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

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.