Fast Phase Screen Simulation Based on a Fractal Iterative Method

Under the influence of atmospheric turbulence, a telescope with diameter larger than atmospheric coherence length cannot reach its diffraction limit. Especially, when the telescope aperture is about 10m or larger atmospheric turbulence will significantly distort the result image. In this case, an Adaptive Optics (AO) system can be used for alleviating the effect. Since an AO system is rather complex, it is necessary to simulate it before actually having it built. Such a simulation normally consists of several parts: the wavefront propagation to the telescope, wavefront reconstruction, wavefront control, and deformable-mirror control. For the first part, a phase screen simulation is traditionally used to provide a series of simulated turbulence layers. Most traditional methods are based on the singular decomposition of the correlation matrix derived from a structure function, their speeds are thus low and the required temporary memory is large. For a simulation of large telescope or of long time, it can be more convenient if the duration of this step is shortened. In this paper, the author adapts a method previously used in wavefront reconstruction, the Fractal Iterative Method with complexity of O(N), to substantially speed up the simulation.