  Refractive Index Tomography is the inverse problem of reconstructing the
continuously-varying 3D refractive index in a scene using 2D projected image
measurements. Although a purely refractive field is not directly visible, it
bends light rays as they travel through space, thus providing a signal for
reconstruction. The effects of such fields appear in many scientific computer
vision settings, ranging from refraction due to transparent cells in microscopy
to the lensing of distant galaxies caused by dark matter in astrophysics.
Reconstructing these fields is particularly difficult due to the complex
nonlinear effects of the refractive field on observed images. Furthermore,
while standard 3D reconstruction and tomography settings typically have access
to observations of the scene from many viewpoints, many refractive index
tomography problem settings only have access to images observed from a single
viewpoint. We introduce a method that leverages prior knowledge of light
sources scattered throughout the refractive medium to help disambiguate the
single-view refractive index tomography problem. We differentiably trace curved
rays through a neural field representation of the refractive field, and
optimize its parameters to best reproduce the observed image. We demonstrate
the efficacy of our approach by reconstructing simulated refractive fields,
analyze the effects of light source distribution on the recovered field, and
test our method on a simulated dark matter mapping problem where we
successfully recover the 3D refractive field caused by a realistic dark matter
distribution.
