Combining light field imaging with particle image velocimetry (PIV), single-camera light field tomographic PIV technology allows for three-dimensional flow field measurements from a single viewpoint, particularly useful in narrow-channel applications where observation windows are limited. However, significant axial stretching of flow tracer particles and the averaging effects inherent in cross-correlation algorithms reduce spatial resolution, limiting the ability of this technology to resolve finer flow structures. While existing methods, including traditional algorithms, data assimilation techniques, and neural networks, attempt to address these challenges, none fully succeed. In this paper, we propose a high-resolution light field tomographic PIV technique based on physics-informed neural networks (PINNs), aimed at enhancing spatial resolution and accurately predicting dense flow field information.

To meet the practical demands of light field PIV, we first analyze the integration of the Navier-Stokes (N-S) equations as prior physical information with a neural network model, constructing a PINN-PIV model for high-resolution three-dimensional flow field prediction. The model is trained using experimental data. Prior to training, three-dimensional velocity fields are segmented into two-dimensional slices, which are then fed into the model for refined predictions. The model’s performance is evaluated through numerical simulation and the reconstruction of Gaussian vortex displacement fields. We compare the results of PINN-PIV with those obtained using traditional cross-correlation methods to validate the effectiveness of the PINN-PIV approach. Finally, we conduct experiments on cylindrical flow using light field tomographic PIV to assess the model’s predictive accuracy on real experimental data.

The numerical reconstruction shows that the global root mean square errors of the predicted u, v, and w displacement components of the Gaussian vortex using the PINN-PIV model are 0.2433, 0.2105, and 0.2423 voxel, respectively. This represents a reduction of 52.36%, 58.95%, and 75.84% compared to traditional cross-correlation methods. Notably, the model significantly improves the prediction accuracy of the w component, which is typically prone to high errors due to stretching effects, thus enhancing depth-direction resolution (Fig. 7). In cylindrical flow field tests, the PINN-PIV model increases the measurement resolution of light field PIV by eightfold. This improvement allows for precise identification and enhancement of vortex structures, which correspond to the alternating vortex shedding in cylindrical wake flows, leading to a detailed characterization of small-scale vortex structures (Fig. 10).

To address the issue of low spatial resolution in single-camera light field tomographic PIV measurements, we propose a high-resolution technique utilizing PINN. By integrating the N-S equations as prior physical information into sparse flow field observational data, we establish a mapping between spatial coordinates and velocity components, enabling high-resolution predictions of dense three-dimensional flow fields. The accuracy of the proposed PINN-PIV fusion model is first assessed using simulated Gaussian vortex data, followed by validation through cylindrical flow field experiments. The results indicate that the PINN-PIV model improves the spatial resolution of flow measurements by eightfold when compared to traditional cross-correlation velocity field computations. It reduces the global root mean square errors of the predicted u, v, and w displacement components by 52.36%, 58.95%, and 75.84%, respectively. Specifically, for the depth-direction w component—typically more affected by reconstruction stretching effects and prone to higher errors—the PINN-PIV model significantly decreases errors, bringing them in line with those of the u and v components. In the cylindrical flow experiment, the model also demonstrates its ability to perform data refinement and smoothing, accurately predicting vortex locations and resolving vortex structures based on limited data. These results confirm that the PINN-PIV fusion model can achieve high-resolution flow field predictions and provide detailed characterizations of flow structures from relatively sparse light field PIV measurement data.