Phase fluctuations method for determining spatiotemporal distributions of the refractive-index structure parameter...

The refractive-index structure parameter is crucial for quantifying turbulence intensity. In this paper, a phase fluctuation (PF) method based on moiré deflectometry with double cross gratings is proposed to simultaneously determine the spatiotemporal distributions of the refractive-index structure parameter. This method addresses the challenge of directly measuring the refractive-index structure parameter using phase fluctuation data from optical turbulence. First, theoretical simulations show that the relative error in temporal and spatial distributions is 0.5% and 2%, respectively, verifying the high accuracy and applicability of our proposed method. Then, a one-hour experiment was conducted in a real atmospheric environment, and the spatiotemporal distributions of the refractive-index structure parameter were successfully measured. The observed fluctuation range aligns with empirical values and demonstrates the stochastic spatiotemporal characteristics of the real atmosphere. Our work introduces an approach for measuring and visualizing the refractive-index structure parameter and provides valuable insights for future turbulence studies.