Recovery of Continuous 3D Refractive Index Maps from

Discrete Intensity-Only Measurements using Neural Fields

The FIRST Neural Field method for Intensity Diffraction Tomography.

Renhao Liu*,1, Yu Sun*,1, Jiabei Zhu2, Lei Tian2, Ulugbek S. Kamilov1
1Computational Imaging Group (CIG), Washington University in St. Louis
2Computational Imaging Systems Lab, Boston University

Paper Preprint Code


Intensity diffraction tomography (IDT) refers to a class of optical microscopy techniques for imaging the 3D refractive index (RI) distribution of a sample from a set of 2D intensity-only measurements. The reconstruction of artifact-free RI maps is a fundamental challenge in IDT due to the loss of phase information and the missing cone problem. Neural fields (NF) has recently emerged as a new deep learning (DL) approach for learning continuous representations of physical fields. NF uses a coordinate-based neural network to represent the field by mapping the spatial coordinates to the corresponding physical quantities, in our case the complex-valued refractive index values. We present DeCAF as the first NF-based IDT method that can learn a high-quality continuous representation of a RI volume from its intensity-only and limited-angle measurements. The representation in DeCAF is learned directly from the measurements of the test sample by using the IDT forward model, without any ground-truth RI maps. We qualitatively and quantitatively evaluate DeCAF on the simulated and experimental biological samples. Our results show that DeCAF can generate high-contrast and artifact-free RI maps and lead to up to 2.1✕ reduction in MSE over existing methods.


Experimental Results



Human buccal epithelial cells


Caenorhabditis elegans


Granulocyte phantom (simulated)



@article{liu2022decaf, title={Recovery of continuous 3D refractive index maps from discrete intensity-only measurements using neural fields}, author={Liu, Renhao and Sun, Yu and Zhu, Jiabei and Tian, Lei and Kamilov, Ulugbek S.}, journal={Nat. Mach. Intell.}, pages = {781--791}, volume = {4}, year={2022} }