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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. 

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.