  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 (OPT), optical diffraction tomography
(ODT), synthetic aperture microscopy, Fourier ptychographic microscopy (FPM),
structured illumination microscopy (SIM), photogrammetry, and optical coherence
refraction tomography (OCRT). 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
plus-or-minus 90 degrees 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 multi-angle 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 do not
restrict FOV for many multi-view 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
multi-angle imaging for microscopic, mesoscopic, and macroscopic applications.
