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1. Computational 3D microscopy with optical coherence refraction tomography

   https://doi.org/10.1364/OPTICA.454860  

   Zhou, Kevin_C; McNabb, Ryan_P; Qian, Ruobing; Degan, Simone; Dhalla, Al-Hafeez; Farsiu, Sina; Izatt, Joseph_A (June 2022, Optica)

   Optical coherence tomography (OCT) has seen widespread success as anin vivoclinical diagnostic 3D imaging modality, impacting areas including ophthalmology, cardiology, and gastroenterology. Despite its many advantages, such as high sensitivity, speed, and depth penetration, OCT suffers from several shortcomings that ultimately limit its utility as a 3D microscopy tool, such as its pervasive coherent speckle noise and poor lateral resolution required to maintain millimeter-scale imaging depths. Here, we present 3D optical coherence refraction tomography (OCRT), a computational extension of OCT that synthesizes an incoherent contrast mechanism by combining multiple OCT volumes, acquired across two rotation axes, to form a resolution-enhanced, speckle-reduced, refraction-corrected 3D reconstruction. Our label-free computational 3D microscope features a novel optical design incorporating a parabolic mirror to enable the capture of 5D plenoptic datasets, consisting of millimetric 3D fields of view over up to $\pm <\#comment/>{75}^{\circ <\#comment/>}$without moving the sample. We demonstrate that 3D OCRT reveals 3D features unobserved by conventional OCT in fruit fly, zebrafish, and mouse samples. 

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2. High-speed multiview imaging approaching 4pi steradians using conic section mirrors: theoretical and practical considerations

   https://doi.org/10.1364/JOSAA.440592  

   Zhou, Kevin_C; Dhalla, Al-Hafeez; McNabb, Ryan_P; Qian, Ruobing; Farsiu, Sina; Izatt, Joseph_A (November 2021, Journal of the Optical Society of America A)

   Illuminating or imaging samples from a broad angular range is essential in a wide variety of computational 3D imaging and resolution-enhancement techniques, such as optical projection tomography, optical diffraction tomography, synthetic aperture microscopy, Fourier ptychographic microscopy, structured illumination microscopy, photogrammetry, and optical coherence refraction tomography. The wider the angular coverage, the better the resolution enhancement or 3D-resolving capabilities. However, achieving such angular ranges is a practical challenge, especially when approaching $\pm <\#comment/>{90}^{\circ <\#comment/>}$or beyond. Often, researchers resort to expensive, proprietary high numerical aperture (NA) objectives or to rotating the sample or source-detector pair, which sacrifices temporal resolution or perturbs the sample. Here, we propose several new strategies for multiangle imaging approaching 4pi steradians using concave parabolic or ellipsoidal mirrors and fast, low rotational inertia scanners, such as galvanometers. We derive theoretically and empirically relations between a variety of system parameters (e.g.,  NA, wavelength, focal length, telecentricity) and achievable fields of view (FOVs) and importantly show that intrinsic tilt aberrations donotrestrict FOV for many multiview imaging applications, contrary to conventional wisdom. Finally, we present strategies for avoiding spherical aberrations at obliquely illuminated flat boundaries. Our simple designs allow for high-speed multiangle imaging for microscopic, mesoscopic, and macroscopic applications. 

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3. 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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4. Standard monomials and invariant theory of arc spaces II: Symplectic group

   https://doi.org/10.1090/jag/834  

   Linshaw, Andrew; Song, Bailin (October 2024, Journal of Algebraic Geometry)

   This is the second in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the Pfaffian variety over $K$. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the symplectic group. 

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5. Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

   https://doi.org/10.21468/SciPostPhys.17.2.034  

   Nikolaenko, Alexander; Zhang, Ya-Hui (January 2024, SciPost Physics)

   Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo couplingJ_K $J_K$at fixed doping x. At large positiveJ_K $J_K$, we confirm the expected conventional Luttinger liquid phase with2k_F=\frac{1+x}{2} $2k_F=\frac{1+x}{2}$(in units of2\pi $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In theJ_K ≤ 0 $J_K\le 0$side, our simulation finds the existence of a fractional Luttinger liquid (LL\star $\star$) phase with2k_F=\frac{x}{2} $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star $\star$) phase in higher dimensions. The LL\star $\star$phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positiveJ_K $J_K$. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) ofJ_K $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around0.035 J $0.035J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponentz=+ $z=+$. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference. 

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