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Neural refractive index field: Unlocking the Potential of Background-oriented Schlieren Tomography in Volumetric Flow Visualization

Yuanzhe He, Yutao Zheng, Shijie Xu, Chang Liu, Di Peng, Yingzheng Liu, Weiwei Cai

TL;DR

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.

Abstract

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.

Neural refractive index field: Unlocking the Potential of Background-oriented Schlieren Tomography in Volumetric Flow Visualization

TL;DR

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.

Abstract

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.
Paper Structure (16 sections, 17 equations, 12 figures, 6 tables, 1 algorithm)

This paper contains 16 sections, 17 equations, 12 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical formulation of BOST
  3. Voxel-based formulation
  4. Neural refractive index field
  5. Numerical and experimental validations
  6. Results
  7. Numerical validation
  8. Experimental validation
  9. Conclusions
  10. Structure of Neural Network
  11. Ray Tracing for Simulation
  12. Image Quality Assessment Metrics
  13. Structural Similarity Index Measure (SSIM)
  14. Correlation Coefficient (CC)
  15. Peak Signal-to-Noise Ratio (PSNR)
  16. ...and 1 more sections

Figures (12)

  • Figure 1: (a) Principle of background-oriented schlieren; (b) Illustration of integrating the gradient of refractive index along light rays in the proposed algorithm; (c) The reconstruction process of NeRIF.
  • Figure 2: (a) Schematic diagram of the experimental setup; (b) Reactor and experimental setup objects.
  • Figure 3: Reconstruction of 3D density field distribution with different noise levels and algorithms
  • Figure 4: 2D slices of reconstructed density field distribution with different noise levels and algorithms
  • Figure 5: Structural similarity and correlation coefficients for different slices of each phantom
  • ...and 7 more figures