On the other hand, non-linear models such as the multi-slice or beam propagation methods mitigate artifacts by modeling multiple scattering. However, they ignore back-scattering and intra-slice scattering and make a paraxial approximation by assuming each slice is infinitesimally thin. In this work, we propose a new 3D scattering model Multi-layer Born (MLB), which treats the object as thin 3D slabs with finite thickness and applies the first Born approximation on each slab as the field propagates through the object, increasing the accuracy significantly. In the meantime, a similar computation complexity is achieved comparing to the previously proposed multi-slice models. Therefore, MLB can achieve accuracy similar to that of FDTD or SEAGLE, a frequency domain solver, with orders of magnitude less computation time. In addition to forward scattering, multiple back-scattering effects are also captured by MLB unlike existing models. We apply MLB to recover the RI distribution of 3D phantoms and biological samples with intensity-only measurements from an LED array microscope and show that the results are superior to existing methods.

Phase imaging provides quantitative structural data about biological samples as an alternative or complementary contrast method to the functional information given by fluorescence imaging. In certain cases, fluorescence imaging is undesirable because it may harm the development of living cells or add time and complexity to imaging pipelines. However, current 3D phase reconstruction methods, such as optical diffraction tomography [1], are often limited to a single-scattering approximation. This limits the amount of scattering that such 3D reconstruction algorithms can successfully handle, and therefore effectively limits the sample thickness that can be successfully reconstructed. More recent methods such as 3D Fourier ptychographic microscopy (FPM) have used intensity-only images combined with multiple-scattering models in order to reconstruct 3D volumes [2]. In practice, however, continuous biological samples on the order of 100 um thick are not well-reconstructed by 3D FPM, due to a lack of diverse information across the volume which creates an ill-posed inverse problem. To mitigate this, we introduce simultaneous detection coding in the form of pupil control to the 3D FPM capture scheme. Simple pupil coding schemes enabled us to capture diverse information across our volume. In concert with a beam propagation model that takes into account multiple scattering, this combination of illumination- and detection-side coding allows us to more stably reconstruct 3D phase for larger-scale biological samples. [1] E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). [2] L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica, 2, 104-111 (2015).

Electron tomography is used in both materials science and structural biology to image features well below the optical resolution limit. Here, we present a new method for high-resolution 3D transmission electron microscopy (TEM) which approximately reconstructs the electrostatic potential of a sample at atomic resolution in all three dimensions. We use phase contrast images captured through-focus and at varying tilt angles, along with an implicit phase retrieval algorithm that accounts for dynamical and strong scattering, providing more accurate results with much lower electron doses than current atomic electron tomography methods. We test our algorithm using simulated images of a synthetic needle geometry dataset composed of an amorphous silicon dioxide shell around a silicon core. By simulating various levels of electron dose, tilt and defocus, missing projections, and regularization methods, we identify a configuration that allows us to accurately determine both atomic positions and species. We also test the ability of our method to recover randomly positioned vacancies in light elements such as silicon, and to accurately reconstruct strongly-scattering elements such as tungsten.

3D imaging methods are limited in accuracy, depth, and resolution when ap plied to thick, multiply-scattering biological samples. We introduce pupil coding in conjunction with illumination coding for 3D Fourier ptychography, resulting in improved reconstruction of large clusters of cells.

Fourier Ptychographic Microscopy (FPM) is a computational imaging method that is able to super-resolve features beyond the diffraction-limit set by the objective lens of a traditional microscope. This is accomplished by using synthetic aperture and phase retrieval algorithms to combine many measurements captured by an LED array microscope with programmable source patterns. FPM provides simultaneous large field-of-view and high resolution imaging, but at the cost of reduced temporal resolution, thereby limiting live cell applications. In this work, we learn LED source pattern designs that compress the many required measurements into only a few, with negligible loss in reconstruction quality or resolution. This is accomplished by recasting the super-resolution reconstruction as a Physics-based Neural Network and learning the experimental design to optimize the network's overall performance. Specifically, we learn LED patterns for different applications (e.g. amplitude contrast and quantitative phase imaging) and show that the designs we learn through simulation generalize well in the experimental setting. Further, we discuss a context-specific loss function, practical memory limitations, and interpretability of our learned designs.

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We demonstrate a 3D phase imaging model for scattering objects with intensity-only measurements taken with patterned illumination in an LED array microscope. 3D refractive index (RI) of polystyrene beads is recovered, and the preliminary results indicate that the proposed model outperforms existing methods in terms of quantitative accuracy of RI.

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.

We demonstrate a tomographic Transmission Electron Microscopy (TEM) imaging modality and reconstruction algorithm that determines 3D positions of strongly scattering atoms. Our simulation-only results show that atomic potentials can be quantitatively recovered at atomic resolution from intensity-only measurements.

Electron tomography is a technique used in both materials science and structural biology to image features well below optical resolution limit. In this work, we present a new algorithm for reconstructing the three-dimensional(3D) electrostatic potential of a sample at atomic resolution from phase contrast imaging using high-resolution transmission electron microscopy. Our method accounts for dynamical and strong phase scattering, providing more accurate results with much lower electron doses than those current atomic electron tomography experiments. We test our algorithm using simulated images of a synthetic needle geometry dataset composed of an amorphous silicon dioxide shell around a silicon core. Our results show that, for a wide range of experimental parameters, we can accurately determine both atomic positions and species, and also identify vacancies even for light elements such as silicon and disordered materials such as amorphous silicon dioxide and also identify vacancies.

We present a microscope system for high-resolution complex-field tomography from intensity-only measurements with illumination angle scanning. Preliminary results using a multi-slice framework show promise in visualizing the 3D structure of a cluster of 3 µm transparent microspheres.

Differential Phase Contrast (DPC) microscopy is a practical method for recovering quantitative phase from intensity images captured with different source patterns in an LED array microscope. Being a partially coherent imaging method, DPC does not suffer from speckle artifacts and achieves 2× better resolution than coherent methods. Like all imaging systems, however, DPC is susceptible to aberrations. Here, we propose a method of algorithmic self-calibration for DPC where we simultaneously recover the complex-field of the sample and the spatially-variant aberrations of the system, using 4 images with different illumination source patterns. The resulting phase reconstructions are digitally aberration-corrected.

We implement 3D phase tomography on an X-ray computed tomography (CT) beamline by adding a sandpaper analyzer in the Fresnel region. Our algorithm solves for 3D phase directly from the raw intensity measurements, while simultaneously estimating the sandpaper phase. We discuss the use of priors to reduce the number of measurements.

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.