Refractive Index Tomography is an inverse problem in which we seek to reconstruct a scene's 3D refractive field from 2D projected image measurements. The refractive field is not visible itself, but instead affects how the path of a light ray is continuously curved as it travels through space. Refractive fields appear across a wide variety of scientific applications, from translucent cell samples in microscopy to fields of dark matter bending light from faraway galaxies. This problem poses a unique challenge because the refractive field directly affects the path that light takes, making its recovery a non-linear problem. In addition, in contrast with traditional tomography, we seek to recover the refractive field using a projected image from only a single viewpoint by leveraging knowledge of light sources scattered throughout the medium. In this work, we introduce a method that uses a coordinate-based neural network to model the underlying continuous refractive field in a scene. We then use explicit modeling of rays' 3D spatial curvature to optimize the parameters of this network, reconstructing refractive fields with an analysis-by-synthesis approach. The efficacy of our approach is demonstrated by recovering refractive fields in simulation, and analyzing how recovery is affected by the light source distribution. We then test our method on a simulated dark matter mapping problem, where we recover the refractive field underlying a realistic simulated dark matter distribution.

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