Synthesizing high-fidelity phase screens from the phase fluctuation correlation function

Kurzfassung

In this publication, a new method for synthesizing high-fidelity phase screens is presented. The method is based on the phase fluctuations correlation function; hence, it is called correlation-based random phase method. By synthesizing the phase screens from a function defined in the spatial domain (i.e., the correlation function) rather than in the frequency domain, the bandwidth error arising while using a single discrete Fourier transform is corrected, allowing the synthesization of phase screens yielding a negligible deviation from the theoretical structure function without the need of any optimization parameters. Originally developed in the field of aeronautics, the correlation-based random phase method is limited by computer arithmetic inaccuracies for grid size that are around 4 times larger than the considered outer scale, an assumption that is often valid while simulating the effects of a turbulent atmosphere on ground-based astronomical telescopes with a large aperture. It is possible to achieve the same accuracy in the case of smaller spatial domains by applying a proper window function, at the cost of increasing the number of pixels (i.e., the computation time). For illustration, the presented method is compared with the widely known random phase method.