A Preliminary Study on the Principle of Linear Effect Scaling Laws for Laser Atmospheric Transmission

Numerical simulations were performed to rapidly predict and evaluate laser beam expansion caused by linear atmospheric transmission effects, such as turbulence and jitter, thereby enhancing the accuracy of the scaling law. Simulation results indicate that the turbulence term coefficient in the beam expansion calibration expression correlates linearly with the initial beam mass and inversely with the transmission distance. By fitting a nonlinear surface, the relationship between the turbulence term coefficient, initial beam mass, and transmission distance was established. Additionally, under turbulence-free conditions, a calibration expression relating initial beam mass to transmission distance was derived. The tracking jitter-term coefficient was determined to be 3.69, effectively characterizing beam expansion due to system jitter error. Based on simulation outcomes, a scaling law model for beam expansion induced by linear atmospheric transmission effects was clearly established. The model closely matched the simulation data, with a root mean square error (RMSE) of 3.88. Compared with existing scaling law simulations, the proposed calibration expression significantly enhances the accuracy in predicting and evaluating beam expansion caused by linear atmospheric transmission effects. It also provides a more precise characterization of variations in beam expansion during laser transmission.