# High-resolution 3D refractive index microscopy of multiple-scattering samples from intensity images

arXiv: https://arxiv.org/abs/1909.00023 · HTML: https://mlsanity.com/paper/1909.00023/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 9 of 9)

- [Recovery of Continuous 3D Refractive Index Maps from Discrete Intensity-Only Measurements using Neural Fields](https://mlsanity.com/paper/2112.00002/) (2021)
- [Single View Refractive Index Tomography with Neural Fields](https://mlsanity.com/paper/2309.04437/) (2023)
- [Physical model simulator-trained neural network for computational 3D phase imaging of multiple-scattering samples](https://mlsanity.com/paper/2103.15795/) (2021)
- [Physics-informed neural networks for diffraction tomography](https://mlsanity.com/paper/2207.14230/) (2022)
- [Double Blind Imaging with Generative Modeling](https://mlsanity.com/paper/2503.21501/) (2025)
- [Neural Inverse Scattering with Score-based Regularization](https://mlsanity.com/paper/2505.14560/) (2025)
- [Optical Diffraction Tomography based on 3D Physics-Inspired Neural Network (PINN)](https://mlsanity.com/paper/2206.05236/) (2022)
- [WaveOrder: A differentiable wave-optical framework for scalable biological microscopy with diverse modalities](https://mlsanity.com/paper/2412.09775/) (2024)
- [Inductively Scalable, Single-Step Neural Surrogates for Wave-Scattering Inverse Problems](https://mlsanity.com/paper/2608.17344/) (2026)

## Abstract (arXiv)

Optical diffraction tomography (ODT) reconstructs a samples volumetric refractive index (RI) to create high-contrast, quantitative 3D visualizations of biological samples. However, standard implementations of ODT use interferometric systems, and so are sensitive to phase instabilities, complex mechanical design, and coherent noise. Furthermore, their reconstruction framework is typically limited to weakly-scattering samples, and thus excludes a whole class of multiple-scattering samples. Here, we implement a new 3D RI microscopy technique that utilizes a computational multi-slice beam propagation method to invert the optical scattering process and reconstruct high-resolution (NA>1.0) 3D RI distributions of multiple-scattering samples. The method acquires intensity-only measurements from different illumination angles, and then solves a non-linear optimization problem to recover the sample 3D RI distribution. We experimentally demonstrate reconstruction of samples with varying amounts of multiple scattering: a 3T3 fibroblast cell, a cluster of C. elegans embryos, and a whole C. elegans worm, with lateral and axial resolutions of 250 nm and 900 nm, respectively.