Background-oriented Schlieren tomography (BOST) is a prevalent method for visualizing intricate turbulent flows, valued for its ease of implementation and capacity to capture three-dimensional distributions of a multitude of flow parameters. However, the voxel-based meshing scheme leads to significant challenges, such as inadequate spatial resolution, substantial discretization errors, poor noise immunity, and excessive computational costs. This work presents an innovative reconstruction approach termed neural refractive index field (NeRIF) which implicitly represents the flow field with a neural network, which is trained with tailored strategies. Both numerical simulations and experimental demonstrations on turbulent Bunsen flames suggest that our approach can significantly improve the reconstruction accuracy and spatial resolution while concurrently reducing computational expenses. Although showcased in the context of background-oriented schlieren tomography here, the key idea embedded in the NeRIF can be readily adapted to various other tomographic modalities including tomographic absorption spectroscopy and tomographic particle imaging velocimetry, broadening its potential impact across different domains of flow visualization and analysis.

This study presents a novel approach for quantificationally reconstructing density fields from shadowgraph images using physics-informed neural networks. The proposed method utilizes the shadowgraph technique visualizing the flow field, enabling reliable quantitative measurement of flow density fields. Compare to traditional methods, which obtain the distribution of physical quality in spatial coordinates case by case. We establish a new end-to-end network that directly from shadowgraph images to physical fields. Besides, the model employs a self-supervised learning approach, without any labeled data. Experimental validations across hot air jets, thermal plumes, and alcohol burner flames prove the model's accuracy and universality. This approach offers a non-invasive, real-time surrogate model for flow diagnostics. It is believed that this technique could cover and become a reliable tool in various scientific and engineering disciplines.