The space-time compensation model for broadband point-ahead and dispersion angle in satellite-to-dynamic ground station optical transmission

The point-ahead angle (PAA), which is superimposed with dispersion-angle (DA) compensation, is an essential beam-steering correction for wide-bandwidth free-space optical (FSO) transmission to compensate for line-of-sight drift induced by relative terminal motion and atmospheric refraction. As orbit height increases and beam divergence decreases, the required pointing accuracy becomes more stringent, proportional to the divergence angle, making PAA&DA compensation increasingly important. This paper proposes a three-dimensional analytical model for the refractive component of the PAA that accommodates mobile ground receivers. Within this framework, we integrate dispersion-angle (DA) compensation into a closed-loop system for broadband communication corrections, offering a unified model for both classical and quantum channels while explicitly correcting the nonequivalence between dispersion deviation and dispersion compensation in traditional models. We also provide the first DA's rapid calculation formulas for common broadband FSO transmission. The DA is typically around 5 micro-radians for ground-to-satellite links, while it is on the order of nano-radians for satellite-to-ground links and can be neglected . Despite having provided the compensation values, the current millisecond-rate compensation frequency remains excessively high. To address this, we introduce the Maximum Tolerance Interval (MTI), which reduces the compensation frequency by two orders of magnitude through deriving the optimal lower bound for the compensation clock under an error tolerance of ≤0.1 times the beam divergence. This framework may offer a high-precision, low-complexity pointing compensation solution, potentially laying the foundation for integrated dynamic networking.