Neural Radiance Fields for tomographic reconstruction in molecular tagging velocimetry

In this work, we present a machine learning-based tomographic reconstruction algorithm to predict the velocity components and pressure for 3D Molecular Tagging Velocimetry (MTV). Volume reconstruction is an ill-posed inverse problem where conventional grid-based methods are computationally expensive, memory-intensive, and prone to artifacts caused by discretization. To address these challenges, we propose a deep learning algorithm, Neural Radiance Fields (NeRF), which models volumetric scenes as continuous functions of 3D spatial coordinates and 2D viewing angles. Our approach integrates NeRF with Navier-Stokes constraints via an optical flow equation, ensuring both the reconstruction and flow variables adhere to known physical laws. We evaluate the performance of the algorithm using experimental wall-normal velocity profiles of a stagnation jet obtained from Plenoptic MTV. The reconstruction is then compared to the results from the Richardson-Lucy deconvolution approach for validation. This method offers a novel solution for high-resolution flow diagnostics of complex flow phenomena at microscale with enhanced precision.