Inner- and outer-scales of turbulent wavefront phase defined through the lens of multi-scale Lévy fractional Brownian motion processes

DARÍO G. PÉREZ; LUCIANO ZUNINO

University of Wales Institute, Cardiff, Wales, United Kingdom

Conferencia; SPIE Europe Remote Sensing 2008; 2008

SPIE

We have previously shown that the Lévy fractional Brownian field family accounts for a complete statistical and analytical description of non-Kolmogorov wavefront phase [Opt. Lett. 33 (6), 572]. This is a nonstationary process having zero mean and stationary increments; then, replicating the well-known properties of the turbulent phase. Opposite to traditional models relying in the stationary (spectral) approximation of the phase, that ultimately leads to non-physical divergences. Our model avoids these pitfalls and gives exact analytical results to many observable quantities: Strehl ratio, angle-of-arrival variance, seeing and Zernike coefficients, and also, a generalized DIMM theory. Nevertheless, some coefficients are slightly below (~5-10%) when compared to other estimates in the occurrence of Kolmogorov turbulence. In the present work we show that this is due to the mono-fractal nature of this model; that is, the absence of inner- and outer-scales. To address this issue we introduce a gaussian stochastic process whose realizations are multi-fractals: the multi-scale Lévy fractional Brownian field.