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.Producing high-quality 3D refractive index maps from 2D intensity-only measurements is a long-standing objective in computational microscopy, with many applications involving the visualization of cellular and subcellular structures. A new method can reconstruct high-contrast and artefact-free images by employing the neural fields technique, which can learn a continuous 3D representation using a neural network that maps spatial coordinates to the refractive index values.

强度衍射层析成像（IDT）是一类光学显微技术，用于从一组仅含强度的二维测量值中对样本的三维折射率（RI）分布进行成像。由于相位信息的丢失和缺失锥问题，无伪影RI图的重建是IDT中的一个基本挑战。神经场最近作为一种学习物理场连续表示的新深度学习方法而出现。该技术使用基于坐标的神经网络，通过将空间坐标映射到相应的物理量（在我们的情况下是复值折射率值）来表示场。我们提出深度连续无伪影RI场（DeCAF）作为一种基于神经场的IDT方法，它能够从仅含强度和有限角度的测量值中学习到高质量的RI体积连续表示。DeCAF中的表示是通过使用IDT正演模型直接从测试样本的测量值中学习得到的，无需任何真实的RI图。我们对模拟和实验生物样本上的DeCAF进行了定性和定量评估。我们的结果表明，DeCAF能够生成高对比度且无伪影的RI图，并且与现有方法相比，均方误差最多可降低2.1倍。从仅含强度的二维测量值中生成高质量的三维折射率图是计算显微术中一个长期的目标，在涉及细胞和亚细胞结构可视化的许多应用中都有需求。一种新方法可以通过采用神经场技术重建高对比度且无伪影的图像，该技术能够使用将空间坐标映射到折射率值的神经网络学习连续的三维表示。