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.

逆问题中，我们试图从二维投影图像测量中重构场景的三维折射场，为此我们引入了一种使用基于坐标的神经网络对场景中的连续折射场进行建模的方法，并通过分析合成方法优化该网络的参数，以实现对折射场的重建。