One step measurement of spatiotemporal distributions of refractive-index structure parameter using deep learning

Accurate measurement of the spatiotemporal distributions of the refractive-index structure parameter is crucial for characterizing atmospheric turbulence intensity and visualizing turbulent flow fields. However, traditional method remains limited by their computational complexity and inefficiency. In this paper, a One-step method for Refractive-index structure parameter Spatiotemporal distributions Measurement based on Deep Learning (DLORSM) is proposed. This method enables the direct one-step prediction of the spatial distributions of the refractive-index structure parameter in two directions using deep learning model and subsequently derives its temporal distributions. Numerical simulations are conducted to compare the DLORSM method with traditional method. The results show that DLORSM method achieves significantly lower errors of 0.17% and 0.16% in estimating spatiotemporal distributions, demonstrating its high accuracy and robustness. Experimental validation under real atmospheric conditions further confirms that DLORSM effectively captures the random fluctuations and structural characteristics of real atmospheric flow fields. This study lays a foundational framework and provides valuable insight into the intelligent measurement of spatiotemporal distributions of atmospheric refractive-index structure parameters using deep learning.