# Single View Refractive Index Tomography with Neural Fields

arXiv: https://arxiv.org/abs/2309.04437 · HTML: https://mlsanity.com/paper/2309.04437/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Eikonal Fields for Refractive Novel-View Synthesis](https://mlsanity.com/paper/2202.00948/) (2022)
- [Gravitationally Lensed Black Hole Emission Tomography](https://mlsanity.com/paper/2204.03715/) (2022)
- [High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images](https://mlsanity.com/paper/1909.00023/) (2019)

## Built on by (most cited first, 8 of 8)

- [Revealing the 3D Cosmic Web through Gravitationally Constrained Neural Fields](https://mlsanity.com/paper/2504.15262/) (2025)
- [Dynamic Black-hole Emission Tomography with Physics-informed Neural Fields](https://mlsanity.com/paper/2602.08029/) (2026)
- [Mapping Dark-Matter Clusters via Physics-Guided Diffusion Models](https://mlsanity.com/paper/2603.14503/) (2026)
- [Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity](https://mlsanity.com/paper/2507.15775/) (2025)
- [Revealing Fine Structure in Protoplanetary Disks with Physics Constrained Neural Fields](https://mlsanity.com/paper/2509.03623/) (2025)
- [Indoor Airflow Imaging Using Physics-Informed Background-Oriented Schlieren Tomography](https://mlsanity.com/paper/2509.14442/) (2025)
- [Neural Fields for NV-Center Inverse Sensing](https://mlsanity.com/paper/2605.13988/) (2026)
- [Generative Diffusion Priors for 3D Mapping of the Dark Universe](https://mlsanity.com/paper/2606.00803/) (2026)

## Abstract (arXiv)

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.