Simulation of Time-dependent Karhunen-Loeve Phase Screens: an Ergodic Approach

Abstract: Time-dependent phase screens in ground-based astronomy are typically simulated in the so-called frozen-screen approximation by establishing a static phase screen on a large pupil and dragging an aperture equivalent to the size of the actual input pupil across this oversized phase screen. The speed of this motion sweeping through the large phase screen is equivalent to a wind speed that changes the phase screen as a function of time. The ergodic ansatz replaces this concept by constructing the structure function in a three-dimensional volume -- a sphere for reasons of computational efficiency -- , sampling phase screens by two-dimensional planar cuts through that volume, and dragging them along the surface normal at some speed which generates a video of a phase screen. This manuscript addresses the linear algebra of populating the three-dimensional volume with phase screens of the von-Karman model of atmospheric turbulence.