Performance Analysis of Spherical Wave-Based Tip-Tilt Compensation for 20.5 km Long-Range Free-Space Optical Communication (FSOC) Links

The 20.5 km terrestrial free-space optical communication (FSOC) link between Mt. Gamak and Mt. Daebong operates in a propagation regime where the transmission distance exceeds the Rayleigh range by approximately four times, rendering diffractive beam spreading dominant. Under this far-field condition, the transmitter can be physically approximated as a point source, and a spherical wave model becomes more appropriate than the conventional plane wave assumption. In this study, a turbulence analysis framework based on Rytov theory is developed to accurately quantify scintillation and angle-of-arrival fluctuations along the long-range horizontal path. Specifically, by integrating a Zernike tip-tilt removal filter into the spherical wave model, we numerically separate the large-scale eddy components suppressed by the control bandwidth from the residual log-irradiance variance. Numerical simulations show that the spherical wave model predicts approximately 39% lower angle-of-arrival variance compared with the plane wave assumption, thereby preventing excessive system design margins. Furthermore, the analysis verifies that a 200 Hz tip-tilt compensation effectively suppresses beam wander from 2.56 μm to 0.33 μm within the diffraction limit, stabilizing the received irradiance. This study provides a rigorous and practically applicable design framework for long-range terrestrial FSOC systems and future satellite–ground laser communication terminals.