Turbulence-degraded wave fronts as fractal surfaces

We identify wave fronts that have passed through atmospheric turbulence as fractal surfaces from the Fractional Brownian motion family. The fractal character can be ascribed to both the spatial and the temporal behavior. The simulation of such wave fronts can be performed with fractal algorithms such as the Successive Random Additions algorithm. An important benefit is that wave fronts can be predicted on the basis of their past measurements. A simple temporal prediction reduces by 34% the residual error that is not corrected by adaptiveoptics systems. Alternatively, it permits a 23% reduction in the measurement bandwidth. Spatiotemporal prediction that uses neighboring points and the effective wind speed is even more beneficial.