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1. Single-pixel fluorescent diffraction tomography

   https://doi.org/10.1364/OPTICA.400547  

   Stockton, Patrick A. ; Field, Jeffrey J. ; Squier, Jeff ; Pezeshki, Ali ; Bartels, Randy A. ( November 2020 , Optica)

   Optical diffraction tomography (ODT) is an indispensable tool for studying objects in three dimensions. Until now, ODT has been limited to coherent light because spatial phase information is required to solve the inverse scattering problem. We introduce a method that enables ODT to be applied to imaging incoherent contrast mechanisms such as fluorescent emission. Our strategy mimics the coherent scattering process with two spatially coherent illumination beams. The interferometric illumination pattern encodes spatial phase in temporal variations of the fluorescent emission, thereby allowing incoherent fluorescent emission to mimic the behavior of coherent illumination. The temporal variations permit recovery of the spatial distribution of fluorescent emission with an inverse scattering model. Simulations and experiments demonstrate isotropic resolution in the 3D reconstruction of a fluorescent object.

    

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2. Diffraction tomography with a deep image prior

   https://doi.org/10.1364/OE.379200  

   Zhou, Kevin C. ; Horstmeyer, Roarke ( April 2020 , Optics Express)

   We present a tomographic imaging technique, termed Deep Prior Diffraction Tomography (DP-DT), to reconstruct the 3D refractive index (RI) of thick biological samples at high resolution from a sequence of low-resolution images collected under angularly varying illumination. DP-DT processes the multi-angle data using a phase retrieval algorithm that is extended by a deep image prior (DIP), which reparameterizes the 3D sample reconstruction with an untrained, deep generative 3D convolutional neural network (CNN). We show that DP-DT effectively addresses the missing cone problem, which otherwise degrades the resolution and quality of standard 3D reconstruction algorithms. As DP-DT does not require pre-captured data or pre-training, it is not biased towards any particular dataset. Hence, it is a general technique that can be applied to a wide variety of 3D samples, including scenarios in which large datasets for supervised training would be infeasible or expensive. We applied DP-DT to obtain 3D RI maps of bead phantoms and complex biological specimens, both in simulation and experiment, and show that DP-DT produces higher-quality results than standard regularization techniques. We further demonstrate the generality of DP-DT, using two different scattering models, the first Born and multi-slice models. Our results point to the potential benefits of DP-DT for other 3D imaging modalities, including X-ray computed tomography, magnetic resonance imaging, and electron microscopy.

    

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3. Self-calibrated 3D differential phase contrast microscopy with optimized illumination

   https://doi.org/10.1364/BOE.450838  

   Cao, Ruiming ; Kellman, Michael ; Ren, David ; Eckert, Regina ; Waller, Laura ( February 2022 , Biomedical Optics Express)

   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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4. Quantitative 3D refractive index tomography of opaque samples in epi-mode

   https://doi.org/10.1364/OPTICA.410135  

   Ledwig, Patrick ; Robles, Francisco E. ( December 2020 , Optica)

   Three-dimensional (3D) refractive index (RI) tomography has recently become an exciting new tool for biological studies. However, its limitation to (1) thin samples resulting from a need of transmissive illumination and (2) small fields of view (typically$\sim <\#comment/>50\text{µ<\#comment/>}\mathrm{m}\times <\#comment/>50\text{µ<\#comment/>}\mathrm{m}$) has hindered its utility in broader biomedical applications. In this work, we demonstrate 3D RI tomography with a large field of view in opaque, arbitrarily thick scattering samples (unsuitable for imaging with conventional transmissive tomographic techniques) with a penetration depth of ca. one mean free scattering path length ($\sim <\#comment/>100\text{µ<\#comment/>}\mathrm{m}$in tissue) using a simple, low-cost microscope system with epi-illumination. This approach leverages a solution to the inverse scattering problem via the general non-paraxial 3D optical transfer function of our quantitative oblique back-illumination microscopy (qOBM) optical system. A theoretical analysis is presented along with simulations and experimental validations using polystyrene beads, and rat and human thick brain tissues. This work has significant implications for the investigation of optically thick, semi-infinite samples in a non-invasive and label-free manner. This unique 3D qOBM approach can extend the utility of 3D RI tomography for translational and clinical medicine.

    

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5. Model and learning-based computational 3D phase microscopy with intensity diffraction tomography

   https://doi.org/10.23919/Eusipco47968.2020.9287407  

   Matlock, Alex ; Xue, Yujia ; Li, Yunzhe ; Cheng, Shiyi ; Tahir, Waleed ; Tian, Lei ( January 2021 , 2020 28th European Signal Processing Conference (EUSIPCO))

   null (Ed.)

   Intensity Diffraction Tomography (IDT) is a new computational microscopy technique providing quantitative, volumetric, large field-of-view (FOV) phase imaging of biological samples. This approach uses computationally efficient inverse scattering models to recover 3D phase volumes of weakly scattering objects from intensity measurements taken under diverse illumination at a single focal plane. IDT is easily implemented in a standard microscope equipped with an LED array source and requires no exogenous contrast agents, making the technology widely accessible for biological research.Here, we discuss model and learning-based approaches for complex 3D object recovery with IDT. We present two model-based computational illumination strategies, multiplexed IDT (mIDT) [1] and annular IDT (aIDT) [2], that achieve high-throughput quantitative 3D object phase recovery at hardware-limited 4Hz and 10Hz volume rates, respectively. We illustrate these techniques on living epithelial buccal cells and Caenorhabditis elegans worms. For strong scattering object recovery with IDT, we present an uncertainty quantification framework for assessing the reliability of deep learning-based phase recovery methods [3]. This framework provides per-pixel evaluation of a neural network predictions confidence level, allowing for efficient and reliable complex object recovery. This uncertainty learning framework is widely applicable for reliable deep learning-based biomedical imaging techniques and shows significant potential for IDT. 

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