Sparse spectrum model for a turbulent phase

Monte Carlo (MC) simulation of phase front perturbations by atmospheric turbulence finds numerous applications for design and modeling of the adaptive optics systems, laser beam propagation simulations, and evaluating the performance of the various optical systems operating in the open air environment. Accurate generation of two-dimensional random fields of turbulent phase is complicated by the enormous diversity of scales that can reach five orders of magnitude in each coordinate. In addition there is a need for generation of the long "ribbons" of turbulent phase that are used to represent the time evolution of the wave front. This makes it unfeasible to use the standard discrete Fourier transform-based technique as a basis for the MC simulation algorithm. We propose a new model for turbulent phase: the sparse spectrum (SS) random field. The principal assumption of the SS model is that each realization of the random field has a discrete random spectral support. Statistics of the random amplitudes and wave vectors of the SS model are arranged to provide the required spectral and correlation properties of the random field. The SS-based MC model offers substantial reduction of computer costs for simulation of the wide-band random fields and processes, and is capable of generating long aperiodic phase "ribbons." We report the results of model trials that determine the number of sparse components, and the range of wavenumbers that is necessary to accurately reproduce the random field with a power-law spectrum.