The Lévy fractional Brownian motion family as a new paradigm in the modeling of turbulent wave-front phase

Abstract

In Perez et al. [J. Opt. Soc. Am. A 21 (10), 2004] we have given a general formalism to model the turbulent wave-front phase by using fractional Brownian motion processes. Moreover, it extends classical results to non- Kolmogorov turbulence: the Strehl ratio and the angle-of-arrival variance are shown to be dependent on the dynamic state of the turbulence. Nevertheless, this model has its drawbacks as it is unable of handling the stationarity of the phase increments over the full inertial range. The Levy fractional Brownian motion (LfBm) family is then introduced here in order to overcome this problem.