Recovery of continuous 3D refractive index maps from discrete intensity-only measurements using neural fields

Intensity diffraction tomography (IDT) refers to a class of optical microscopy techniques for imaging the three-dimensional refractive index (RI) distribution of a sample from a set of two-dimensional intensity-only measurements. The reconstruction of artefact-free RI maps is a fundamental challenge in IDT due to the loss of phase information and the missing-cone problem. Neural fields has recently emerged as a new deep learning approach for learning continuous representations of physical fields. The technique 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 Deep Continuous Artefact-free RI Field (DeCAF) as a neural-fields-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 artefact-free RI maps and lead to an up to 2.1-fold reduction in the mean squared error over existing methods.