Inversion of Atmospheric Coherence Length Using Optical Flow-based Convolutional Neural Networks

The atmospheric coherence length is a key parameter for quantitatively describing the strength of optical turbulence and is crucial for laser propagation, astronomical observation, and turbulence-degraded image restoration. Although existing studies have widely used convolutional neural networks (CNNs) to retrieve this parameter from single-frame distorted images, they fail to fully utilize the dynamic characteristics of turbulence. To address this, this study proposes a CNN-based inversion model incorporating dynamic optical flow features. By integrating the optical flow method with CNNs, the model captures and utilizes the turbulent motion information between consecutive image frames. The input to the model is the optical flow displacement field calculated from two successive image frames, and the angle-of-arrival fluctuation variance derived from the optical flow is incorporated into the loss function as a physical constraint. This design significantly enhances sensitivity to subtle image distortions induced by weak turbulence, effectively overcoming the performance bottleneck of traditional static single-frame input models under weak turbulence conditions.

The model was trained on a simulated dataset and validated using measured data obtained on June 13-14, 2022, at Science Island in Hefei, Anhui Province, China. The measured data were collected synchronously by an atmospheric coherence length monitor and an imaging device over a 500-meter horizontal near-ground propagation path. The study systematically compared the performance of four classic CNN architectures (AlexNet, VGGNet, EfficientNet, CVTStegoNet) with and without the incorporation of TV-L1 optical flow features. The results show that the introduction of optical flow features universally and significantly improves the inversion accuracy and robustness of the models under different turbulence strengths. Specifically, the method achieved faster training convergence and superior generalization performance across all tested models. On a test set comprising 4,500 training samples and 500 independent validation samples, the model with integrated optical flow features reduced the root mean square error (RMSE) and mean relative error (MRE) by an average of approximately 40%, while the coefficient of determination (R²) was generally above 0.99. Among the four models, the fused model based on AlexNet achieved the best overall performance.

This work demonstrates the critical role of utilizing turbulent dynamic features in enhancing the accuracy of inversion models, offering a novel and practical deep learning solution for high-precision, real-time detection of the atmospheric coherence length.