Light-field micro-particle image velocimetry (Micro-PIV) technology enables three-dimensional micro-scale flow field measurements using a single camera. The implementation of light-field Micro-PIV involves capturing light-field images, reconstructing the three-dimensional spatial distribution of tracer particles, and analyzing the particle field through cross-correlation methods to measure micro-scale flow fields. The rapid and accurate reconstruction of three-dimensional spatial particle distribution remains crucial for precise velocity field measurement. Traditional reconstruction techniques, including Lucy?Richardson iterative deconvolution, demonstrate inefficiencies and significant axial elongation of reconstructed particles. Despite various optimizations, these conventional algorithms retain inherent limitations. Recent research has introduced deep learning-based methods for particle field reconstruction. However, purely data-driven deep learning models exhibit limited reconstruction accuracy and generalization performance, often producing artificial particles and residual axial elongation effects. This paper addresses these limitations by proposing a physics-informed deep learning for particle reconstruction (PIDLR) model that incorporates physical constraints into deep learning processes to enhance particle field reconstruction quality and model generalization capability.

The methodology comprises several key steps. Initially, a particle field reconstruction network based on the U-Net architecture undergoes training using the particle distribution-optical field image dataset. The process then incorporates a forward imaging mechanism model to refine the pre-trained inverse reconstruction network, followed by performance evaluation. Numerical reconstruction methods assess the PIDLR model’s reconstruction quality and accuracy, comparing its performance against purely data-driven deep learning models. The final phase involves experimental measurement of laminar flow on a Y-typed microfluidic chip, comparing the velocity measurement accuracy between the proposed model and the purely data-driven U-Net model to evaluate practical application effectiveness.

Reconstruction of numerical simulation data indicates that within the tracer particle concentration range from 0.4 ppm (particle per microlens) to 1.2 ppm, the PIDLR model outperforms the U-Net model by improving the reconstruction quality factor by 16.31% (Fig. 8). In addition, it also reduces the degree of axial stretching and thus improves the axial resolution (Fig. 7). For the experimental validation, the three-dimensional velocity field within a Y-typed microfluidic chip is calculated through cross-correlation algorithm. The PIDLR model effectively captures the flow characteristics at various locations inside the Y-shaped channel (Fig. 11). At the central cross-section of the channel (z=50 μm), the velocity distribution derived from the PIDLR model exhibits a strong agreement with the theoretical velocity field (Fig. 13). Additionally, a quantitative comparison of velocity measurements in the xoy plane reveals that the average relative errors for PIDLR and U-Net are 14.82% and 11.35%, respectively. These findings confirm that PIDLR can realize the velocity field measurement with higher accuracy than the purely data-driven U-Net model, thus demonstrating its practical potential.

This paper presents a PIDLR model for three-dimensional particle spatial distribution in light field micro-particle image velocimetry, addressing the limitations of purely data-driven deep learning models. Numerical simulations and experimental flow measurements of a Y-shaped microchannel demonstrate the model’s effectiveness. Within the particle concentration range of 0.4?1.2 ppm, simulation results reveal that PIDLR improves the reconstruction quality factor by 16.31% and enhances axial resolution by 33.47% compared to the U-Net model. For particle concentrations outside the training dataset range (0.3 ppm and 1.3 ppm), PIDLR achieves an average reconstruction quality factor up to 10% higher than the U-Net model, demonstrating superior reconstruction performance and generalization ability. In Y-shaped microchannel laminar flow measurements, the velocity field calculated using PIDLR shows a relative error of 11.35% compared to theoretical values, outperforming the U-Net model’s 14.82% error. These results validate the effectiveness of the PIDLR model in improving velocity field measurement accuracy.