  Multimode fibers recently emerged as compact minimally-invasive probes for
high-resolution deep-tissue imaging. However, the commonly used silica fibers
have a relatively low numerical aperture (NA) limiting the spatial resolution
of a probe. On top of that, light propagation within the solid core generates
auto-fluorescence and Raman background, which interferes with imaging. Here we
propose to use a hollow-core fiber to solve these problems. We experimentally
demonstrate spatial wavefront shaping at the multimode hollow-core fiber output
with tunable high-NA. We demonstrate raster-scan and speckle-based compressive
imaging through a multimode hollow-core fiber.
