The fractional Brownian motion property of the turbulent refractive within Geometric Optics

摘要

We introduce fractional Brownian motion processes (fBm) as an alternativemodel for the turbulent index of refraction. These processes allow toreconstruct most of the refractive index properties, but they are notdifferentiable. We overcome the apparent impossibility of their use within theRay Optics approximation introducing a Stochastic Calculus. Afterwards, wesuccessfully provide a solution for the stochastic ray-equation; moreover, itsimplications in the statistical analysis of experimental data is discussed. Inparticular, we analyze the dependence of the averaged solution against thecharacteristic variables of a simple propagation problem.